surface area

surface area (countable and uncountable, plural surface areas)

(geometry) The total area on the surface of an object.


decagonal

[dɪˈkæɡənəɫ]


trisection

en-noun

trisection (countable and uncountable, plural trisections)

A traditional (but impossible) mathematical problem was to achieve trisection using a straight edge and compass.

(geometry) The division of an angle into three equal parts.


pullback

differential geometry
differential geometry

(differential geometry) The map between cotangent bundles of manifolds corresponding to a smooth map between smooth manifolds, which at each point is the dual map to the corresponding pushforward.


tiling

tiling (countable and uncountable, plural tilings)

(geometry) A tessellation; the covering of a plane with shapes, without overlaps or gaps.


inverse Fourier transform

inverse Fourier transform (plural inverse Fourier transforms)

(mathematics) A mathematical operation that transforms a function for a discrete or continuous spectrum into a function for the amplitude with the given spectrum; an inverse transform of the Fourier transform.


real line

(mathematics) The real number system, viewed as a line.


step function

(mathematics) A function from the real line to a finite subset of the real line.


helicoid

From Ancient Greek ἑλικοειδής (helikoeidḗs); morphologically, from helico- + -id.

(mathematics) A minimal surface in the form of a flattened helix


slab

From Middle English sclabbe, slabbe, of uncertain origin; possibly from *slap, related to dialectal slappel (“portion, piece”), along with slape (“slippery”), sleip (“smooth piece of timber”), borrowed through Old Norse sleipr from Proto-Germanic *slaipaz, from Proto-Indo-European *(s)leyb-. See also Norwegian sleip (“slippery”) and Icelandic sleipur.

(geometry) A region between two parallel lines in the Euclidean plane, or between two parallel planes in three-dimensional Euclidean space, or between two hyperplanes in higher dimensions.


evolute

centres of curvature
centre of curvature

(geometry) A curve comprising the centres of curvature of another curve.

evoluta

a curve comprising the centres of curvature of another curve


fast Fourier transform

fast Fourier transform (plural fast Fourier transforms)

discrete Fourier transform
discrete Fourier transform

A member of a certain family of algorithms for efficiently computing the discrete Fourier transform of data.


monotonic function

monotonic function (plural monotonic functions)

independent variable
independent variable

(mathematics) A function that either never decreases or never increases as its independent variable increases.


rectilinear

en-adj

rectilinear (comparative more rectilinear, superlative most rectilinear)

more rectilinear (comparative)
most rectilinear (superlative)

/ˌɹɛktɪˈlɪniɚ/

/ˌɹɛktɪˈlɪnɪə/

From post-Classical Latin; either from rectilīneāris or from rectilīneus (whence rectiline) + -ar, in both cases ultimately deriving from rectus (“straight”) + līnea (“line”).

(geometry, art) Formed from straight lines.


monotone function

en-noun

monotone function (plural monotone functions)

monotone Funktion

order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)

Where defined, the first derivative of a monotone function never changes sign, although it may be zero.

Section 1 contains Lebesgue's main tool, a theorem saying that monotone functions on the line are differentiable almost everywhere.

2005, Anthony W. Knapp, Basic Real Analysis, Springer, page 357:

Monotone functions on #x5B;a,b#x5D; have nice properties. For example, they are integrable on #x5B;a,b#x5D; and have only a countable number of jump discontinuities. In this section, we shall also show that every monotone function is a function of bounded variation, and hence the class #x5C;mathit#x7B;BV#x7D;(#x5B;a,b#x5D;) contains the class of monotone functions on #x5B;a,b#x5D;.

2011, Saminathan Ponnusamy, Foundations of Mathematical Analysis, Springer, page 469:

We saw in the previous section that monotone functions have some nice properties. For example, a monotone function is continuous except possibly on a countable set. They are also closed under scalar multiplication, and the sum of two increasing functions is increasing. (Exercise (4) on page 103). However, the difference and product of two monotone functions are not necessarily monotone (Exercise (5) on page 103).

2013, Donald Yau, A First Course in Analysis, World Scientific, page 104:

(calculus) A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).

monotone Funktion

calculus: real function that either never decreases or never increases

nondecreasing function

function that never decreases as its independent variable increases

nonincreasing function

function that never increases as its independent variable increases


twotino

This provides a possible explanation for the low fraction of twotinos compared to plutinos in the Kuiper belt.

2009, A. C. Quillen, “Resonances in Galactic and Circumstellar Disks”, in G. Contopoulos, P. A. Patsis, editors, Chaos in Astronomy: Conference 2007, Springer, page 199:

Plutinos are Kuiper belt objects in a 2:3 resonance (a = 39.4 AU) with Neptune and are named after Pluto since these bodies have orbits similar to Pluto. Twotinos are objects that are in a 1:2 resonance (a = 47.8 AU) with Neptune.

2017, Thomas H. Burbine, Asteroids, Cambridge University Press, page 234:

These objects have been given the name of twotinos (rhymes with "plutinos").
Interestingly, there are very few low-eccentricity TNOs beyond the twotinos.

2021, Barbara Ryden, Bradley M. Peterson, Foundations of Astrophysics, Cambridge University Press, page 276:

(astronomy) Any astronomical object, on the apparent outer edge of the Kuiper Belt, whose orbit has a 1:2 resonance with the planet Neptune.

Resonant trans-Neptunian object#1:2 resonance ("twotinos", period ~330 years)


(geometry) Synonym of pentacontagon: A 50-sided polygon.


rigidification

/ɹɪˌd͡ʒɪdɪfɪˈkeɪʃən/

(geometry) A form of isomorphism applied between line bundles.


differential geometry

differential geometry (usually uncountable, plural differential geometries)

1945, Eric Temple Bell, The Development of Mathematics, 2nd Edition, 1992 Republication, page 358,
[…] projective differential geometries of the American and Italian schools do not seem to have attracted physicists.

1962, I. M. James, The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry, page 189,
The general theory of manifolds of class 2 is a sub-class of differential geometries, which contain the theory of affine connections, curvature and osculating sub-spaces.

Note that projective differential geometry is a basis for Euclidean and non-Euclidean differential geometries since metric properties of submanifolds of Euclidean and non-Euclidean spaces should only be added to their projective properties.

1993, M. A. Akivis, V. V. Goldberg, Projective Differential Geometry of Submanifolds, page v:

In this sense, C#x7B;k#x5F;0#x7D; is the natural hypothesis of differentiability in the particular question of differential geometry.

2012, Heinrich W. Guggenheimer, Differential Geometry, page 145:

mathematical analysis
mathematical analysis

differentiable manifold
differentiable manifold

(geometry, mathematical analysis) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra.


objective function

objective function (plural objective functions)

(mathematics) A function to be maximized or minimized in optimization theory.


Riemann zeta function

Riemann zeta function (usually uncountable, plural Riemann zeta functions)

Named after German mathematician Bernhard Riemann.

named-after

It is straightforward to show that the Riemann zeta function has zeros at the negative even integers and these are called the trivial zeros of the Riemann zeta function.

2004, Paula B. Cohen, “Interactions between number theory and operator algebras in the study of the Riemann zeta function (d'apres Bost-Connes and Connes)”, in David Chudnovsky, Gregory Chudnovsky, Melvyn Bernard Nathanson, editors, Number Theory: New York Seminar 2003, Springer,, page 87:

The Riemann zeta-function (which has no relation to the Weierstrass function of Chapter 8, and must not be confused with it) was originally of interest because of its connection with number theory. Since then it has served as the model for a proliferation of "zeta-functions" throughout mathematics. Some mention of the Riemann zeta-function, and treatment of the prime number theorem as an asymptotic result have become a topic treated by writers of introductory texts in complex variables.

2008, Sanford L. Segal, Nine Introductions in Complex Analysis, Revised edition, Elsevier (North-Holland), page 397:

2009, Arthur T. Benjamin, Ezra Brown (editors), Biscuits of Number Theory, Mathematical Association of America, page 195,
The Riemann zeta function is the function ζ(s)=∑ₙ₌₁ ᪲n⁻ˢ for s a complex number whose real part is greater than 1. […] The historical moments include Euler's proof that there are infinitely many primes, in which he proves
ζ(s)=∏ₚₚᵣᵢₘₑ(1-1/(pˢ))⁻¹
as well as Riemann's statement of his hypothesis and several others. Beineke and Hughes then define the moment of the modulus of the Riemann zeta function by
I_k(T)=1/T∫₀ ᪲|ζ(1/2+it)|²ᵏdt
and take us through the work of several mathematicians on properties of the second and fourth moments.

analytic continuation
analytic continuation

(number theory, analytic number theory, uncountable) The function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.

Riemann-zeta-functie

analytic continuation of a function defined as the sum of a Dirichlet series


U-shaped

en-adj

U-shaped (comparative more U-shaped, superlative most U-shaped)

more U-shaped (comparative)
most U-shaped (superlative)

a U-shaped valley

Having a cross-section similar in appearance to a broad U.


homographic

From homo- + -graphic; alternatively, homograph + -ic.


nummular

nummular (comparative more nummular, superlative most nummular)

more nummular (comparative)
most nummular (superlative)

From Latin nummulus (“(small amount of) money”) + English -ar (suffix forming adjectives with the sense ‘of, pertaining to, or near’). Nummulus is the diminutive of nummus (“a coin; piece of money”) + -ulus (diminutive suffix); while nummus is from Doric Greek νοῦμμος (noûmmos), from Ancient Greek νόμος (nómos, “kind of coin”), from νέμω (némō, “to deal out, dispense, distribute”) (from Proto-Indo-European *nem- (“to distribute; to give; to take”)) + -ος (-os, suffix forming nouns).

硬幣形的

flattened with a rounded form; coin-shaped

NUMMULAR […] An epithet applied to the sputa in phthisis, when they flatten at the bottom of the vessel, like a piece of money.

[1839, Robley Dunglison, “NUMMULAR”, in Medical Lexicon. A New Dictionary of Medical Science, […], 2nd edition, Philadelphia, Pa.: Lea and Blanchard, successors to Carey and Co., →OCLC, page 421, column 2:

(by extension) Flattened with a rounded form, as a disc; coin-shaped.

(pathology, obsolete) Of sputum: forming flat, round shapes (formerly thought to be a symptom of tuberculosis).


utility function

en-noun

utility function (plural utility functions)

(game theory) A mathematical function that assigns a real number to every element of the outcome space in a way that captures the agent's preferences over both simple and compound lotteries.


quadrate

From Middle English quadrat, quadrate, from Latin quadrātum. Doublet of quadrat; compare also quadrant (“square or quadrangle”).

At which command, the powers militant
That stood for heav'n, in mighty quadrate joyn'd.

1667, John Milton, “Book V”, in Paradise Lost. […], London: […] [Samuel Simmons], and are to be sold by Peter Parker […]; [a]nd by Robert Boulter […]; [a]nd Matthias Walker, […], →OCLC; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873, →OCLC, lines 61-62:

(geometry) A plane surface with four equal sides and four right angles; a square; hence, figuratively, anything having the outline of a square.


spherule

From Latin sphērula, sphaerula, from sphēra, sphaera (“sphere”) + -ula (diminutive suffix).


spiral of Archimedes

spiral of Archimedes (plural spirals of Archimedes)

(mathematics) A spiral that increases in distance from the point of origin at a constant rate.


Archimedean spiral

Archimedean spiral (plural Archimedean spirals)

Named after Archimedes of Syracuse (c. 287 – c. 212 BC), a Greek mathematician, physicist, engineer, inventor, and astronomer.

Max flees and tries to visit Sol, only to find that he has died. Max searches his house and finds mathematical scribblings similar to his own. On a Go board, with its pieces arranged in an Archimedean spiral, Max finds a piece of paper with the 216-digit number.

2010 November 16, Wikipedia contributors, “Pi (film)”, in English Wikipedia, Wikimedia Foundation:

Archimedean spiral
Archimedes of Syracuse

Archimédova spirála

a spiral that increases in distance from the point of origin at a constant rate


attractor

(mathematics, physics) A set of points or states to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed.


major axis

halkaisija

diameter of a circle — see also diameter

(geometry) The longest diameter of an ellipse, running through the center and foci, with its ends being the widest points of the shape.


semimajor axis

Coordinate term: semiminor axis

(geometry) Half of the major axis of a circle or ellipse.

半長軸

half of the major axis of a circle or ellipse

(geometry) Half of the distances between the two branches of a hyperbola.


orbital plane

The plane of ecliptic is the orbital plane of the earth and the other planets in the solar system.

(astronomy) The surface (plane) that contains an orbit.


pentahedron

pentahedron (plural pentahedrons or pentahedra)

pentahedrons (plural)
pentahedra (plural)

Their tent was too small for them to stand, a long but low pentahedron, in shape like the triangular glass prism Saeed used to have as a child, with which he would refract sunlight into little rainbows.

2017, Mohsin Hamid, Exit West, Hamish Hamilton, page 106:

(geometry) A polyhedron with five faces.


subconical

(geometry, mycology) Shaped somewhat like a cone.


apolar

(geometry) Orthogonal under the polar pairing between the symmetric algebra of a vector space and its dual.


octonion

(mathematics) An 8-dimensional nonassociative extension of a quaternion with a real part and 7 imaginary parts (each a real multiple of a distinct square root of −1).


rhombitruncated icosidodecahedron

rhombitruncated icosidodecahedron (plural rhombitruncated icosidodecahedrons)

(geometry) An Archimedean solid composed of 122 faces, 120 vertices, and 240 edges.


stellate

en-verb

stellate (third-person singular simple present stellates, present participle stellating, simple past and past participle stellated)

stellates (present singular third-person)
stellating (participle present)
stellated (participle past)
stellated (past)

Borrowed from Latin stēllātus (“starry”), from stēlla (“star”) + -ātus (“-ate”, adjectival suffix); equivalent to stella + -ate.

af

(geometry) To extend the edges or planes of a polyhedron to form a new shape.


sail curve

(geometry) A catenary-generated curve in the form of a cross-section of a sail filled by wind.


septagon

From Latin septem (“seven”) + Ancient Greek γωνία (gōnía, “angle”), equivalent to septa- + -gon.

(proscribed) A polygon with seven sides and seven angles.


totient

From Latin totiēns (“so many times, so often”). Coined by English mathematician James Joseph Sylvester in 1879.

coin

(mathematics) The number of positive integers not greater than a specified integer that are relatively prime to it.


Heron's formula

The formula A=√, where a, b, and c are the sidelengths of a triangle, s is its semiperimeter, and A is its area.


oblatum

From Late Latin oblātus (oblatus), from Latin ob (“in front of, before”) + lātus (“broad, wide”), (modelled after and contrasting with prolatus (“extended, lengthened”)).

(geometry) An oblate spheroid; a figure described by the revolution of an ellipse about its minor axis.


half-line

(geometry) ray; a line extending indefinitely in one direction from a point.


analytic geometry

Having thus noted the distinction between Analytic Geometry and Geometry, let us note in what way it differs from Algebra.

1889, Arthur Sherburne Hardy, Elements of Analytic Geometry, Ginn, published 1891, page 12:

1921, Claude Irwin Palmer, William Charles Krathwohl, Analytic Geometry, McGraw-Hill, page 261,
In plane analytic geometry, all the points and lines are confined to one plane.

2018, Peter Kuhfittig, Technical Calculus with Analytic Geometry, 5th Edition, Cengage Learning (BROOKS/COLE), page 1,
Analytic geometry may be defined as the study of classical geometry by means of algebra.

(geometry) The subbranch of geometry that investigates geometrical figures via the mathematical properties of their representations in a coordinate system.


equipotential

A region whose every point has the same potential.


binary logarithm

en-noun

binary logarithm (plural binary logarithms)


circular sector

circular sector (plural circular sectors)

(geometry) A portion of a circle enclosed by two radii and an arc.


cosinus

Learned borrowing from New Latin cosinus, abbreviation of complementi sinus. Doublet of cosine.

lbor

When I came to these very buildings to pass my examination I knew far better the names of all the plants in this garden than the theory of the cubic roots or the long formulæ of the sum of two cosinus.

1884, A[lbert] A[ugustin] Fauvel, Chinese Plants in Normandy, Hong Kong: […], page 4, column 1:

So, in the helicopteron, as the helix is at the same time a sustaining plane, it should be likened to a surface moving horizontally, and in which, consequenty, the resistance to motion will be to the lifting power as the sinus is to the cosinus of the angle formed by such plane with the horizon.

1884 November 29, “Aerial Navigation”, in Scientific American: A Weekly Journal of Practical Information, Art, Science, Mechanics, Chemistry, and Manufactures, volume LI, number 22, New York, N.Y.: Munn & Co., translation of original by Victor Tatin in La Nature, page 342, column 1:

And according to our choice of a symmetrical conjunction or opposition, all the cosinuses are reduced to 1, namely to coefficients build up solely by scalar Keplerian elements a, e.

1949, Contributions from the Astronomical Institute of the Charles University Prague, page 38:

The variations are described in terms of cycles of sinuses and cosinuses.

1996, Pentti Zetterberg, Matti Eronen, Markus Lindholm, “Construction of a 7500-Year Tree-Ring Record for Scots Pine (Pinus sylvestris, L.) in Northern Fennoscandia and its Application to Growth Variation and Palaeoclimatic Studies”, in Heinrich Spiecker, Kari Mielikäinen, Michael Köhl, Jens Peter Skovsgaard, editors, Growth Trends in European Forests (European Forest Institute Research Report; No. 5), Springer-Verlag Berlin Heidelberg, →ISBN, page 15:

Basically, the rotation of the matrix of the factor loadings L represents its post-multiplication, i.e. L* = LO by the rotation matrix O, which itself resembles one of the matrices included in the classical rotational Lie groups SO(m) (containing the specific m–fold combination of sinuses and cosinuses.

2007, Vladimir G. Ivancevic, Tijana T. Ivancevic, “Introduction: Human and Computational Mind”, in Computational Mind: A Complex Dynamics Perspective (Studies in Computational Intelligence; 60), Springer-Verlag Berlin Heidelberg, →ISBN, →LCCN, section 1 (Natural Intelligence and Human Mind), pages 60–61:


hypergeometric series

en-noun

hypergeometric series (plural hypergeometric series)

(mathematics) Any power series such that the ratio of the (k+1)-th and the k-th terms is a rational function of the natural integer k.


hypergeometric

hypergeometric series
hypergeometric series

(mathematics) Pertaining to mathematical entities of different kinds (series, functions, equations, ...) but strictly related to hypergeometric series


tropical geometry

The adjective tropical was chosen by some French mathematicians in honor of the Brazilian pioneer of the field, Imre Simon.

(mathematics) A recent branch of geometry that can be described as a piecewise linear version of real algebraic geometry.


Gaussian distribution

Gaussian distribution (plural Gaussian distributions)


normal distribution

normal distribution (plural normal distributions)

φ_(μ,σ²)(x)=1/(σ√),e²)/(2σ²))=1/σφ((x-μ)/σ), x∈ℝ.

It begins with the normal distribution, which is the limiting form of the sample sum over an arbitrary population.

2008, James L. Johnson, Probability and Statistics for Computer Science, Wiley, page 437:

The normal distribution is the backbone of traditional statistics. We learn very early in our statistics training that the distribution of sample means, regardless of the shape of the parent distribution, approaches a normal distribution as the sample size increases.

2012, Larry Pace, Beginning R: An Introduction to Statistical Programming, Apress, page 103:

The development of the general theories of the normal distributions began with the work of de Moivre (1733, 1738) in his studies of approximations to certain binomial distributions for large positive integer n > 0.

2014, Mohammad Ahsanullah, B.M. Golam Kibria, Mohammad Shakil, Normal and Student's t Distributions and Their Applications, Springer (Atlantis Press), page 7:

probability distribution
probability distribution

probability density function
probability density function

(statistics) Any of a family of continuous probability distributions such that the probability density function is the Gaussian function


dirigent

From Latin dīrigēns, present participle of dīrigō.

The straight line in which the vertical polar plane cuts the plane of the circle of contact is called the dirigent. As there are in general two circles of contact, there are two dirigents, and they are parallel to the diretrices.

1877, James Booth, A Treatise on Some New Geometrical Methods, page 348:

In this case, to which Sphero-Cartesians, and all other sphero-quadrics, whose dirigents are small circles, are analogous in Spherics, the dirigent conic F must also have double contact with S.

1891, Proceedings of the London Mathematical Society, volume 21, page 308:

(dated, geometry) The line of motion of a describent line or surface that in so moving defines a plane or solid figure; a directrix.


hyperhypercube

Extension of hypercube; hyper- + hypercube.

(mathematics) A five-dimensional figure, usually cube-like.


probability density

probability density (plural probability densities)

(probability theory) probability density function


bicapped

(geometry, of a prism) Having a cap (in the shape of a pyramid) at each end

(physical chemistry, of a molecule) Having the shape of such a prism


directrix

directrix (plural directrixes or directrices)

directrixes (plural)
directrices (plural)

From Latin directrix; equivalent to direct + -trix.

(geometry) A line used to define a curve or surface; especially a line, the distance from which a point on a conic has a constant ratio to that from the focus.

richtlijn

a line used to define a curve or surface


triskaidecagon

A polygon having thirteen sides and thirteen angles.


tetrakaidecagon

a polygon having fourteen sides and fourteen angles


zerogon

(geometry) A circle visualized as a polygon having no edges or vertices.


henagon

From Ancient Greek: εἷς (heîs, “one”) + γωνία (gōnía, “angle”).

A polygon having one edge and one angle.


tridecagon

(geometry) A polygon having thirteen sides and thirteen angles.


apeirogon

/əˈpiːɹɵɡɑn/

/əˈpeɪ̯ɹɵɡɑn/

Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) apeirogon or a hypercyclic apeirogon.

1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247:

In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.

1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, →ISBN, page 27:

[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.

2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, →ISBN, page 217:

There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.

2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:

(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;

A type of generalised polygon with a countably infinite number of sides and vertices;
(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.


monogon

A geodesic with multiple points contains at least one simple monogon.

1955, Herbert Busemann, The Geometry of Geodesics, page 295:

There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.

1981, Harold Abelson, Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics, →ISBN, page 262:

2003, Gordon Baker, translator and editor, Ludwig Wittgenstein and Friedrich Waismann, The Voices of Wittgenstein: The Vienna Circle, Routledge, →ISBN, page 409,
We explain to somebody what is a regular quadrilateral constructed within the circle; then a regular triangle and a regular bi-angle. Now we ask him to draw a regular monogon by analogy, and we probably think that he cannot do this. But what if he draws a point on the circle and says that it is a regular monogon?

(geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#x2B;2 edges, and 4s#x2B;2 faces. Of these faces, 4s#x2B;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.

1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231:

2002, Tao Li, "Laminar Branched Surfaces in 3–manifolds", Geometry & Topology 6, page 158,
There is no monogon in M-int(N(B)), ie, no disk D⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B).

a. 2006, Thilo Kuessner, "A survey on simplicial volume and invariants of foliations and laminations", in, Paweł Walczak, et al., editors, Foliations 2005, →ISBN, page 295,
An end-compressing monogon for F is a monogon properly embedded in the complimentary region C which is not homotopic (rel. boundary) into ∂C.

(geometry) A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge.


tetradecagon

(geometry) A polygon having fourteen sides and fourteen angles.


digon

From di- (prefix meaning ‘two’) + -gon (suffix forming the names of plane figures containing a given number of angles).

confix

monogon · digon · trigon · tetragon · pentagon · hexagon · heptagon · octagon · nonagon · decagon · undecagon · dodecagon · see also Category:English terms suffixed with -gon

They [the students] also came upon new and unusual mathematical figures: the digon, a two-sided polygon on a spherical space, and the apeirogon, an open polygon with infinitely many sides […]. All these discoveries brought up even more questions. Is a circle a polygon? What makes an octagon an octagon – its eight vertices, its eight sides, or both? Can a polygon cross itself? Does a polygon need to be closed?

2013, Brent Davis, Moshe Renert, chapter 6, in The Math Teachers Know: Profound Understanding of Emergent Mathematics, New York, N.Y., Abingdon, Oxfordshire: Routledge, →ISBN, page 102:

(geometry) A polygon having two edges and two vertices.

digono

A pair of parallel undirected edges in a multigraph.

A pair of antiparallel edges in a directed graph.


dynamical system

en-noun

dynamical system (plural dynamical systems)

(mathematics, physics) A system which is time-dependent.


Gaussian

List of things named after Carl Friedrich Gauss


French curve

A drafting template having edges of various curvatures, used for drawing smoothly-curved lines.


(astrophysics) Abbreviation of Lagrange point 1, located between the larger and smaller objects along a line connecting the two.


Coordinate term: L1

That is, for almost all late second language (L2) learners, the phonetic realization of phonological structures in the L2 is markedly different from native-language patterns.

2008, Jette G. Hansen Edwards, Mary L. Zampini, Phonology and Second Language Acquisition, John Benjamins Publishing, →ISBN, page 153:

This advantage was pertinent in the Hong Kong context where English is largely an L2 language, although would not be expected to be as large in an L1 context.

2017, Di Zou, James Lambert, “Feedback methods for student voice in the digital age”, in British Journal of Educational Technology, volume 48, number 5, page 1085:

A second language (a language being learned, as opposed to mother tongue).


amphichiral

(geometry, physical chemistry) superimposable on its mirror image; achiral


achiral

(geometry, physical chemistry) superimposable on its mirror image; amphichiral


cylindrically

en-adv

cylindrically (comparative more cylindrically, superlative most cylindrically)

more cylindrically (comparative)
most cylindrically (superlative)


hyperbolic plane

en-noun

hyperbolic plane (plural hyperbolic planes)

(mathematics) A topological space homeomorphic to a plane (or open disk) and equipped with a hyperbolic metric.


sinusoid

(mathematics) A curve having the shape of a sine wave.


circumcenter

LL-Q1860 (eng)-Flame, not lame-circumcenter.wav

(geometry) The center of a circumcircle (the circle that passes through every vertex of a given triangle or other cyclic polygon).


triangular prism

triangular prism (plural triangular prisms)


probit

LL-Q1860 (eng)-Flame, not lame-probit.wav

Blend of probability + unit. Coined by Chester Ittner Bliss in 1934: “These arbitrary probability units have been termed ‘probits’…”

The probit function, the inverse of the cumulative distribution function.


minimal surface

minimal surface (plural minimal surfaces)

(mathematics) Any surface that has the least possible surface area of those into which it could transform; typically the shapes of soap bubbles that span wire frames


gyroid

Coordinate term: lattice

(mathematics) An infinitely connected periodic minimal surface containing no straight lines.


mediatrix

mediatrix (plural mediatrices or mediatrixes)

mediatrices (plural)
mediatrixes (plural)

From Late Latin mediātrīx, feminine of mediātor.

[…] the intersection of the normal at M to the parabola with the mediatrix of the line […]

2000, Jean H. Gallier, Curves and surfaces in geometric modeling, page 105:

(geometry) The line that is perpendicular to a line segment and intersects the line segment at its midpoint.


nonchiral

(geometry, physical chemistry) Not chiral.


cyclide

(mathematics) Any of a class of surfaces, described by quartic expressions, that are related to spherical surfaces


stellated

en-adj

stellated (comparative more stellated, superlative most stellated)

more stellated (comparative)
most stellated (superlative)

(geometry) Of a polyhedron, having its edges or planes extended to form a new shape.


isosceles trapezoid

en-noun

isosceles trapezoid (plural isosceles trapezoids)

A quadrilateral with two parallel sides and a separate pair of congruent sides which are not parallel.

等腰梯形

quadrilateral with two parallel sides and separate pair of congruent sides that are not parallel


limit cycle

(systems theory) A closed trajectory in phase space of a dynamical system having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches minus-infinity.


rod-shaped

en-adj

rod-shaped (comparative more rod-shaped, superlative most rod-shaped)

more rod-shaped (comparative)
most rod-shaped (superlative)

Anthrax goes through two very different stages in its life cycle. One is a microscopic rod-shaped bacterium called bacillus anthracis, easy to grow in the lab but fragile and easily killed in the open.

S. pombe is a rod shaped organism, and during its cell cycle it grows mostly in length with little change in diameter.

1981, PCL John, The Cell Cycle, page 86:

The rod-shaped E. coli phages share a common host range with the RNA-containing E. coli phages, a coincidence which probably unites unrelated viruses.

1965, “Small Bacteriophages”, in Advances in Virus Research, volumes 1-11, pages 343–4:

(biology) Specifically, describing a form of bacterium.


halfspace

(geometry) Either of the two parts of a three-dimensional object cut by a two-dimensional plane


trochoid

From Ancient Greek τροχοειδής (trokhoeidḗs), from τροχός (trokhós, “wheel”) + εἶδος (eîdos, “form, image”).

(geometry) The curve traced by a point on a circle as it rolls along a straight line


trochoid

trochoid (comparative more trochoid, superlative most trochoid)

more trochoid (comparative)
most trochoid (superlative)

(malacology, of a shell or fossil) High-spired; conical.


bounded function

en-noun

bounded function (plural bounded functions)

(mathematics) Any function whose values remain bounded by some constant.


stereotomy

From French stéréotomie, from Ancient Greek στερεός (stereós, “solid”) + -τομία (-tomía, “-cut”).

uder

Here your countenance brightened up, and, perceiving your lips move, I could not doubt that you murmured the word ‘stereotomy’, a term very affectedly applied to this species of pavement.

1841, Edgar Allan Poe, The Murders in the Rue Morgue:

(geometry, masonry) The cutting or dissection of solids.


osculatory

en-adj

osculatory (comparative more osculatory, superlative most osculatory)

more osculatory (comparative)
most osculatory (superlative)

A circle may be osculatory with a curve, at a given point.

(geometry) Relating to, or having the properties of, an osculatrix; capable of osculation.


sphericity

en-noun

sphericity (countable and uncountable, plural sphericities)

From spheric + -ity. In the geometrical sense, defined by the geologist Hakon Wadell in 1935.

(geometry, countable) The ratio of the surface area of a given particle to the surface area of a sphere with the same volume.

pallonmuotoisuus

ratio of particle surface area to sphere surface area


traverse

From Middle English traversen, from Old French traverser, from Latin trans (“across”) + versus (“turned”), perfect passive participle of Latin vertere (“to turn”).

(geometry) A line lying across a figure or other lines; a transversal.


radial curve

(mathematics) Any of a family of curves that are the loci of points that have a defined relationship between a fixed point and the centre of curvature at each point on another curve


osculating circle

osculating circle (plural osculating circles)

(geometry, for any point on a curve) The circle that has the same tangent, and the same curvature at the point on the curve.


birectangular

Unlike a normal triangle, a spherical triangle can be birectangular because the sum of its angles is greater than 180 degrees.


cycler

We took samples from the tubes in the cycler at regular intervals

(biochemistry) Ellipsis of thermal cycler.; a machine for creating multiple copies of DNA sequences.


cycloidal arch

cycloidal arch (plural cycloidal arches)

[Alt: Picture of the relevant components of a cycloidal arch](architecture) An arch that has a cycloidal shape, wherein the span of the arch is some factor of pi*rise.


dihedron

(geometry) A polyhedron having two faces


astrodynamics

The study of the motion of rockets and spacecraft, usually from Newton's laws of motion, Newtonian gravity, and Kepler's laws


galactic year

(astronomy) The time taken for the Solar System to orbit around the center of the Milky Way Galaxy, estimated to be from 225 to 250 million years.


flexagon

(geometry) A flat model made from folded strips of paper that can be folded, or flexed, to reveal a number of hidden faces.

флексаго́н

a flat model made from folded strips of paper


circular segment

circular segment (plural circular segments)

(geometry) A region of a circle bounded by an arc and the chord connecting the endpoints of the arc.


orthant

Consider preferences defined over the nonnegative orthant by (x_1,x_2)≻(y_1,y_2) if x_1+x_2<y_1+y_2 […]

1992, Hal R. Varian, Microeconomic Analysis (3rd ed.), Norton, p. 114

(geometry) A n-dimensional generalization of the quadrant (in two-dimensional Cartesian space) and octant (in three-dimensional space).


Fourier series

Named after French mathematician and physicist Joseph Fourier (1768-1830), who pioneered research into such series and their application to problems of heat transfer and vibration.

1951 [Blackie & Son], R. C. H. Young (translator), Konrad Knopp, Theory and Application of Infinite Series, [1947, Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, 4th Edition], 1990, Dover, Unabridged unaltered reprint of 2nd English Edition, page 493,
As we have seen (pp. 369—370), the question of the necessary and sufficient conditions under which the Fourier series of an integrable function converges and represents the given function is one which presents very great difficulties.

2001, David Cruz-Uribe (translator), Javier Duoandikoetxea Zuazo, Fourier Analysis, [1995, Javier Duoandikoetxea Zuazo, Análisis de Fourier], American Mathematical Society, page 20,
There are excellent discussions of Fourier series and integrals in Katznelson [10] and Dym and McKean [4]. The book by R. E. Edwards [5] is an exhaustive study of Fourier series from a more modern perspective.

Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable.

2006, K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3rd edition, Cambridge University Press, page 415:

(mathematics, mathematical analysis) Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials).

フーリエ級数

フーリエきゅうすう,fūrie kyūsū


epitrochoid

A geometric curve traced by a fixed point on one circle which rotates around the perimeter of another circle. Examples include the shape of the Wankel engine


hypotrochoid

(geometry) A geometric curve traced by a fixed point on the radius line outside one circle which rotates inside the perimeter of another circle.


dodecadodecahedron

dodecadodecahedron (plural dodecadodecahedra or dodecadodecahedrons)

dodecadodecahedra (plural)
dodecadodecahedrons (plural)

/ˌdəʊdɛkəˈˌdəʊdɛkəˈhiːdɹən/

/ˌdəʊdɪkəˈˌdəʊdɪkəˈhiːdɹən/

(geometry) A nonconvex polyhedron with twenty-four faces, thirty vertices, and sixty edges.


hyperplane

(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)

nadrovina

an n-dimensional generalization of a plane


quadratrix

quadratrix (plural quadratrices or quadratrixes)

quadratrices (plural)
quadratrixes (plural)

(mathematics) A curve having ordinates which are a measure of the area (or quadrature) of another curve.


arccotangent

(trigonometry) An inverse of the cotangent function. Symbol: arccot


generant

en-adj

generant (comparative more generant, superlative most generant)

more generant (comparative)
most generant (superlative)

/ˈd͡ʒɛnəɹənt/


generant

/ˈd͡ʒɛnəɹənt/


disphenoid

From di- (“twice, double”) + sphenoid (“wedge-shaped crystal or bone of the skull”).

prefix

The mineral chalcopyrite commonly crystallizes in disphenoids that are very difficult to distinguish from tetrahedrons.

1949, Edward Salisbury Dana, Minerals and How to Study Them, page 32:

1973, H. S. M. Coxeter, 3rd Edition, unnumbered page,
To make a model of a disphenoid, cut out an acute angled triangle and fold it along the joins of the mid-points of the sides. The disphenoid is said to be rhombic or tetragonal according as the triangle is isosceles or scalene.

If you rotate the [tetragonal] disphenoid 90° around its 2-fold axis and then perform the operation of inversion through the center-point of the object, it will occupy its original position again.

1977, Elizabeth A. Wood, Crystals and Light: An Introduction to Optical Crystallography, Revised edition, page 8:

In addition it should be remarked that there are two types of disphenoids, with different symmetries: the tetragonal disphenoid (having isosceles facets) and the rhombic one.

1993, Horst Martini, “A Hierarchical Classification of Euclidean Polytopes with Regularity Properties”, in Tibor Bisztriczky, Peter McMullen, Rolf Schneider, Asia Ivic Weiss, editors, Polytopes: Abstract, Convex and Computational, Proceedings of the NATO Advanced Study Institute, page 83:

(geometry) A non-regular tetrahedron whose four faces are congruent acute-angled triangles.

bisphenoid

non-regular tetrahedron with congruent faces


hyperboloid

A particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign.


sine ratio

right-angled triangle
right-angled triangle

(trigonometry) The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.


DFT

en-noun

DFT (countable and uncountable, plural DFTs)

discrete Fourier transform
discrete Fourier transform#English

(mathematics) Initialism of discrete Fourier transform.


discrete Fourier transform

discrete Fourier transform (plural discrete Fourier transforms)

(mathematics) The process of converting a discrete time-based function into its frequency-based representation.


arccosecant

(trigonometry) function that is the compositional inverse of the cosecant function. Symbol: arccsc


arcsecant

(trigonometry) function that is the compositional inverse of the secant function. Symbol: arcsec


sinistrorse

en-adj

sinistrorse (comparative more sinistrorse, superlative most sinistrorse)

more sinistrorse (comparative)
most sinistrorse (superlative)


concyclic

(geometry, of a set of points) Lying on a common circle.


barycenter

(geometry) The centroid, the geometric center of a plane figure


semirounded

Neither fully rounded nor angular; somewhat rounded


superhelix

en-noun

superhelix (plural superhelices or superhelixes)

superhelices (plural)
superhelixes (plural)

(molecular biology) The shape formed by a helix which in turn is twisted into a larger helix


isosurface

an isosurface representing a concentration of 10 grams per cubic meter

(computer graphics, geometry) A surface that represents points of a constant value within a volume of space


semimajor

a semimajor radius

(geometry) Of or pertaining to the semimajor axis, the long axis of an ellipse


computable function

computable function (plural computable functions)

(computer science) A mathematical function that can be computed using an abstract computation machine such as Turing machine.


cuboidal

en-adj

cuboidal (comparative more cuboidal, superlative most cuboidal)

more cuboidal (comparative)
most cuboidal (superlative)

A cuboidal block was formed.

(geometry) Of, pertaining to, or having the shape of a cuboid


additive function

en-noun

additive function (plural additive functions)

(mathematics) A unary function that preserves the addition operation; a unary function f such that for any x and y: f(x + y) = f(x) + f(y).


hypergeometry

hypergeometry (countable and uncountable, plural hypergeometries)

A geometry in more than three dimensions.


coplanarity

coplanarity (countable and uncountable, plural coplanarities)

(geometry, of at least two things, usually lines) The state or characteristic of being within the same plane.


Minkowski spacetime

Minkowski spacetime (plural Minkowski spacetimes)

Named after German mathematician Hermann Minkowski (1864–1909).

named-after

(mathematics, relativity) A geometrically flat spacetime, i.e. one with zero curvature.


LTO

en-noun

LTO (countable and uncountable, plural LTOs)

Coordinate term: DLT

(computing) Initialism of Linear Tape-Open, an open standard computer storage tape format having a single spooled cartridge with half-inch tape.

Linear Tape-Open

(software compilation) Initialism of link-time optimization.

Coordinate term: TLI

lunar transfer orbit
lunar transfer orbit#English

(space science, countable) Initialism of lunar transfer orbit.

lithium titanate oxide
lithium titanate oxide#English

(electrochemistry, uncountable) Initialism of lithium titanate oxide (“Li₄Ti₅O₁₂”).


LTO

w:Land Transportation Office (Philippines)

(Philippines) Initialism of Land Transportation Office.


magic circle

(mathematics) An arrangement of natural numbers on circles such that the sum of the numbers on each circle and the sum of numbers on diameter are identical.


monogonal

(geometry) Of or pertaining to a monogon.


monogonal

(geometry, of a line) That passes through exactly one vertex (of a polygon or polyhedron).


horocycle

(geometry) A curve in hyperbolic geometry whose normals all converge asymptotically.


horoball

Coined by William Thurston (1946-2012), American mathematician. See horosphere and ball.

(hyperbolic geometry) A horosphere together with the space above it.


developable

en-adj

developable (comparative more developable, superlative most developable)

more developable (comparative)
most developable (superlative)

(geometry, of a surface) Described by a moving right line, and such that consecutive positions of the generator intersect each other, allowing the surface to be developed into a plane.


spherical angle

en-noun

spherical angle (plural spherical angles)

(geometry) A particular dihedral angle, the angle between two intersecting arcs on a sphere, measured by the angle between the planes containing the arcs.


semiregular

It will be seen below that this semiregular polyhedron is of importance in its relationship to periodic minimal surfaces serving as a conceptual reference.

1993, H. Terrones, A. L. MacKay, “The Geometry of Hypothetical Curved Graphite Structures”, in H. W. Kroto, J.E. Fischer, Deann Cox, editors, The Fullerenes, page 115:

In a semiregular tessellation, there is an isometry of the plane carrying any vertex to any other vertex.

1998, David A. Singer, Geometry: Plane and Fancy, page 35:

While one of the semiregular polyhedra was mentioned by Plato, their first serious study is attributed to Archimedes.

2003, Saul Stahl, Geometry from Euclid to Knots, published 2010, page 272:

One that we will consider here is the semiregular tessellation—a tessellation of two or more regular polygons that are arranged so that the same polygons appear in the same order around each vertex point. The tessellation at the left in Figure 9.38 is a semiregular tessellation because the two figures are a square and a regular octagon. The tessellation at the right in Figure 9.38 is not a semiregular tessellation because the two figures are a square and a nonregular octagon.[…]There are only eight possible semiregular tessellations.

2011, Tom Bassarear, Mathematics for Elementary School Teachers, page 583:

(geometry, of a polyhedron or tessellation of the plane) Uniform (isogonal and isotoxal) with regular faces of two or more types, such that each vertex is surrounded by the same polygons in the same order.


Goldilocks zone

Goldilocks zone (plural Goldilocks zones)

So called because, like the third of the three bowls of porridge in the fairy tale Goldilocks, it is neither too hot nor too cold, but just right.

This plot may be a map of another type of Goldilocks zone for habitable ocean worlds—one base on composition.

2021, Kevin Hand, Alien Oceans: The Search for Life in the Depths of Space, Princeton University Press, →ISBN, page 43:


habitable zone

The zone around a star where a planet could experience temperatures like those on Earth, allowing for the possible existence of liquid water and of life.

zona d'habitabilitat

the planetary zone that could sustain life


zonotope

(geometry) A polytope formed by the Minkowski sum of a zonohedron's line segments in any dimension.


inscribable

(geometry) That can be inscribed; whose vertices all lie on a sphere.


zonohedron

(geometry) A special case of convex polyhedron, in which every face of the polyhedron is a polygon with point symmetry.

chamfered cube
rhombic dodecahedron
zonohedron


tetrahedralizable

(geometry) That can be divided into tetrahedra.


icosidodecahedron

icosidodecahedron (plural icosidodecahedra or icosidodecahedrons)

icosidodecahedra (plural)
icosidodecahedrons (plural)

LL-Q1860 (eng)-Flame, not lame-icosidodecahedron.wav

[…]together to form not only regular polyhedrons but rhombicosidodecahedrons, truncated icosidodecahedrons, and such.

1961, The New Yorker, Volume 37, Part 4, page 172:

1992, Jean-Louis Verger-Gaugry, Quasicrystals and the Concept of Interpenetration in m35-approximant Crystals with Long-range Icosahedral Atomic Clustering, A. R. Yavari, Ordering and Disordering in Alloys, Elsevier Applied Science, page 498,
A succession of 10 concentric icosidodecahedra centered at (0, 0, 0), forming a geometric sequence (the nᵗʰ one is τⁿ larger than the first one), is also put into evidence.

The edges of the octahedron form three squares; the edges of the cuboctahedron form four hexagons, and the edges of the icosidodecahedron form six decagons.

2004, David Darling, The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes, page 263:

Thus, there is a star octahedron, three star dodecahedrons, and fifty-nine star icosidodecahedrons.

2004, Marc-Alain Ouaknin, The Mystery of Numbers, unnumbered page:

The dark-gray (online: red) icosahedra are part of the B clusters, the light-gray dodecahedra of the B’ clusters, and the (online: blue) icosidodecahedra of the M clusters.

2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 306:

Polyhedrons include prisms; pyramids; the Platonic solids, including tetrahedrons, cubes, octahedrons, dodecahedrons, and icosahedrons; the Archimedean solids, such as cuboctahedrons and icosidodecahedrons; and the Johnson solids, such as square pyramids and triangular cupolas (dome-shape).

2010, Debra Ann Ross, Master Math: Geometry, Cengage Learning, page 306:

An Archimedean solid with thirty-two regular faces (twelve pentagons and twenty triangles).


hexecontahedron

From Ancient Greek ἑξήκοντα (hexḗkonta, “60”) + -hedron, from Ancient Greek ἕδρα (hédra, “geometric face”).


strange attractor

en-noun

strange attractor (plural strange attractors)

The term was coined by David Ruelle and Floris Takens.

(mathematics) An attractor that has a non-integer dimension or whose dynamics on it are chaotic.


starlike

en-adj

starlike (comparative more starlike, superlative most starlike)

more starlike (comparative)
most starlike (superlative)

the growth theorem for holomorphic starlike mappings

(geometry) Convex; having the property that any line segment joining any mapped point to a specified point in the domain lies entirely in the domain.


antipole

A line drawn from a point on a circle to its antipole will cross through the center.

(geometry) A position directly opposite (possibly also used figuratively).


prototile

(geometry) Any of the minimal set of non-congruent shapes from which a larger set of shapes, some of which may be congruent, can be produced.


megagon

Find the constant of proportionality for a decagon, kilogon, and megagon.

1999, Mark Dugopolski, College Algebra and Trigonometry, page 505:

There can exist a regular polygon with 1000 sides (this might be called a "regular kilogon"), 1,000,000 sides (a "regular megagon"), or 1,000,000,000 sides (a "regular gigagon").

2003, Stan Gibilisco, Geometry Demystified:

A megagon is close to the perfection of a circle — a kind of generational transmutation.

2007, Arthur Greenberg, From Alchemy to Chemistry in Picture and Story:

(geometry) A polygon with one million sides.


chemical structure

en-noun

chemical structure (plural chemical structures)

(physical chemistry) The arrangement of chemical bonds between atoms in a molecule (or in an ion or radical with multiple atoms), specifically which atoms are chemically bonded to what other atoms with what kind of chemical bond, together with any information on the geometric shape of the molecule needed to uniquely identify the type of molecule.


lateral area

(geometry) The sum of the areas of the lateral (vertical) faces of a cylinder, cone, frustum, or the like.


signum function

signum function (plural signum functions)

(mathematics) The function that determines the sign of a real number, yielding -1 if negative, +1 if positive, or otherwise zero.


tridecagonal

(geometry) Having thirteen sides and angles, similar to a tridecagon.

13-kulmion muotoinen

having thirteen sides and thirteen angles


hendecagonal

(geometry) Having eleven sides and angles; similar to a hendecagon


Reuleaux triangle

Reuleaux triangle (plural Reuleaux triangles)

Named after Franz Reuleaux, 19th-century German engineer, who used Reuleaux triangles in his machine designs.

(geometry) A figure consisting of three circular arcs, each centered on the intersection of the other two.


hyperellipse

The hyperellipse is defined by (x/a)ⁿ + (y/b)ⁿ = 1 with b ≤ a, where n is the shape parameter and a and b are the axes along the x and y axes, respectively.

2003, M. M. Yovanovich and E. E. Marotta, "Thermal Spreading and Contact Resistances", chapter 4 of Adrian Bejan and Allan D. Kraus (editors), Heat Transfer Handbook, Wiley-IEEE, page 286

(geometry) A superellipse: a curve in two dimensions of a certain type, a generalization of the ellipse.

(geometry) Specifically, a superellipse with an exponent (shape parameter) greater than that of the ellipse (two).

This algorithm extends the model of RNS by incorporating multiple hypershape (hypersphere, hyperrectangle, or hyperellipse) detector representation in the unit hypercube [0, 1]ⁿ (Balachandran et al., 2007).

2008, Dipankar Dasgupta, Luis Fernando Niño, Immunological Computation: Theory and Applications, CRC Press, →ISBN, page 97:

(geometry) A multi-dimensional manifold of a certain type, a generalization of the ellipse and ellipsoid.


blockwise

(geometry) Allowing movement vertically or horizontally only, as if navigating the edges of a grid pattern.


tractrix

(geometry) A curve that satisfies the following property: that segment of the tangent line that lies between the point of tangency and a fixed line has length independent of the point of tangency chosen.


fourth dimension

(algebraic geometry) The fourth coordinate indicating a position along the fourth axis.


ungula

Borrowed from Latin ungula (“claw, hoof”), from unguis (“nail, claw, hoof”).

(geometry) A section of a cylinder, cone, or other solid of revolution, cut off by a plane oblique to the base; so called from its resemblance to the hoof of a horse. [[File:Ungula (PSF).png|thumb|]]


superficies

Borrowing from Latin superficiēs (“top, surface”), from super- (“above, over”) + faciēs (“form, configuration, shape”). Doublet of surface.

af

(geometry) A two-dimensional magnitude that has length and breadth; especially such a surface that forms the boundary of a solid.

The Superficies was compoſed of ſeveral bits of Wood, about the bigneſs of a Dye, but ſome larger than others.

1726 October 28, [Jonathan Swift], “The Author Permitted to See the Grand Academy of Lagado. […]”, in Travels into Several Remote Nations of the World. […] [Gulliver’s Travels], volume II, London: […] Benj[amin] Motte, […], →OCLC, part III (A Voyage to Laputa, Balnibarbi, Glubbdubdribb, Luggnagg, and Japan), page 72:

The visible, external surface of a body.


CDF

Initialism of cumulative distribution function.


pseudocubic

(geometry) describing a rhombohedral structure that is almost cubic


polychoron

en-noun

polychoron (plural polychorons or polychora)

From poly- (“many”) + -choron (“room”), from Ancient Greek πολύς (polús, “many, much”) and χῶρος (khôros, “room”).

uder

(mathematics) A four-dimensional polytope


homothecy

Let us determine the center and the ratio of this homothecy.

1950, Duke Mathematical Journal, Duke University Press, page 76:

The restriction of B to S_b is a homothecy of scale b.

1981, Kenneth Joseph Arrow, Michael D. Intriligator, Handbook of Mathematical Economics, North-Holland, page 1720:

Proposition 7.4 Homothecies preserve circles. That is, for any homothecy h and any circle C, h(C) is a circle as well.[…]Were we willing to do the same with homothecies, we would meet an obstruction: the composition of two homothecies is not necessarily a homothecy.

2013, Felipe Cucker, Manifold Mirrors: The Crossing Paths of the Arts and Mathematics, Cambridge University Press, page 161:


homothety

From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).

The product of two homotheties with the same centre is a homothety with that centre.

1927, Henry George Forder, The Foundations of Euclidean Geometry, page 178:

One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.

1972, Clayton W. Dodge, Euclidean Geometry and Transformations, published 2004, page 106:

Since homotheties are determined by the fixed point, called the center of the homothety, and by the similitude ratio λ, we shall denote by h_(P,λ) the homothety with center P and similitude ratio λ.

2011, Agustí Reventós Tarrida, Affine Maps, Euclidean Motions and Quadrics, Springer Undergraduate Mathematics Series, page 69:

(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point.

homothecy

isotropic scaling transformation with a fixed point


Peano curve

Named after its discoverer, Giuseppe Peano.

(mathematical analysis) A space-filling curve in the 2-dimensional plane.


space-filling curve

en-noun

space-filling curve (plural space-filling curves)

From space-filling curves it can be deduced that ℝ² and ℝ³ have the same cardinality as ℝ.

(mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)


polylogarithm

(mathematics) A function of complex numbers related to logarithms.

polilogaritmo

a function of complex numbers related to logarithms


horosphere

A modern scientific coinage, probably from a Latinized spelling of Ancient Greek ὅρος (hóros, “boundary”) (not to be confused with ὧρος (hôros, “year”), which gave rise to many time-related terms) + sphere

An n-1-dimensional hyperplane in hyperbolic n-dimensional space: it is (in the Poincaré disk) Euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) Euclidean-parallel to the boundary hyperplane.


Poincaré disk

The hyperbolic plane, viewed as a disk so that Euclidean circles and lines Euclidean-perpendicular to the disk's surface are hyperbolic lines.


mascle

From Middle English mascle, maskel, from Old French mascle, macle, from Medieval Latin mascula, from a Germanic source (compare English mesh). Doublet of mail.

(historical) A lozenge-shaped piece of metal, used in making scale mail.


pentachoron

pentachoron (plural pentachorons or pentachora)

pentachorons (plural)
pentachora (plural)

From penta- (“five”) + -choron (“room”), from Ancient Greek πέντε (pénte, “five”) and χῶρος (khôros, “room”).

A triangle becomes a tetrahedron (a type of pyramid), then a pentachoron (a hyperpyramid).

2008, George Musser, The Complete Idiot's Guide to String Theory, page 174:

Geometrically, K₃ relates to a triangle, K₄ a tetrahedron, K₅ a pentachoron, etc.

2008, Prabhakar Gupta et al., Design and Analysis of Algorithms, page 356:

The tetrahedron is a 3-simplex whose 4-simplex analog is the pentachoron, a four-dimensional body which can be orphographically ^([sic]) projected onto a quincrux (as well as a pentagram and other shapes).

2013, Caspar Henderson, The Book of Barely Imagined Beings, page 7:

(mathematics) A four-dimensional object analogous to a tetrahedron, constructed out of five tetrahedra.


quadric

LL-Q1860 (eng)-Flame, not lame-quadric.wav

(mathematics) A surface or curve whose shape is defined in terms of a quadratic equation

quadrique

surface whose shape is defined in terms of a quadratic equation


bigon

(rare) A polygon having two edges and two vertices.


pentacontagon

From pentaconta- (“50”) + -gon (“-sided”), from Ancient Greek πεντήκοντᾰ (pentḗkonta, “50”) and γωνία (gōnía, “corner”).


Catalan solid

From Catalan (“a surname”) + solid, named for Belgian mathematician Eugène Charles Catalan.

1993, E. Heil, H. Martini, 1.11: Special convex bodies, P. M. Gruber, J. M> Wills (editors), Handbook of Convex Geometry, Volume A, page 352,
These duals are also called Catalan solids, because Catalan was the first mathematician who described all of them, cf. Brückner (1900, p. 160). Some of the Catalan solids are much older, e.g., the rhombic dodecahedron, which plays a role in crystallography (cf. chapter 37), and the rhombic triacontahedron, which is of some importance also in the theory of quasicrystals (cf. chapter 3.5).

The set of thirteen such duals is historically designated the Catalan solids. Perhaps the most striking feature of a Catalan solid is that it is composed of just one kind of face that is not a regular polygon. A face of a Catalan solid can be simply constructed by the Dorman-Luke construction [3, 4, 6, 16], which is based on a dualization process known as polar reciprocation [6], with respect to the midsphere.

2003, Rona Gurkewitz, Bennett Arnstein, Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, page 4:

As the most complex of the Catalan solids, the disdyakis triacontahedron has 1680 geometrical elements surrounding its axis, according to Table 1, whilst 2400 elements surround it when its faces are divided into their sectors, i.e., 720 elements are added by this division. These numbers are ten times the corresponding numbers for the simplest Catalan solid.

2009, Stephen M. Phillips, The Mathematical Connection Between Religion and Science, page 270:

(geometry) The dual polyhedron of any Archimedean solid.


penteract

(mathematics) A five-dimensional hypercube.


nine-point circle

en-noun

nine-point circle (plural nine-point circles)

So called because the circle passes through nine points of interest: the feet of the three altitudes, the centers of the three sides, and the midpoints of the segments which join the triangle's vertices with its orthocenter.

That circle which passes through the feet of the altitudes of a given triangle.


gömböc

From Hungarian gömböc (“short, plump person; gömböc”).

bor

(geometry) A convex shape which, if made of a uniformly dense material, has one stable equilibrium orientation and one unstable equilibrium orientation.


saddle point

(geometry) A point in the range of a smooth function, every neighbourhood of which contains points on each side of its tangent plane.


bicorn

Borrowed from Latin bicornis (“two-horned; two-pronged”). Compare French bicorne (“two-cornered hat; two-horned monster”) and Middle English bicorne (“two-horned anvil; two-pronged fork; fabulous (two-horned) beast”). Doublet of bicorne.

cog

(mathematics) A plane curve having two cusps.


T-shaped

en-adj

T-shaped (comparative more T-shaped, superlative most T-shaped)

more T-shaped (comparative)
most T-shaped (superlative)

丁字

having a shape similar to a capital letter T

A-shaped - B-shaped - C-shaped - D-shaped - E-shaped - F-shaped - G-shaped - H-shaped - I-shaped - J-shaped - K-shaped - L-shaped - M-shaped - N-shaped - O-shaped - P-shaped - Q-shaped - R-shaped - S-shaped - T-shaped - U-shaped - V-shaped - W-shaped - X-shaped - Y-shaped - Z-shaped


ar-

Shortened from area (because the function describes the area under a hyperbola), by analogy with arc-, the corresponding prefix for the circular trigonometric functions.

(mathematics, trigonometry) Used to form the names of inverse hyperbolic trigonometric functions, and the symbols for these functions.


hypoellipse

(geometry) A superellipse with an exponent (shape parameter) smaller than that of the ellipse, i.e. less than two.


logit

LL-Q1860 (eng)-Flame, not lame-logit.wav

Blend of logistic + unit, by analogy with probit, coined by Joseph Berkson in 1944: “I use this term [logit] for ln p/q following Bliss, who called the analogous function which is linear on x for the normal curve ‘probit.’”

operatorname logit(p)= log (p/(1-p))= log (p)- log (1-p).!,

(mathematics) the inverse of the "sigmoid" or "logistic" function used in mathematics, especially in statistics. The logit of a number p between 0 and 1 is given by the formula:


-angle

(geometry, of a two-dimensional shape) having the specified number of internal angles


isoperimetric

(geometry) Having the same perimeter; applied to the problem of finding a plane figure of the largest possible area whose boundary has a specified length


hyperkähler

(geometry, of a manifold) Being a quaternionic analogue of a Kähler manifold.


constructible

destructible

antonym(s) of “capable of being constructed”

(geometry, of a regular polygon) That can be constructed in a plane using only a pair of compasses and a straightedge.

(algebraic geometry, of a subset of the spectrum of a noetherian ring) Admitting description as a finite union of locally closed (with respect to the Zariski topology) sets.


EGA

Éléments de géométrie algébrique
w:Éléments de géométrie algébrique

(algebraic geometry) Initialism of Éléments de géométrie algébrique.


nonprimitive

(computing, geometry) An object that is not a primitive.


bicone

(geometry) The three-dimensional shape swept by revolving an isosceles triangle around its edge of unequal length, or by joining two identical right circular cones, base to base.


pons asinorum

From New Latin pons asinorum, from Latin pōns (“bridge”) + genitive plural of asinus (“donkey”). Literally, “bridge of donkeys”.

[H]e had scarce advanced beyond the Pons Asinorum, when his ardour abated, the test of truth by demonstration did not elevate him to those transports of joy with which his preceptor had regaled his expectation; and before he arrived at the fortieth and seventh proposition, he began to yawn drearily […].

1751, [Tobias] Smollett, The Adventures of Peregrine Pickle […], volume (please specify |volume=I to IV), London: Harrison and Co., […], →OCLC:

(geometry) A proposition in Euclid stating that the angles at the base of an isoceles triangle are equal.


cologarithm

(mathematics) The logarithm of the reciprocal of a number (equal to the negative of the original logarithm)


triacontahedron

en-noun

triacontahedron (plural triacontahedra or triacontahedrons)

triacontahedra (plural)
triacontahedrons (plural)

From Ancient Greek τρῐᾱ́κοντᾰ (triā́konta) + -hedron.


-choron

From Ancient Greek χῶρος (khôros, “room”).

(geometry) Used to form the names of 4-dimensional solids bounded by a certain number of cells/polyhedra (polychora).


holyhedron

John Conway of Princeton University offered a reward in the 1990s to anyone producing a holyhedron, a polyhedron with a finite number of faces and with a hole in every face. […] Conway had predicted that someone will eventually find a holyhedron with fewer than 100 faces.

1969, Charles Miller, Vern Heeren, John Hornsby, Margaret Morrow, Jill Van Newenhizen, Mathematical Ideas, 11th edition:

(geometry) A polyhedron with a finite number of faces and with a polygonal hole in every face, the holes' boundaries sharing no point with each other or the face's boundary.


banana-shaped

en-adj

banana-shaped (comparative more banana-shaped, superlative most banana-shaped)

more banana-shaped (comparative)
most banana-shaped (superlative)


hourglass-shaped

hourglass-shaped (comparative more hourglass-shaped, superlative most hourglass-shaped)

more hourglass-shaped (comparative)
most hourglass-shaped (superlative)

Having a shape or cross-section like that of an hourglass.


exotic sphere

A manifold (of any dimension) homeomorphic to a sphere but not diffeomorphic to the standard sphere.


dihedral angle

Any two dihedral angles are to one another as the angles contained by perpendiculars drawn as in the last proposition.

1830, Pierce Morton, Geometry, Plane, Solid and Spherical, London: Baldwin and Cradock, page 136:

The remaining dihedral angles are the source of essentially all the interesting variability in protein conformation.

1981, Jane S. Richardson, “The Anatomy and Taxonomy of Protein Structure”, in C. B. Afinson, John T. Edsall, Frederic M. Richards, editors, Advances in Protein Chemistry, volume 34, page 173:

The significance of small dihedral angles is readily apparent in Fig. 6.20, where the shape of the intersection is shown for angles of 10° and 1°.

2009, Reza Abbaschian, Lara Abbaschian, Robert E. Reed-Hill, Physical Metallurgy Principles, Cengage Learning, page 176:

(geometry) The angle between two planes.


isogeny

en-noun

isogeny (countable and uncountable, plural isogenies)

It is clear that if G#x5F;2 is connected, then two of the defining properties of an isogeny imply the third.

2000, Marc Hindry, Joseph H. Silverman, Diophantine Geometry: An Introduction, Springer, page 95:

2002, Mireille Fouquet, François Morain, Isogeny Volcanoes and the SEA Algorithm, Claus Fieker, David R. Kohel (editors), Algorithmic Number Theory: 5th International Symposium, Proceedings, Springer, LNCS 2369, page 279,
Lemma 2.2 Let E be an elliptic curve such that Z [π] is maximal at 𝓁. If there exists an 𝓁-isogeny of E, then this 𝓁-isogeny is an horizontal 𝓁-isogeny.

2005, Fred Diamond, Jerry Shurman, A First Course in Modular Forms, Springer, page 29,
The dual isogeny of an isomorphism is its inverse. The dual of a composition of isogenies is the composition of the duals in the reverse order. If φ is an isogeny and ̂φ is its dual then the formulas φ(z+Λ)=mz+Λ', φ(z'+Λ')=( operatorname φ/m)z'+Λ show that also
φ∘̂φ=[ operatorname deg(φ)]=[ operatorname deg(̂φ)],
so that φ is in turn the dual isogeny of its dual ̂φ. Isogeny of complex tori, rather than isomorphism, will turn out to be the appropriate equivalence relation in the context of modular forms.

(algebraic geometry, category theory) An epimorphism of group schemes that is surjective and has a finite kernel.


catenoid

(geometry) A three-dimensional surface formed by rotation of a catenary

caténoïde

Three-dimensional surface formed by rotation of a catenary


cuboctahedral

(geometry) Of, pertaining to, or having the form of a cuboctahedron


nestohedron

generalized permutahedron
generalized permutahedron

(geometry) For a building set B, the Minkowski sum of the simplices Δ_S as S ranges over B. (Here Δ_S is the standard simplex of S, i.e., the convex hull of the (nonzero endpoints of the) standard unit vectors eᵢ for i in S.) Every nestohedron is a generalized permutahedron.


domeshaped

en-adj

domeshaped (comparative more domeshaped, superlative most domeshaped)

more domeshaped (comparative)
most domeshaped (superlative)


supercircle

(geometry) A special case of a superellipse having equal semimajor and semiminor axes.


sextic

(mathematics) An algebraic equation or function of the sixth degree, e.g. a polynomial of degree 6; a curve surface etc. describing such an equation or function, especially a quantic of the sixth degree.


projectivization

Let us consider the vector space T#x5F;p. Its projectivization #x7B;PT#x7D;#x5F;p, is a projective space, which is obtained from T#x5F;p, by factorization relative to the collinearity of vectors. The projectivization #x7B;PT#x7D;#x5F;p is a set of straight lines, passing through the point p. Under projectivization, the cone C(2,r) becomes a manifold S(1,r-1) of dimension r.

1992, Maks A. Akivis, Alexander M. Shelekhov, translated by Vladislav V. Goldberg, Geometry and Algebra of Multidimensional Three-Webs, Springer, page 11:

1997, M. E. Alferieff (translator), Alexei Kostrikin, Yuri Manin, Linear Algebra and Geometry, Gordon and Breach Science Publishers, Paperback, page 233,
Therefore, the projectivization P(f) is determined only on the complement U_f=P(L)P( ker f).

The projectivization of a two-dimensional irregular equation (1.1) is a holomorphic vector field on #x5C;mathbbP¹#x5C;times#x5C;left#x5C;#x7B;#x5C;vertt#x5C;vert#x3C;1#x5C;right#x5C;#x7D; having a pair of singularities on the fiber #x5C;mathbbP¹#x5C;times 0 (which correspond to the eigenlines of the matrix A(0), the coordinate lines in our case).[…]Now the preceding corollary applied to the family of projectivizations says that the horizontal separatrices converge to the sectorial separatrices of the projectivized nonperturbed equation.

2004, Alexey Glutsyuk, “Confluence of singular points and Stokes phenomena”, in Yulij Ilyashenko, Christiane Rousseau, Gert Sabidussi, editors, Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Kluwer Academic, page 290:

(mathematics, algebraic geometry, birational geometry) A process (more formally, a mapping) that, given a vector space, specifies an associated projective space; (loosely) the projective space so specified.


chair conformation

en-noun

chair conformation (plural chair conformations)

(organic chemistry) the most stable chemical conformation of a six-member single bonded carbon ring such as cyclohexane


square wave

(mathematics, engineering, signal processing) A function or waveform that alternates regularly and instantaneously between two levels.


subfigure

(geometry) A figure (geometric form) that is part of another.


cylindricity

cylindricity (countable and uncountable, plural cylindricities)

(uncountable, geometry) The quality of being cylindrical.

(countable, geometry) A three-dimensional geometric tolerance that controls how much a feature can deviate from a perfect cylinder.


cantellation

(geometry) An operation in any dimension that cuts a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex.


pseudosphere

(geometry) A surface generated by rotating a tractrix about its asymptote; a tractricoid

(geometry) Any of various surfaces with constant negative Gaussian curvature.


projectivity

projectivity (countable and uncountable, plural projectivities)

projective transformation
projective transformation

(geometry) projective transformation, homography


Apollonian circle

Apollonian circle (plural Apollonian circles)

(geometry) Any circle in two families of circles such that every circle in the first family intersects every circle in the second family orthogonally and vice versa.


hemiellipse

(geometry) A shape obtained by cutting an ellipse in half along one of its axes


homography

homography (countable and uncountable, plural homographies)

/həʊˈmɒɡɹəfɪ/

A homography on a real projective plane can be specified by a mapping from one set of four non-collinear points to another set of four non-collinear points. Given such a specification, then the 3-by-3 homography matrix may be computed by means of the DLT (Direct Linear Transformation) algorithm.

(geometry) An isomorphism between projective spaces that maps straight lines to straight lines.


heliosynchronous

A heliosynchronous orbit is an orbit [around the Earth] whose plane precesses by [a little less than] one degree a day around the line of the poles, thus keeping the same position in relation to the Earth-Sun line.

1987, Pierre Lellouche, Satellite warfare: a challenge for the international community, Institut français des relations internationales, United Nations Institute for Disarmament Research, United Nations:

Describing an orbit around the Earth where each passage in the same direction along a given latitude will occur throughout the year at the same true solar time.


conoid

(geometry) A Catalan surface all of whose rulings intersect some fixed line

A parabolic conoid is a paraboloid; an elliptic conoid is an ellipsoid.

(geometry) A solid formed by the revolution of a conic section about its axis


hexatetrahedron

(geometry) A cube truncated by two tetrahedra


isogonal

/ʌɪˈsɒɡənəl/


GEO

genetically engineered organism
genetically engineered organism#English

Initialism of genetically engineered organism.


circumcircle

(geometry) A circle that passes through every vertex of a given triangle (or other polygon where possible).

circumferència circumscrita

a circle that passes through every vertex of a given polygon


hemiellipsoid

(geometry) Either of the halves into which an ellipsoid is divided by a plane of symmetry


calceiform

en-adj

calceiform (comparative more calceiform, superlative most calceiform)

more calceiform (comparative)
most calceiform (superlative)

From Latin calceus (“calceus, footwear”) + English -form (“-shaped”) after the model of French calcéiforme.

(chiefly botany) Shoe-shaped, shaped like a shoe.


octonionic

(mathematics) Of or pertaining to octonions.


egg-shaped

egg-shaped (comparative more egg-shaped, superlative most egg-shaped)

more egg-shaped (comparative)
most egg-shaped (superlative)


glome

Borrowed from Latin glomus (“a ball”). Compare globe.

LL-Q1860 (eng)-I learned some phrases-glome.wav

(geometry) A hypersphere in 4-dimensional Euclidean space defined as the set of all points that are at a given distance from a given point, also called a 3-sphere.


hypercycle

(hyperbolic geometry) A curve whose points have the same orthogonal distance from a given straight line.


tetradecagonal

(geometry) Having the form of a tetradecagon


truncus

From Latin truncus. Doublet of tronk and trunk.

(geometry) A curve in the Cartesian plane consisting of all points (x,y) satisfying an equation of the form f(x)=a/(x+b)²+c where a, b, and c are given constants.


reptation

en-noun

reptation (countable and uncountable, plural reptations)

(geometry) The motion of one plane figure around another, so that the longest diameter of one shall come into line with the shortest of the other.


full circle

по́лный цикл

full turn back to the original direction or orientation

Arcs are measured in degrees, with 360° in the full circle.

2007, Carolyn C. Wheater, Geometry, page 193:


superpath

(graph theory) The path that contains a particular subpath.


subpath

(graph theory) A path making up part of a larger path (the superpath).


trilogarithm

(mathematics) The form of polylogarithm having a base of three


dilogarithm

In two space-time dimensions, we arrive at a result in terms of elliptic dilogarithms.

2015, Luise Adams, Christian Bogner, Stefan Weinzierl, “The Elliptic Sunrise”, in arXiv:

(mathematics) The form of polylogarithm having a base of two


isogonic

en-adj

isogonic (comparative more isogonic, superlative most isogonic)

more isogonic (comparative)
most isogonic (superlative)


hyperdynamics

(physics) The extension of dynamics to systems of more than three dimensions


quindecagonal

quindecagonal (comparative more quindecagonal, superlative most quindecagonal)

more quindecagonal (comparative)
most quindecagonal (superlative)

(geometry) Shaped like a quindecagon; fifteen-sided.


quasiregular

The lattice points that lie in this plane are the vertices of the regular tessellation {3, 4} of equilateral triangles, and the other points just mentioned are the vertices of the quasiregular tessellation #x5C;begin#x7B;Bmatrix#x7D;3#x5C;#x5C;4#x5C;end#x7B;Bmatrix#x7D; of triangles and hexagons [9, p. 60].

1981, H. S. M. Coxeter, “The Derivation of Schoenberg's Star Polytopes from Schoute's Simplex Nets”, in Chandler Davis, Branko Grünbaum, F.A. Sherk, editors, The Geometric Vein: The Coxeter Festschrift, page 151:

There are two quasiregular polyhedra not having identical regular faces: the cuboctahedron (dymaxion) and the icosidodecahedron.

1996, Wolfgang Schueller, The Design of Building Structures, page 540:

2007, V. A. Blatov, O. Delgado-Friedrichs, M. O'Keeffe, D. M. Proserpio, Periodic nets and tilings: possibilities tor analysis and design of porous materials: Proceedings of the 15th International Zeolite Conference, Ruren Xu, Jiesheng Chen, Zi Gao, Wenfu Yan (editors), From Zeolites to Porous MOF Materials, page 1642,
If we allow the coordination figure to be a quasiregular polyhedron (a polyhedron with one kind of vertex and edge, but two kinds of face) there is just one possibility compatible with translational symmetry – a cuboctahedron.

Two semiregular polyhedra are classified as so-called quasiregular polyhedra. They have two kinds of faces, and each face of one kind is entirely surrounded by faces of the other kind.

2007, Istvan Hargittai, Magdolna Hargittai, Symmetry through the Eyes of a Chemist, page 89:

(geometry, of a polyhedron or tessellation) That is semiregular with regular faces of precisely two types that alternate around each vertex.


snub cube

From cubus simus, Kepler's name for this solid.

1995, R. H. Hardin, N. J. A. Sloane, Codes (Spherical) and Designs (Experimental), Robert Calderbank (editor), Different Aspects of Coding Theory: American Mathematical Society Short Course, Proceedings of Symposia in Applied Mathematics, Volume 50, page 183,
Robinson [67] showed in 1961 that the best packing of 24 points is achieved by the vertices of a regular snub cube, one of the Archimedean solids (cf. [20]).

1996, William P. Schaefer, The Snub Cube in the Glanville Courtyard of the Beckman Institute at the California Institute of Technology, The Chemical Intelligencer, reprinted in 2015, Balazs Hargittai, István Hargittai (editors), Culture of Chemistry: The Best Articles on the Human Side of 20th-Century Chemistry from the Archives of the Chemical Intelligencer, page 55,
A wooden model, though, showed that with a sufficiently strong flow, the entire surface of the solid could be wet; we were given the go-ahead to install a five-foot-tall, granite snub cube in the fountain.

Two of these are chiral pairs, the dextro snub cube and its chiral partner, the laevo snub cube; the third is the regular orbit of T_d point symmetry, while the fourth is the regular orbit of Tₕ symmetry.

2005, Charles M. Quinn, Patrick Fowler, David Redmond, Computational Quantum Chemistry II: The Group Theory Calculator, page 44:

equilateral triangle
equilateral triangle

(geometry) An Archimedean solid with thirty-eight faces, of which six are squares (no two of which share a vertex) and thirty-two are equilateral triangles.

cubus sinus

polyhedron with 6 square and 32 triangular faces


pseudo-Riemannian manifold

en-noun

pseudo-Riemannian manifold (plural pseudo-Riemannian manifolds)

differential geometry
differential geometry

(differential geometry) A generalization of a Riemannian manifold


Riemannian geometry

Riemannian geometry (usually uncountable, plural Riemannian geometries)

From Riemannian + geometry, after German mathematician Bernhard Riemann.

Riemannian geometry was introduced by Riemann in 1854 as the n-dimensional generalization of the theory of curved surfaces of the 3D Euclidean space.

2001, Miklós Farkas, Dynamical Models in Biology, page 171:

Such geometries are called Riemannian geometries; they are characterized by invariant distances (for example, the space-time interval) that depend at most on the squares of the coordinate distances (∆x or ∆t).

2005, John F. Hawley, Katherine A. Holcomb, Foundations of Modern Cosmology, 2nd edition, page 235:

Riemannian geometry has found many applications in science, the most spectacular of these being the theory of relativity.[…]Every Riemannian geometry has geodesics, which are defined as the shortest curves joining two points.

2010, Saul Stahl, Geometry from Euclid to Knots, page 22:

At the beginning of the seventies, A. Gray generalized the classical holonomy concept by introducing a classification principle for non-integrable special Riemannian geometries [and] discovered in this context nearly Kähler manifolds in dimension six and nearly parallel G₂-manifolds in dimension seven.

2010, Ilka Agricola, “Chapter 9: Non-integrable geometries, torsion, and holonomy”, in Vicente Cortés, editor, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, page 278:

The concepts of Riemannian geometry are familiar: length, angle, distance, and curvature, among others. Historically tied to the origins of differential geometry, and with such familiar concepts, Riemannian geometry is often presented in textbooks as being synonymous with differential geometry itself, instead of as one differential-geometric structure among many.

2013, Andrew McInerney, First Steps in Differential Geometry: Riemannian, Contact, Symplectic, page 195:

(mathematics, geometry) The branch of differential geometry that concerns Riemannian manifolds; an example of a geometry that involves Riemannian manifolds.


Riemannian manifold

Riemannian manifold (plural Riemannian manifolds)

Named after German mathematician Bernhard Riemann (1826–1866). See also Riemannian.

variété riemannienne

real, smooth differentiable manifold equipped with a Riemannian metric

By definition, a Riemannian manifold M has at each point p a tangent space T#x5F;pM equipped with a positive-definite inner product, g#x5F;p; information about these inner products is encoded in the Riemannian metric tensor, g.

In this chapter we extend the study of eigenvalues to Riemannian manifolds whose curvature may not be constant, but is, nevertheless, bounded.

1984, Isaac Chavel, Eigenvalues in Riemannian Geometry, Academic Press, page 55:

Further, a much harder theorem, due to J. Nash [31], says that a separable Riemannian manifold of dimension d can be isometrically embedded in #x5C;textstyle#x5C;mathbbRᴺ with N#x5C;le#x7B;#x5C;tfrac 1 2#x7D;d(d#x2B;1)(3d#x2B;11).

2000, Daniel W. Stroock, An Introduction to the Analysis of Paths on a Riemannian Manifold, American Mathematical Society, page 165:

Before we delve into the general theory of Riemannian manifolds, we pause to give it some substance by introducing a variety of "model Riemannian manifolds" that should help to motivate the general theory.

2018, John M. Lee, Introduction to Riemannian Manifolds, 2nd edition, Springer, page 55:

(differential geometry, Riemannian geometry) A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;

differential geometry; Riemannian geometry; differential geometry; Riemannian geometry

differential geometry; Riemannian geometry; more formally

A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;
(more formally) an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.


fourgon

(geometry) A polygon with four sides; a quadrilateral.


square the circle

en-verb

square the circle (third-person singular simple present squares the circle, present participle squaring the circle, simple past and past participle squared the circle)

squares the circle (present singular third-person)
squaring the circle (participle present)
squared the circle (participle past)
squared the circle (past)

The problem of squaring the circle is the problem of determining the ratio of the circumference of a circle to the diameter, which is called π.

1946, Bertrand Russell, History of Western Philosophy, I.24:

(geometry) To construct a square with the same area as a given circle by using only a finite number of steps with compass and straightedge, a task which is mathematically impossible.

رَبَّعَ الدائِرة

to construct a square with the same area as a circle

square peg in a round hole

semantic overlap regarding a difficult problem


intersphere

(geometry) A sphere that is tangent to every edge of a given polyhedron.


subtense

(geometry) A line which subtends, especially the chord of an arc.

(geometry) The angle subtended by a line at a point.


subcontrary

Two planes drawn through the vertex of the cone parallel to the plane of the circular base , and that of a subcontrary section, are called by Chasles the cyclic planes of the cone

1852, John Mulcahy, Principles of Modern Geometry:

(geometry) Having, or being in, a contrary order; said of a section of an oblique cone having a circular base made by a plane not parallel to the base, but so inclined to the axis that the section is a circle; applied also to two similar triangles when so placed as to have a common angle at the vertex, the opposite sides not being parallel.


trihedral

(geometry) Having three plane faces that meet at a common point


contingence

en-noun

contingence (countable and uncountable, plural contingences)

Borrowed from Latin contingentia, from contingēns, present passive participle of contingō (“I make contact with, I am touching”).


squircle

At the NCI, the applicator shapes most often used are circular or "squircular." The squircle applicator has one square and one round end, and it is beveled so that the circular end is longer.

1985, Hospital Practice, volume 20, page 131:

(algebraic geometry) A closed quartic curve having properties intermediate between those of a square and a circle.

kwadratokrąg

shape intermediate between a square and a circle


isohedral

(geometry) Describing a polyhedron or a tiling all of whose faces are the same.


hypercone

(geometry) A four-dimensional surface related to the three-dimensional cone


conchoid

From Latin concha (“mussel”) (from Ancient Greek κόγχη (kónkhē)) + -oid or directly from Ancient Greek κογχοειδής (konkhoeidḗs), referring to the curved outline of a mussel shell or anything in this form.

The conchoid of a circle with respect to a point on the circle is a cardioid if the fixed distance is equal to the diameter of the circle.

The Conchoid of Nicomedes is the conchoid of a straight line with respect to a point not on the line.

1815, Charles Hutton, Pappus, entry in A Philosophical and Mathematical Dictionary, Volume 2, page 147,
He next treats of the properties of the Conchoid, which Nicomedes invented for doubling the cube; applying it to the solution of certain problems concerning Inclinations, with the finding of two mean proportionals, and cubes in any proportion whatever.

The classical conchoid construction is a non-orthogonal polar-curvilinear construction in which equal distances along a line are marked off from its point of intersection with a curve for various positions of the line as it rotates about a point.

1982, J. Lee Kavanau, Curves and Symmetry, volume 1, page 3:

These curves are called conchoids of Nicomedes after the ancient Greek scholar Nicomedes. He called them conchoids because the shape of their outer branches resembles that of a conch shell or mussel shell.

2007, James Stewart, Single Variable Calculus, volume 2, page 662:

One of the best choices is the conchoid, according to Newton the simplest curve after the circle.

2009, Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method, page 68:

(mathematics, geometry) Any of a family of curves defined as the locus of points p, such that each p is on a line that passes through a given fixed point P and intersects a given curve, C, and the distance from p to the point of intersection with C is a specified constant (note that for nontrivial cases two such points p satisfy the criteria, and the resultant curve has two parts).


prismoid

(geometry) A prismatoid that has planar sides, and the same number of vertices in both of its parallel planes.


hyperbolism

hyperbolism (countable and uncountable, plural hyperbolisms)

(countable, geometry) A blow-up of a curve at a point.


semisquare

(geometry) A right isocoles triangle, or such figure of which two form a square.


arbelos

From Ancient Greek ἄρβηλος (árbēlos) or ἄρβυλος (árbulos), literally "shoemaker's knife".

(geometry) A plane region bounded by a semicircle of diameter 1, connected to semicircles of diameters r and (1 − r), all oriented the same way and sharing a common baseline.


salinon

From Ancient Greek *σάλινον (*sálinon, unattested), presumably from and meaning the same as Latin salīnum (“salt-cellar”), derived from sal (“salt”) (compare salillum).

bor

(geometry) A particular figure bounded by four semicircles.


excircle

Also since the circle of inversion cuts both excircles orthogonally, each excircle inverts into itself.

1979, Dan Pedoe, Circles: A Mathematical View, published 1995, page 10:

Extend the sides of triangle QRS and construct the three excircles: One excircle is tangent to side QR and rays SQ and SR; one excircle is tangent to side SR and rays QS and QR; and one excircle is tangent to side SQ and rays RS and RQ.

1999, Art Johnson, Famous Problems and Their Mathematicians, Teacher Ideas Press, page 174:

Lemma 4.9 (The Diameter of the Incircle). Let ABC be a triangle whose incircle is tangent to #x5C;overline#x7B;BC#x7D; at D. If #x5C;overline#x7B;DE#x7D; is a diameter of the incircle and ray AE meets #x5C;overline#x7B;BC#x7D; at X, then BD#x3D;CX and X is the tangency point of the A-excircle to #x5C;overline#x7B;BC#x7D;.
Incircles and excircles often have dual properties.

2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads, page 61:

(geometry) An escribed circle; a circle outside a polygon (especially a triangle, but also sometimes a quadrilateral) that is tangent to each of the lines on which the sides of the polygon lie.


real function

(mathematics) A function whose range is a subset of the set of real numbers.


complex function

en-noun

complex function (plural complex functions)

(mathematics) A function whose range is a subset of the set of complex numbers.

kompleksifunktio

a function whose range is a subset of the set of complex numbers

komplexe Funktion

with the additional constraint of the domain being a subset of the complex numbers


real plane

(set theory) The Cartesian product of two real lines.


characteristic function

characteristic function (plural characteristic functions)

(mathematics, probability theory) A complex function completely defining the probability distribution of a real-valued random variable

karakteristinen funktio

a complex function completely defining a probability distribution


hemiequilateral

(geometry) Describing the shape of a triangle formed by cutting an equilateral triangle in half through one of the apices


describent

Latin dēscrībēns, present participle of dēscrībō (“I describe”).


evolvent

Latin ēvolvēns, ēvolventis (“unrolling”), present participle of ēvolvō (“I unroll”).


linear functional

linear functional (plural linear functionals)

(mathematics) A linear mapping from a vector space to its field of scalars.


positive linear functional

positive linear functional (plural positive linear functionals)

mathematical analysis
mathematical analysis

(mathematical analysis) A kind of linear functional which yields a non-negative scalar when given a non-negative function as parameter.


equidecomposability

(geometry) The quality of being equidecomposable.


equidecomposable

(geometry, of two forms) Capable of being decomposed into a number of pieces that can be reassembled into either of the two.


hypercylinder

(mathematics) A four-dimensional analog of a cylinder


arithmetic spiral

arithmetic spiral (plural arithmetic spirals)

It is a spiral whose equation in polar coordinates is linear, which would thus, when quantized, yield an arithmetic progression.

The Parker spiral is the shape of the Sun's magnetic field as it extends through the solar system. Unlike the familiar shape of the field from a bar magnet, the Sun's extended field is twisted into an arithmetic spiral by the magnetohydrodynamic influence of the solar wind.

(mathematics) A spiral that increases in distance from the point of origin at a constant rate.


linear operator

linear operator (plural linear operators)

(mathematics, functional analysis) An operator L such that for functions f and g and scalar λ, L (f + g) = L f + L g and L λf = λ L f.


GTO

geostationary transfer orbit
geostationary transfer orbit#English

(space science) Abbreviation of geostationary transfer orbit.


TLI

trans-lunar injection
trans-lunar injection#English

(space science) Initialism of trans-lunar injection.


(astrophysics) Abbreviation of Lagrange point 5, located 60 degrees behind the smaller object along its orbit around the larger object.


(astrophysics) Abbreviation of Lagrange point 3, located 180 degrees away from the smaller object and slightly outside the smaller object's orbit around the larger object.