(astrophysics) Abbreviation of Lagrange point 4, located 60 degrees ahead of the smaller object along its orbit around the larger object.


Lagrange point

Named after Joseph Louis Lagrange, who discovered the points L₄ and L₅, building on earlier work by Leonhard Euler, and in 1772 published an essay on the three-body problem.

Mathematically, the Lagrange points represent solutions to a restricted form of the three body problem in which the mass of one object is assumed negligible compared to that of the two principal bodies—as, for example, an artificial satellite and the Earth-Moon system.

Lagrange points are significant for lunar development in that raw materials, such as near-Earth objects (NEOs) can be safely stored at L-4 and L-5 prior to mining and processing.

2008, David Schrunk, Burton Sharpe, Bonnie L. Cooper, Madhu Thangavelu, The Moon: Resources, Future Development and Settlement, Springer, Praxis Publishing, page 57:

The $1.27-billion (1 billion euros) SOHO satellite was launched in 1995 and is flying a joint mission between NASA and the European Space Agency (ESA). It watches solar activity from an orbit about the Lagrange Point 1, a gravitationally stable spot between Earth and the sun that is about 932,000 miles (1.5 million kilometers) from our planet.

2013 July 28, Megan Gannon, “Spacecraft Sees Giant 'Hole' In the Sun”, in news.yahoo.com, retrieved 2013-07-29:

For science several of the Lagrange points are important. The question of access to Lagrange points or GSO slots emerges as these become congested.

2016, Francis Lyall, Paul B. Larsen, Space Law, Taylor & Francis (Routledge), page 247:

(astrophysics, orbital mechanics) A point in an orbital configuration of a two-body system where a small object affected only by gravity can theoretically be stationary relative to the two larger objects.


Lagrangian point

en-noun

Lagrangian point (plural Lagrangian points)

(astrophysics) Alternative form of Lagrange point


isocapacitary

(geometry) Having the same capacity; applied to the problem of finding an extremum for an integral over a space of a specified capacity.


Trojan planet

(astrophysics) a planet that occupies a Trojan point of a star system


Trojan moon

(astrophysics) A pseudo-moon that occupies a Trojan point of a system.


horocyclic

In two-dimensional Euclidean geometry using a polar coordinate system, horocyclic flow is either the circular convergence toward or away from a point or the rotational flow around a point.

Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic 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:

(geometry) Relating to a set of points that are all equidistant (keeping other coordinates constant) from some constant point.


Trojan point

point troyen

(astrophysics) any L4 and L5 Lagrange points

(astrophysics) the L4 and L5 Lagrange points of the Sun-Jupiter orbital configuration

point troyen

(astrophysics) by extension, any L4 and L5 Lagrange points


Trojan asteroid

Trojan asteroid (plural Trojan asteroids)

Derived from the names of the first three Trojan asteroids found (Achilles, Patroclus, Hektor)

(astrophysics) an asteroid occupying the Trojan points of the Sun-Jupiter system

(astrophysics) by extension, any asteroid occupying a Trojan point


en-adj

4-dimensional (comparative more 4-dimensional, superlative most 4-dimensional)

more 4-dimensional (comparative)
most 4-dimensional (superlative)

Alternative spelling of four-dimensional.


2-dimensional (comparative more 2-dimensional, superlative most 2-dimensional)

more 2-dimensional (comparative)
most 2-dimensional (superlative)

Alternative spelling of two-dimensional.


3-dimensional (comparative more 3-dimensional, superlative most 3-dimensional)

more 3-dimensional (comparative)
most 3-dimensional (superlative)

Alternative spelling of three-dimensional.


hepteract

(mathematics) A seven-dimensional hypercube


hexeract

(mathematics) A six-dimensional hypercube


octeract

(mathematics) An eight-dimensional hypercube


enneract

(mathematics) A nine-dimensional hypercube


rhombicuboctahedron

en-noun

rhombicuboctahedron (plural rhombicuboctahedra or rhombicuboctahedrons)

rhombicuboctahedra (plural)
rhombicuboctahedrons (plural)

From Latin rhombicuboctahaedron,
referring to the fact that the twelve of the square faces lie in the same planes as the twelve faces of the rhombic dodecahedron, the dual of the cuboctahedron. (See rhombicuboctahedron on Wikipedia.Wikipedia)

Therefore eight triangles and eighteen (that is, twelve and six) squares join up to make an icosihexahedron, which I call a truncated cuboctahedral rhombus or a rhombicuboctahedron.

1997, Johannes Kepler, E. J. Aiton, Alistair Matheson Duncan, Judith Veronica Field, transl., The harmony of the world, American Philosophical Society, page 119:

The gaps in a face-centered cubic packing of square sharing rhombicuboctahedra can be filled by cubes and tetrahedra (Fig. 2.4(h)).

2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 55:

So, for instance, covering up the right-hand side of our example (as in Figure 20.2(a)), we see that the rhombicuboctahedron does indeed have three types of face: two four-sided ones and one three-sided one.

2016, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 273:

small rhombicuboctahedron
small rhombicuboctahedron

(geometry) An Archimedean solid with eight triangular and eighteen square faces; the small rhombicuboctahedron.

rombikuboktaedri

polyhedron with 8 triangular and 18 square faces

斜方立方八面体

しゃほうりっぽうはちめんたい

菱形立方八面体

りょうけいりっぽうはちめんたい


hexafoil

A design with six round semicircular petals stemming from a central circle.


SDG

SDG (countable and uncountable, plural SDGs)

synthetic differential geometry
w:synthetic differential geometry

(geometry) Initialism of synthetic differential geometry.


law of cosines

(trigonometry) A generalization of the Pythagorean theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.


coöriginal

/ˌkəʊəˈɹɪdʒənəl/

/ˌkoʊəˈɹɪd͡ʒənəl/

In operations on lines in space, it is convenient to substitute for some of the given lines other lines, equal, and therefore parallel, to the given ones, but passing through a point in space common to themselves and the other given lines; so that all the lines may be coöriginal.

1859 October (pub. 1860 October), John Daniel Runkle (editor), The Mathematical Monthly, volume II, № I, pages 29–31: W.P.G. Bartlett, “The Elements of Quaternions”, part I: “Lines”, § 4

(geometry, of a line) Originating from the same point in space.


hendecahedron

hendecahedron (plural hendecahedrons or hendecahedra)

hendecahedrons (plural)
hendecahedra (plural)

(geometry) A polyhedron with eleven faces.


coterminal

When you try to draw two coterminal angles on a circle, you will find that you only get one line.

(geometry, of two angles) Differing only by a whole number of complete circles.

coterminal

angle differing only by a whole number of complete circles


oblongum

(geometry, archaic) A prolate spheroid; a figure described by the revolution of an ellipse about its greater axis.


fixpoint

It feels like I've stepped through the looking glass and am wandering in a topsy-turvy world where the fixpoints we have lived with for decades have gone. Not just moved... gone.

2020 June 3, Stefanie Foster, “Comment: The recovery starts here”, in Rail, page 3:


hemicube

(geometry) An abstract regular polyhedron containing half the faces of a cube.


cross-ratio

(geometry) A special number associated with an ordered quadruple of collinear points, particularly points on a projective line, and preserved by the fractional linear transformations.

birapport

a special number associated with an ordered quadruple of collinear points, particularly points on a projective line, and preserved by the fractional linear transformations


Zariski topology

Zariski topology (plural Zariski topologies)

After Russian-born American mathematician Oscar Zariski (1899—1986), regarded as one of the most influential algebraic geometers of the 20th century.

The Zariski topology allows tools from topology to be used in the study of algebraic varieties, even when the underlying field is not a topological field.

Thus the Zariski open subsets are 'very big'; in particular, the Zariski topology is highly non-Hausdorff.
A further difference with the classical topology is that the Zariski topology on the product X#x5C;timesY of two affine varieties is stronger than the product of the Zariski topologies on X and Y.

1994, V. I. Danilov, “II. Algebraic Varieties and Schemes”, in I. R. Shafarevich, editor, Algebraic Geometry I: Algebraic Curves, Algebraic Manifolds and Schemes, Springer, page 184:

In particular, “singular” is a local notion, where “local” so far was mainly considered with respect to the Zariski topology. However, since the Zariski topology is so coarse, small neighbourhoods in the Zariski topology might not be local enough.

2008, Gert-Martin Greuel, Gerhard Pfister, A Singular Introduction to Commutative Algebra, 2nd edition, Springer, page 523:

If Y#x5C;subseteqKⁿ is an affine variety, then by definition the Zariski topology on Y has the subvarieties of Y as closed sets.

2011, Gregor Kemper, A Course in Commutative Algebra, Springer, page 34:

algebraic subvarieties
algebraic subvariety

(algebraic geometry) Originally, a topology applicable to algebraic varieties, such that the closed sets are the variety's algebraic subvarieties; later, a generalisation in which the topological space is the set of prime ideals of a commutative ring and is called the spectrum of the ring.


explementary angles

(geometry) A pair of angles that sum to 360 degrees.


conjugate angles

(geometry) A set of angles that sum to 360 degrees.


Cassini oval

Named after the astronomer Giovanni Domenico Cassini, who studied them in 1680.

(geometry) A plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant (related to an ellipse, for which the sum of the distances is constant).


psc

(geometry) Abbreviation of parallax second.


infinity symbol

infinity symbol (plural infinity symbols)

A lemniscate; the figure ∞ that represents infinity.


quadrantal

From Latin quadrantālis (“quarter, containing the fourth part of a measure”).

der

quadrantal space; quadrantal triangle; quadrantal versor

(geometry) Of or relating to a quadrant, or included in the fourth part of a circle.


achirality

(geometry, physical chemistry) The characteristic of being achiral; the absence of chirality.


Describes a 3D film experience that is supplemented with synchronized physical effects.


gravitational slingshot

en-noun

gravitational slingshot (plural gravitational slingshots)


gravity assist

/ˈɡɹævɪti əˈsɪst/

After going into orbit around Jupiter with a gravity assist from the volcanic moon Io, Galileo will spend 22 months studying the planet.

1989 October 10, Warren E. Leary, “Galileo's Itinerary”, in New York Times, retrieved 2011-09-04:

Cassini is supposed to swing by Earth in 1999 for a gravity assist that would sling it out toward Saturn.

1997 September 22, Dick Thompson, Michael D. Lemonick, “Nukes in Space”, in Time:

MESSENGER successfully flew by Mercury yesterday, gaining a critical gravity assist that will enable it to enter orbit about Mercury in 2011.

2009 Oct. 2, "MESSENGER Gains Critical Gravity Assist For Mercury Orbital Observations," spacedaily.com (retrieved 4 Sep. 2011)

(astrophysics) The favorable alteration of the speed and trajectory of a spacecraft as a result of its passing near to a celestial body.

painovoimalinko

the favorable alteration of the speed and trajectory of a spacecraft as a result of its passing near to a celestial body


trihexagonal

(geometry) Pertaining to a semiregular tiling of the Euclidean plane with two triangles and two hexagons alternating on each vertex.


hexoctahedron

hexoctahedron (plural hexoctahedrons or hexoctahedra)

hexoctahedrons (plural)
hexoctahedra (plural)

(geometry) A solid with forty-eight equal triangular faces.


gyrocircle

(hyperbolic geometry) A hyperbolic circle in gyrovector space.


gyroquadrilateral

(hyperbolic geometry) A quadrilateral in gyrovector space.


gyrodiagonal

(hyperbolic geometry) A diagonal in gyrovector space.


gyrotriangle

(hyperbolic geometry) A triangle in gyrovector space.


gyrogeodesic

(hyperbolic geometry) A geodesic in gyrovector space.


gyroparallelogram

The 6 faces of a parallelepiped are parallelograms while, in general, the 6 faces of a gyroparallelepiped are not gyroparallelograms.

2005, Ungar Abraham Albert, Analytic Hyperbolic Geometry:

(hyperbolic geometry) A hyperbolic quadrilateral whose two gyrodiagonals intersect at their gyromidpoints, analogous to a parallelogram in Euclidean space.


Airy function

(physics) A function, denoted by Ai(x), that is a solution to the Airy equation.


multilobe

Coordinate term: unilobe


enneagonal

enneagonal angle

(geometry) In the form of an enneagon; having nine angles.


curvilinead

(geometry, obsolete) An instrument for drawing curved lines.


orthotomy

(geometry) The property of cutting at right angles.


cucumiform

en-adj

cucumiform (comparative more cucumiform, superlative most cucumiform)

more cucumiform (comparative)
most cucumiform (superlative)

First attested in a glossary in 1826, in a fragment in 1838, and in a grammatical sentence in 1892; formed by the suffixation of cucumi-, the short i-stem of the Latin cucumis (“cucumber”), with the English -form; compare the earlier New Latin cucumeriformis (1703), cucumiformis (1791) and French cucumeriforme (1777), cucumiforme (1804).

Cucumiform (Cucumiformis). Cucumber-shaped. Whose longitudinal section is oblong, and transverse circular.

1826, William Kirby, William Spence, An Introduction to Entomology, volume IV, page 265:

She was there, tumbling the marvelous cucumiform weights down upon a chest which looked as though it would cave in under such manna.

1955, William Gaddis, The Recognitions, Harcourt, Brace, page 329:

Uncharacteristically for him, Lord Vetinari laughed out loud. He very nearly gloated at the downfall of his enemy and slammed his copy of the Ankh-Morpork Times, open at the crossword page, on to his desk. ‘Cucumiform, shaped like a cucumber or a variety of squash! l thumb my nose at you, madam!’

2011, Terry Pratchett,, Snuff: Discworld Novel 39, page 17:

Shaped like a cucumber; having the form of a cylinder tapered and rounded at the ends, and possibly curved.


retrosnub

great retrosnub icosidodecahedron

small retrosnub icosicosidodecahedron

(geometry) Derived from a simpler, regular polyhedron by the addition of extra triangular faces in the back.


excentral

excentral (comparative more excentral, superlative most excentral)

more excentral (comparative)
most excentral (superlative)


subtangent

(geometry) The part of the axis contained between the ordinate and tangent drawn to the same point in a curve.


scalenohedron

en-noun

scalenohedron (plural scalenohedrons or scalenohedra)

scalenohedrons (plural)
scalenohedra (plural)

Though the hexagonal scalenohedron is derived from the double twelve-faced pyramid, by the development of half its faces, and might be constructed from that figure, it is more readily obtained from the positive or negative rhomboid which may be supposed to be inscribed in the scalenohedron.

1859, James Tennant, Walter Mitchell, Mineralogy and Crystallography: Being a Classification of Crystals According to Their Form, page 408:

By bringing together the rhombohedron and the scalenohedron, as has been done in Fig. 119, it will be noticed that the lateral edges of the two forms have a similar position towards the axes, so that for every scalenohedron there must be a rhombohedron whose lateral edges coincide with the lateral edges of the other form. This rhombohedron is called the inscribed rhombohedron of the scalenohedron.

1866, Josiah Parsons Cooke, Elements of Chemical Physics, page 154:

1907, Benjamin K. Emerson, Joseph H. Perry, The Green Schists and Associated Granites and Porphyries of Rhode Island, US Geological Survey, Bulletin Number 311, page 24,
Other steep scalenohedrons of the principal zone are also often present, sometimes in addition to y, sometimes taking its place.

Calcite crystals show a great variety of habits — acute and obtuse rhombohedra and scalenohedra, prisms, and thin tabular forms.

1940, John W. Evans, George MacDonald Davies, Elementary Crystallography, page 111:

(geometry, mineralogy, crystallography) A polyhedron having twelve sides, each in the form of a scalene triangle, that is topologically equivalent to a hexagonal bipyramid and whose middle section can be said to inscribe a rhombohedron.


cissoid

From Ancient Greek κισσός (kissós, “ivy”) + εἶδος (eîdos, “form, image”).

The cissoid of a circle and a line is a conchoid

(geometry) Any of a family of curves defined as the locus of a point, P, on a line from a given fixed point and intersecting two given curves, C₁ and C₂, where the distance along the line from C₁ to P remains constant and equal to the distance from P to C₂.


crunodal

crunodal curve

crunodal cubic

(geometry) Possessing, or characterized by, a crunode.


amblygon

(geometry, obsolete, rare) An obtuse-angled shape, especially an obtuse triangle.


curvative

Examination of waves larger than 60 metres will depend on the accuracy with which the spatial derivatives (tilts, curvatives, etc.) of the surface can be obtained.

1977, IEEE Council on Oceanic Engineering, Oceanic Engineering Society (U.S.), Oceans:

This equation is descriptive of a Cornu spiral, a spiral whose curvative increases linearly with arclength.

1981, 25th IEEE Machine Tools Conference, 1981:

Assume first that this region is exactly linear, with no curvative (i.e., ∂2ρ/∂x2 = 0).

2010, Daniel M. Zuckerman, Statistical Physics of Biomolecules, →ISBN, page 288:

differential geometry
differential geometry

(differential geometry) The first partial derivative of a function that describes a surface.


triquadrantal

A triquadrantal triangle is one whose three sides are quadrants, and whose three angles are consequently right angles.


spheroconic

(geometry) A non-plane curve formed by the intersection of the surface of an oblique cone with the surface of a sphere centred at the cone's vertex.


surfel

en-verb

surfel (third-person singular simple present surfels, present participle surfelling, simple past and past participle surfelled)

surfels (present singular third-person)
surfelling (participle present)
surfelled (participle past)
surfelled (past)

She shall no oftener powder her hair, [or] surfel her cheeks, […] but she shall as often gaze on my picture.

1633, Iohn Ford [i.e., John Ford], Loues Sacrifice. A Tragedie […], London: […] I[ohn] B[eale] for Hugh Beeston, […], →OCLC, (please specify the page):

(obsolete, transitive) To wash with a cosmetic water, said by some to be prepared from sulphur.


surfel

(computer graphics) A unit square between voxels.


cylindroid

The intrados of a simple vault is generally formed of the portion of the surface of a cylinder, cylindroid, or sphere, never greater than that of half the solid; and the springing lines of the coussinet, which terminate the walls from which the vault rises, are generally straight lines, parallel to the axis of the cylinder or cylindroid.

1830, Sir David Brewster, The Edinburgh Encyclopaedia, page 523:

(geometry) A cylinder with elliptical cross-section.

(geometry) A certain three-dimensional surface described by a moving straight line, used to illustrate the motions of a rigid body and the forces that act upon it.


orthotomic

(geometry) The line that joins the poles of the common chord on two orthotomic circles.

(geometry) The envelope of the family of circles that have centers on a specified curve and which pass through a specified point.


tautochrone

From Ancient Greek ταὐτός (tautós, “the same”) + χρόνος (khrónos, “time”).

der

An inverted cycloid with its base horizontal is a tautochrone.

(mathematics) A curve, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall.


Steiner point

(geometry) The point on the circumcircle of a triangle that lies at the intersection of three lines through the vertices of the triangle, where those lines are parallel to the corresponding sides of the first Brocard triangle.

(geometry) The geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex of the system.

(geometry) Any of the 20 points located at the 3 by 3 intersections of the 60 Pascal lines which are produced by extending the triplets on opposite sides of a conic section in Pascal's theorem for all permutations of verices.


bimedial

(geometry, of a line) Being the sum of two lines commensurable only in power (such as the side and diagonal of a square).


amblygonal

en-adj

amblygonal (comparative more amblygonal, superlative most amblygonal)

more amblygonal (comparative)
most amblygonal (superlative)


interaxis

The principles of analytical geometry afford the means of determining how much the interaxes of the regular octahedron must be increased or diminished to equal the interaxes in these different forms.

1854, James Dwight Dana, A System of Mineralogy, Comprising the Most Recent Discoveries, page 106:

Owing to this I was only able, by breaking a number of the quartz pieces, to obtain one small crystal representing a distorted rhombic dodecahedron 8 0(110), i.e, one extended in the line of an octahedral or trigonal interaxis, giving it the appearance of an hexagonal prism terminated by a rhombohedron (see fig. 2) in striking resemblance to dioptase.

1885, George H. F. Ulrich, “Notes on some Mineral Occurrences At Dusky Sound, West coast of Middle Island, New Zealand”, in The New Zealand Journal of Science, volume 1, page 309:

When the position is as given in the stereographic projection in Fig. 265, the angle over the axial-plane polar edges is the more acute, but if the pole were placed nearer to the crystallographic than to the interaxis, as in the case of the dihexagonal pyramid {2131} of beryl shown in Fig . 266, the case would be reversed.

1911, Alfred Edwin Howard Tutton, Crystallography and Practical Crystal Measurement, page 306:

In the traditional valence bond approach above, the decrease of the bron position parameter improves the bond strength of the (sp³)_z hybrid, but it increases the misfit between direction of the boron-metal interaxis and direction (z-axis) of (sp³)_z hybrid.

1968, Forrest L. Carter, “Valence Bonding in Some Refractory Transition Metal Compounds with High Coordination”, in NBS Special Publication, page 548:

(geometry) A line from the center of a regular solid to the center of one of its edges.


osculatrix

From New Latin osculātrīx (literally “female kisser”), from Latin osculor (“to kiss”) + -trīx.

bor

(geometry) A curve whose contact with a given curve at a given point is of a higher order (or involves the equality of a greater number of successive differential coefficients of the ordinates of the curves taken at that point) than that of any other curve of the same kind.


Green's function

en-noun

Green's function (plural Green's functions)

Named after the British mathematician George Green, who first developed the concept in the 1830s.

differential equation
differential equation

(mathematics) a type of function used in the analysis of inhomogeneous differential equations.

Greense functie

function used to analyse differential equations


radius vector

radius vector (plural radii vectores or radius vectors)

radii vectores (plural)
radius vectors (plural)

(geometry) Of a point, a vector going from the origin to that point; equivalently, the transpose of the point.


tractory

Latin tractorius (“of drawing”), from trahere, tractum (“to draw”).


Fourier sine series

Fourier sine series (plural Fourier sine series)

a Fourier series consisting solely of sine functions


Fourier cosine series

Fourier cosine series (plural Fourier cosine series)

a Fourier series consisting solely of cosine functions


bicircular

a bicircular curve

(geometry) Having nodes at the two circular points at infinity.


error function

normally distributed
normal distribution

(mathematics, statistics, probability theory) A sigmoid function giving the probability that a measurement, under the influence of normally distributed errors with standard deviation, is within a certain distance from the mean value.


anticomplementary

en-adj

anticomplementary (comparative more anticomplementary, superlative most anticomplementary)

more anticomplementary (comparative)
most anticomplementary (superlative)


semiparabola

en-noun

semiparabola (plural semiparabolas or semiparabolae)

semiparabolas (plural)
semiparabolae (plural)

(geometry) One branch of a parabola, terminating at the principal vertex of the curve.


trisoctahedron

trisoctahedron (plural trisoctahedrons or trisoctahedra)

trisoctahedrons (plural)
trisoctahedra (plural)


osculant

From Latin osculans, osculantis, present participle of osculari (“to kiss”). See osculate.

(geometry) Tangent, touching at a single point.


osculant

(geometry) The point at which two tangent curves touch.


conchospiral

the constant angle according to which each traces its conchospiral.

A kind of spiral curve found in certain univalve shells.


subcardioid

(geometry) Partially or imperfectly cardioid.


septangle

(geometry) A figure which has seven angles; a heptagon.


crunode

Probably from Latin crux (“a cross”) + English node.

(geometry, archaic) node (point where one branch of a curve crosses another branch)


Didonia

In allusion to the classical story of Queen Dido, who was granted the land she could encompass with a piece of bull hide.

And hence, by Meusnier's theorem, the difference of the squares of the curvatures of curve and surface is constant; the curvature of the surface meaning here the reciprocal of the radius of the sphere which osculates in the reduction of the element of the Didonia.

1867, Peter Guthrie Tait, An Elementary Treatise on Quaternions:

(geometry) The curve which on a given surface and with a given perimeter contains the greatest area.


semiangle

(geometry) an angle of half a given size


calceolate

en-adj

calceolate (comparative more calceolate, superlative most calceolate)

more calceolate (comparative)
most calceolate (superlative)

From Latin calceolus (“little shoe, slipper”) + -ate (adjective-forming suffix), from calceus (“calceus, footwear”) + -olus (diminutive noun-forming suffix), from calx (“heel”) + -eus (adjective-forming suffix).

af

(chiefly botany) Slipper-shaped, shaped like a slipper.


nodated

en-adj

nodated (comparative more nodated, superlative most nodated)

more nodated (comparative)
most nodated (superlative)

From Latin nodatus, past participle of nodare (“to make knotty”), from nodus (“knot”). See node.

Form A to b or B to b, along the circular arc (see fig. 4), the paths of a series of points will give a gradation of symmetrical double nodated figures between the arc of a circle and the cuspidated tirangular figure. This is the first or finite series of symmetrical double nodated lines.

1830, The Mechanics' Magazine, Museum, Register, Journal, and Gazette, page 232:


tractricoid

(geometry) A surface formed by revolving a tractrix about its asymptote.


cuspate

cuspate (comparative more cuspate, superlative most cuspate)

more cuspate (comparative)
most cuspate (superlative)

From cusp + -ate (adjective-forming suffix).

Shorelines are molded into smooth arcuate bays interrupted by cuspate horns.

1999 April 2, B. T. Werner, “Complexity in Natural Landform Patterns”, in Science, volume 284, number 5411, →DOI, pages 102–104:


JWST

(NASA, space science, US) Initialism of James Webb Space Telescope.


striction

(geometry) The definition of a geometric shape as all points with some relationship to a central point, curve, etc., for example, a circle is the striction of all points at a distance of the radius from a single point.


line of striction

en-noun

line of striction (plural lines of striction)

(geometry) The line on a skew surface that cuts each generator in that point of it that is nearest to the succeeding generator.


orthotope

(geometry) The generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.


law of sines

(trigonometry) A statement that relates the lengths of the sides of a triangle to the sines of its angles.


rigol

→ Welsh: rhigol (“groove, furrow”)

From Middle English rigol, from Middle French rigole. Doublet of rail, regal, regula, and rule.

doublet

(nautical) A ridge or channel above a porthole to redirect water flow from dripping inside the vessel.


pentacron

From Ancient Greek πέντε (pénte, “five”) + ἄκρον (ákron, “summit”).

(geometry) A solid with five summits or angular points.


sexangle

From Latin sexangulus (“sexangular”), from sex (“six”) + angulus (“angle”). Compare French sexangle and English hexangular; sex- + angle.

the super parts being taken from the Quadrangle will form the Sexangle

1828, James Wilson (translator), Claudius Ptolomaeus, The Tetrabiblos:


cyclohedron

(geometry) A certain (n−1)-dimensional polytope that is useful in studying knot invariants.


covertex

(geometry) A point of intersection between an ellipse and its minor axis.


bialtitude

(geometry) A perpendicular to two opposite edges of a tetrahedron.


orthocentric

(geometry, of a tetrahedron) Having all three pairs of opposite edges perpendicular.

(geometry) Of or relating to a set of four points in the plane, one of which is the orthocenter of the triangle formed by the other three.


Ackermann function

(computing theory) One of the simplest and earliest examples of a total computable function that is not primitive recursive.


elliptic curve

So called because it is the locus of an elliptic function.

(algebraic geometry) The algebraic set of an equation which equates the square of one variable to a reduced cubic polynomial in another variable, over some field, and such that the discriminant of the reduced cubic is non-zero.


Dirac delta function

en-noun

Dirac delta function (plural Dirac delta functions)

Named after English physicist Paul Dirac.

named-after

(mathematics) A function of one real argument, whose value is zero when the argument is nonzero, and whose integral is one over any interval that includes zero.


dextrorse

en-adj

dextrorse (comparative more dextrorse, superlative most dextrorse)

more dextrorse (comparative)
most dextrorse (superlative)

From Latin dextrorsum, contracted from dextrovorsum, dextroversum (“toward the right side”), from dexter (“right”) + versus, vorsus, past participle of vertere, vortere (“to turn”).


paracentric

(geometry) A planar curve having the property that, when its plane is placed vertically, a body descending along it, by the force of gravity, will approach to, or recede from, a fixed point or centre, by equal distances in equal times.


roundrect

Blend of rounded + rectangle. In 1981, a function for quickly creating rounded rectangles was added to the Apple program LisaGraf (later renamed QuickDraw) created by Bill Atkinson at the request of Steve Jobs, with the program referring to this shape as the "RoundRect."

The iPhone is, officially, King of Design: when even Intel is mirroring your new roundrect bezels, you have won that particular game.

2007 September 21, Rob Beschizza, “Intel Touts Toys of Future At Conference”, in Wired:

(computer graphics) A rectangle with rounded corners.


apotome

Apotome
Euclid's Elements
Pythagoreanism#Music

Borrowing from Ancient Greek ἀποτομή (apotomḗ, “cutting off”). The musical sense originates from the Pythagorean tradition. The mathematical sense is attested in Euclid's Elements (Book X, proposition 73, et seq.).

bor

Yet it is not until Book X that the properties of such a line (with greater length is an apotome and lesser length a first apotome) are explained and not until Book XIII that this type of line is applied, which will be discussed in more detail later.[…]The likewise is true of apotomes (X. 97).

2012, Jade Roskam, “Book X of The Elements: Ordering Irrationals”, in Bharath Sriraman, editor, Crossroads in the History of Mathematics and Mathematics Education, Information Age Publishing, page 210:

2014, Jacques Sesiano (translator), Liber Mahameleth, Part Two: Translation, Glossary, [12th c, Anonymous (possibly John of Seville), Liber Mahameleth], Springer, page 767,
If some number and the root of the root of a number are multiplied by the corresponding apotome, the result will be an apotome.

(mathematics, geometry) The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the diagonal and side of a square.

ἀποτομή

difference between two quantities commensurable only in power


homaloidal

Ancient Greek ὁμαλός (homalós, “even, level”) + + -oid.

uder

(geometry) flat; even; applied to surfaces and spaces in which the definitions, axioms, and postulates of Euclid respecting parallel straight lines are assumed to hold true.


hypervolume

(geometry) A volume in more than three dimensions.


enneahedron

en-noun

enneahedron (plural enneahedrons or enneahedra)

enneahedrons (plural)
enneahedra (plural)

The enneahedron is a simple all-space filler discovered by myself, based on the cubic antiprism, again omitted by Wood.

1968, Design, numbers 229-234, unnumbered page:

1996, Michael O'Keeffe, Bruce G. Hyde, Crystal Structures, Number 1: Patterns & Symmetry, page 350,
This is based on a packing of 36-vertex icosahedra [5¹².6⁸] and enneahedra (4³.5⁶].

In Figure 9.10.3 we see a projection of the skeleton of an enneahedron (a solid with nine faces). All the faces of this enneahedron are quadrilaterals.

2015, Claudi Alsina, Roger B. Nelsen, A Mathematical Space Odyssey: Solid Geometry in the 21st Century, page 191:

(geometry) A polyhedron with nine faces.


parallelotope

Blend of parallelogram + polytope. Popularized by Canadian geometer H.S.M. Coxeter.

1983 [North Holland/Elsevier], Robert S. Borden, A Course in Advanced Calculus, 1998, Dover, page 83,
Suppose now that P is a k-dimensional parallelotope, 1<k<n, in Eⁿ.

1997, Daniel A. Klain, Gian-Carlo Rota, Introduction to Geometric Probability, Cambridge University Press, Accademia Nazionale dei Lincei, page 30,
We develop next a theory of invariant valuations for the lattice of finite unions of orthogonal parallelotopes, having edgers parallel to a fixed frame. […] This follows from the basic fact that the intersection of two parallelotopes is a parallelotope.

It has 2ᵏ gyrovertices, k#x2B;1 of which are the gyropoints of S, and k 2#x7B;k-1#x7D; gyroedges, in full analogy with parallelotopes.

2015, Abraham Albert Ungar, Analytic Hyperbolic Geometry in N Dimensions, Taylor & Francis (CRC Press), page 187:

(geometry) A generalization of parallelogram and parallelepiped into a figure of arbitrary dimensionality.

Harold Scott MacDonald Coxeter
parallelotope


SOHCAHTOA

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

(mnemonic, trigonometry) sine: opposite over hypotenuse, cosine: adjacent over hypotenuse, tangent: opposite over adjacent


projective plane

projective plane (plural projective planes)

Generally, a projective plane of "order" N has N²+N+1 points, and the same number of lines.

2004, David S. Dummit with Richard M. Foote, chapter 6, in Abstract Algebra, page 210

(geometry) A plane in which any pair of distinct points determine a line and any pair of distinct lines intersect at a point.


trimery

(geometry) The condition of being trimeric.


pentamery

(geometry) the condition of being pentameric


supercatenoid

(algebra, geometry) a geometric surface constituting a transition between a cube (or similar surface) and a catenoid.


supershape

(geometry) Any closed curve that is a generalization of a superellipse; it is defined by a superformula


superegg

(geometry) A surface formed by rotating a superellipse about one of its axes.


superquadric

(geometry) A three-dimensional relative of a superellipse (or similar curve).


porism

From Ancient Greek πόρισμα (pórisma, “a deduction from a previous demonstration”).

der

(geometry, number theory) A proposition affirming the possibility of finding such conditions as will render a certain determinate problem indeterminate or capable of innumerable solutions.


mixtilinear

en-adj

mixtilinear (comparative more mixtilinear, superlative most mixtilinear)

more mixtilinear (comparative)
most mixtilinear (superlative)

Latin mixtus (“mixed”) + English linear.

A mixtilinear angle is an angle contained by a straight line and a curve.

(geometry) Containing, or consisting of, lines of different kinds (straight, curved, etc.).


affine variety

en-noun

affine variety (plural affine varieties)

(algebraic geometry) A set of points (in n-dimensional space) which satisfy a set of equations which have a polynomial of n variables on one side and a zero on the other side.


explementary

Two angles whose sum is a circle (360°) are explementary angles, and either is the explement of the other.

2002, Nathaniel Bowditch, American Practical Navigator, page 317:

(geometry) Of or relating to the explement


hyperface

(geometry) A hyperplane that forms a boundary of a polytope


triangle wave

From triangle + wave, named for its triangular shape when graphed.

(mathematics, engineering) A function or waveform that alternately ramps linearly upwards and then downwards.


sawtooth wave

From sawtooth + wave, named for its resemblance to the jagged teeth of a saw when graphed.

(mathematics, engineering) A function or waveform that repeatedly ramps upwards (usually linearly) and then sharply drops.

鋸齒波

function or waveform that ramps upwards and then sharply drops


heterocentric

en-adj

heterocentric (comparative more heterocentric, superlative most heterocentric)

more heterocentric (comparative)
most heterocentric (superlative)

The purpose of this paper is to develop a complete and general theory of aperture referral in linear optics for dioptric systems that may be heterocentric and astigmatic. Apertures may be elliptical and decentred. Referral transforms the geometry of an aperture.

2011, William F. Harris, “Aperture referral in heterocentric astigmatic systems”, in Ophthalmic and Physiological Optics, volume 31, number 6, →DOI, →ISSN, page 603:

(geometry) Having different or multiple centres.


triforce

From Japanese トライフォース (toraifōsu), from English tri- + force. First used in the Legend of Zelda video game franchise for a magical artefact in that fictional universe.

A shape composed of three equilateral triangles arranged in such a manner that a fourth triangle of identical size, but pointing the opposite direction, could fit between them.

三角之力

Shape composed of three triangles in a specific alignment


linear form

In #x5C;mathbb#x7B;R#x7D;ⁿ, if vectors are represented as column vectors, then linear forms are represented as row vectors, and their action on vectors is given by the matrix product, with the row vector on the left and the column vector on the right.

1961 [Prentice-Hall], Richard A. Silverman (translator), Georgi E. Shilov, An Introduction to the Theory of Linear Spaces, 1974, Dover, page 66,
A more general linear form in the same space is the expression
f(x)=∑ₖ₊₁ⁿc_kζₖ
with arbitrary fixed coefficients c_1,c_2…,c_n.

In the theory of distributions, functions are replaced by linear forms on an auxiliary vector space, whose members are called test functions.

1998, F. G. Friedlander, M. Joshi, Introduction to the Theory of Distributions, 2nd edition, Cambridge University Press, page 2:

In order to better understand the effect of reducing a K-vector subspace V#x5C;subseteqP#x5F;d modulo a generic linear form, we generalize Proposition 5.5.18 as follows.

2005, Martin Kreuzer, Lorenzo Robbiano, Computational Commutative Algebra 2, Springer, page 264:


selective service
w:Selective Service System

A selective service class denoting that the registrant is already a reserve member of the armed forces or a student taking military training, as in ROTC or an accepted aviation cadet applicant.


heptacontagon

(geometry) A polygon with seventy edges.


tetracontagon

Blend of tetra- (“4”) + Ancient Greek τεσσαράκοντα (tessarákonta, “40”) + -gon (“-sided”), from γωνία (gōnía, “corner”).

der

τεσσαράκοντα


K-theory

From circa 1960. The K stands for German Klasse (“class”).
The theory developed out of algebraic geometry after the 1957 publication of work by German-born French mathematician Alexander Grothendieck.

algebraic K-theory

study of rings generated by vector bundles

K'''-theory as an independent discipline is a fairly new subject, only about 35 years old.

1994, Jonathan Rosenberg, Algebraic K-Theory and Its Applications, Springer, page 1:

K'''-theory was developed by Atiyah and Hirzebruch in the 1960s based on work of Grothendieck in algebraic geometry. It was introduced as a tool in C^*-algebra theory in the early 1970s through some specific applications described below. Very briefly, K'''-theory (for C^*-algebras) is a pair of functors, called K₀ and K₁, that to each C^*-algebra A associate two Abelian groups K₀(A) and K₁(A).

2000, M. Rørdam, F. Larsen, Flemming Larsen, N. Laustsen, An Introduction to K-Theory for C*-Algebras, Cambridge University Press, page ix:

topological K-theory
topological K-theory

(uncountable, algebra, algebraic geometry, algebraic topology) The study of rings R generated by the set of vector bundles over some topological space or scheme;

The study of rings R generated by the set of vector bundles over some topological space or scheme;
(dated, obsolete) that part of algebraic topology comprising what is now called topological K-theory.


Minkowski space

en-noun

Minkowski space (plural Minkowski spaces)

Named after Hermann Minkowski (1864–1909), a German mathematician and professor.

special relativity
special relativity#English

(mathematics, physics) A four-dimensional real vector space equipped with an inner product of signature (−,+,+,+) or (+,−,−,−), in which special relativity is formulated

ミンコフスキー空間

four-dimensional vector space in which special relativity is formulated


pedal curve

(geometry) For a plane curve C and a given fixed point P, the locus of points X such that PX is perpendicular to a tangent to the curve passing through X.


polytetrahedron

A uniform convex polychoron made up of 600 tetrahedral cells; a hexacosichoron.


In every vertex of the 5-cell, 8-cell and 120-cell there are 4 concurring edges; in every vertex of the 24-cell, 8 edges.

1896, American Journal of Mathematics, page 181:

1988, Unnamed translator, L. A. Sidorov, Confuguration, article in Michiel Hazewinkel (editor) Encyclopaedia of Mathematics: An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’, Volume 2: C, page 309,
For example, a 5-cell is bounded by five three-dimensional tetrahedra, an 8-cell by eight cubes, etc., the 5-cell and the 24-cell being duals of each other (the points correspond to spaces and lines to planes).

If we call a regular polytope with m facets an m-cell, then in E⁴ we have the 5-cell with tetrahedral facets (the simplex), the 8-cell with cubic facets (the hypercube), the 16-cell with tetrahedral facets (the regular cross-polytope), the 24-cell with octahedral facets, the 120-cell with dodecahedral facets, and the 600-cell with tetrahedral facets.

2007, Steven R. Lay, Convex Sets and Their Applications, page 230:

Later in the same document, President Hall listed all of the university's four-dimensional models: four Brill models—the 5-cell, 8-cell, 16-cell, and 24-cell—along with seven spun glass models by T. P. Hall that "illustrated rotations."

2008, Tony Robbin, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, page 16:

(geometry) A four-dimensional polytope, analogous to a tetrahedron, whose five bounding facets are tetrahedra.

kvinĉelo

four-dimensional polytope analogous to a tetrahedron

4-dimensional polytope analogous to a tetrahedron


hexadecachoron

hexadecachoron (plural hexadecachorons or hexadecachora)

hexadecachorons (plural)
hexadecachora (plural)

From hexadeca- (“sixteen”) + -choron (“room”), from Ancient Greek ἕξ (héx, “six”), δέκα (déka, “ten”) and χῶρος (khôros, “room”).

confix

In a world with four spatial dimensions, for example, we can construct only six regular solids, viz pentatope, tesseract, hexadecachoron, icositetrachoron, hecatonicosachoron and hexacosichoron.

2005, V H Satheesh Kumar, P K Suresh, Are We Living in a Higher Dimensional Universe?, page 3:

We have chosen the surfaces of a pentatope (5-cell) as well as a hexadecachoron (16-cell), which are simple standard triangulations of a 3-sphere, shown in figure (7), as our underlying lattices.

2009, P. Khavari, C. C. Dyer, Aspects of Causality in Parallelisable Implicit Evolution Scheme, page 7:

In four dimensions, surprisingly, there are three space-filling convex regular polychora: the tesseract (the hypercube in ℝ⁴), the hexadecachoron, and the icositetrachoron.

2011, Jin Akiyama, Ikuro Sato, The element number of the convex regular polytopes, page 271:

(mathematics) A four-dimensional object analogous to an octahedron, constructed out of sixteen tetrahedra.


hecatonicosachoron

en-noun

hecatonicosachoron (plural hecatonicosachorons or hecatonicosachora)

hecatonicosachorons (plural)
hecatonicosachora (plural)

From hecaton- (“one hundred”) + icosa- (“twenty”) + -choron (“room”), from Ancient Greek ἑκατόν (hekatón, “one hundred”) εἴκοσι (eíkosi, “twenty”) and χῶρος (khôros, “room”).

uder

The pentachoron, the hecatonicosachoron, and the hexacosichoron all have dichoral angles which are not divisors of 2π, and consequently, they are not space-filling.

The hecatonicosachoron (dodecaplex or 120-cell) and the hexacosichoron (tet- raplex or 600-cell) are also unique polychora, which have no analogs in higher dimensions.

2012, Andrzej Katunin, Fractals based on regular convex polytopes, page 57:

The pentachoron, hypercube, orthoplex, hecatonicosachoron, and hexacosichoron are analogues of the ordinary Platonic solids.

2012, Richard Elwes, How to Solve the Da Vinci Code:

(geometry) A four-dimensional object analogous to a dodecahedron, constructed out of one hundred and twenty dodecahedra, arranged 4 to a vertex.

正百二十胞体

せいひゃくにじゅうほうたい


octachoron

en-noun

octachoron (plural octachorons or octachora)

From octa- (“eight”) + -choron (“room”), from Ancient Greek ὀκτά- (oktá-, “eight”) and χῶρος (khôros, “room”).

Our 16-point 4D constellation is described by the set {(±1,±1,±1,±1)}, which is indeed the set of vertices of a tesseract (i.e., a regular octachoron) [4].

2012, Yequn Zhang, Murat Arabaci, Ivan B. Djordjevic, Rate-Adaptive Four-Dimensional Nonbinary LDPC-Coded Modulation for Long-Haul Optical Transport Networks, page 3:

The Schlegel diagram from this figure is a projection of a regular octachoron from the 4-D space to the 3-D space through a point beyond one of its facets.

2013, Milorad Cvijetic, Ivan B. Djordjevic, Advanced Optical Communication Systems and Networks, page 357:

...completing the notation for the vertices of an elementary lattice octachoron.

2013, Paul Jennings, Frank Nijhoff, On an elliptic extension of the Kadomtsev-Petviashvili equation, page 4:

(mathematics) A four-dimensional object analogous to a cube, constructed out of eight cubes.


hexacosichoron

hexacosichoron (plural hexacosichorons or hexacosichora)

hexacosichorons (plural)
hexacosichora (plural)

From hexacosi- (“six hundred”) + -choron (“room”), from Ancient Greek ἑξακόσιοι (hexakósioi, “six hundred”) and χῶρος (khôros, “room”).

uder

Fig. 5 shows a polar representation of 5880 rotations generated by subsampling the hexacosichoron.

2007, J.R. Plaisier, L. Jiang, J.P. Abrahams, Cyclops: New modular software suite for cryo-EM:

The present paper deals with a collection of 60 rays in a 4-dimensional real vector space represented by the vertices of a hexacosichoron (i.e. a 4-dimensional analogue of the icosahedron).
Comment: the reviewer uses the word, the reviewed paper uses 600-cell only.

2011. Artur E. Ruuge, review MR2594002 (2011d:81017) of Waegell, Mordecai and Aravind, P. K., "Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem.", Journal of Physics A 43 (2010), no. 10, 105304

The hexacosichoron with an edge-length of 2φ⁻¹ could be constructed from the next permutations of its 120 vertices.

(mathematics) A four-dimensional object analogous to an icosahedron, constructed out of six hundred tetrahedra, arranged 20 to a vertex.


icositetrachoron

en-noun

icositetrachoron (plural icositetrachorons or icositetrachora)

icositetrachorons (plural)
icositetrachora (plural)

From icosi- (“twenty”) + tetra- (“four”) + -choron (“room”), from Ancient Greek εἴκοσι (eíkosi, “twenty”) τέτταρες (téttares, “four”) and χῶρος (khôros, “room”).

There are six convex regular 4-polytopes; five of these are the higher dimensional analogs of the Platonic solids, and one additional figure, the icositetrachoron, has no three-dimensional equivalent.

2011, Jin Akiyama, Ikuro Sato, The element number of the convex regular polytopes, page 270:

The icositetrachoron (hyperdiamond, octaplex or 24-cell) is the most unique polychoron, because it has no direct analog in any other dimension.

2012, Andrzej Katunin, Fractals based on regular convex polytopes, page 56:

Shape of Nature comes from a unique, optimally symmetric geometric object: the sixth platonic element, the icositetrachoron (or 24-cell regular polytope), crystallized as a hyperdiamond network, mathematically and physically made of loops and connections.

2012, Raymond Aschheim, Spin foam with topologically encoded tetrad on trivalent spin networks:

(mathematics) A four-dimensional object with no regular three-dimensional analogue, constructed out of twenty-four octahedra.


According to this table the tetrahedron corresponds to the 5-cell, the cube to the 8-cell ("hypercube"), the octahedron to the 16-cell, the dodecahedron to the 120-cell and the icosahedron to the 600-cell. The 24-cell is an additional body in four-dimensional space which is dual to itself.

1988, Klaus Mainzer, Symmetries of Nature: A Handbook for Philosophy of Nature and Science, published 1996, page 159:

Similarly in dimension eight there is the quaternionic projective plane which we can think of as a 4-sphere with an 8-cell attached, and in dimension sixteen there is a Cayley projective plane which has similar properties.

1996, John Milnor, “Growing Up in the Old Fine Hall”, in Hugo Rossi, editor, Prospects in Mathematics: Invited Talks on the Occasion of the 250th Anniversary of Princeton University, page 6:

Of these nine, five are finite structures in Euclidean space and include the simplex, {3,3,3} (or 5-cell), the four-dimensional cube {4,3,3} (or 8-cell) and its dual {3,3,4} (or 16-cell), and the 120-cell {5,3,3} and its dual {3,3,5} (or 600-cell).

1997, J. François Gabriel, editor, Beyond the Cube: The Architecture of Space Frames and Polyhedra, page 412:

(geometry) A four-dimensional polytope, analogous to a cube, whose eight bounding facets are cubes; a tesseract.

4-dimensional polytope analogous to a cube


1995, J. Bokowski, On the Construction of Equifacetted 3-Spheres, Neil L. White, Invariant Methods in Discrete and Computational Geometry: Proceedings of the Curaçao Conference, page 303,
P. McMullen has pointed out to the author that he has constructed an interesting equifacetted 3-sphere in his Ph.D.Thesis by starting with the 600-cell.

The dual to the 120-cell is the 600-cell. The 600-cell is a 4-dimensional convex regular polytope with 600 facets. Its Schläfli symbol of the^([sic]) 600-cell is {3, 3, 5}. It is a 4-dimensional analogue of the icosahedron, constructed by the golden ratio on the edges of an octohedron.

2005, Lawrence B. Crowell, Quantum Fluctuations of Spacetime, volume 25, World Scientific Series in Contemporary Chemical Physics, page 329:

The other two figures are the 120-cell and 600-cell which form a dual pair as is clear from their Schläfli symbols being the reverse of each other.

2012, John Barnes, Gems of Geometry, 2nd edition, page 79:

(geometry) A four-dimensional polytope, analogous to an icosahedron, whose 600 bounding facets are tetrahedra.


The octagonal projection of the regular 24-cell {3,4,3} reveals that the 24 vertices of this 4-dimensional polytope can be distributed as 16 + 8: the 16 vertices of the 4-cube γ₄ = {4,3,3} and the 8 vertices of its dual, the 16-cell β₄ = {3,3,4}. This view of the 24-cell is less well-known than the dodecagonal projection, in which the β₄ appears as two squares of different sizes joined by 8 equilateral triangles.

1995, Harold Scott Macdonald Coxeter, “Paper Three: Two Aspects of the Regular 24-Cell in Four Dimensions”, in F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Iviċ Weiss, editors, Kaleidoscopes: Selected Writings of H.S.M. Coxeter, page 25:

2002, T. Robbin, Formian for art and mathematics, G. A. R. Parke, P. Disney (editors), Space Structures 5, Proceedings of the 5th International Conference on Space Structures, Volume 1, page 445,
One more example of a four dimensional tessellation is given using the 24-cell, see Fig 2.

The regular polytope with Schläfli symbol {3,4,3}, the so-called 24-cell, can be obtained from the 16-cell as follows. The vertices of the 24-cell are the midpoints of the 24 edges of the 16-cell.

2002, Gabor Toth, Glimpses of Algebra and Geometry, 2nd edition, page 385:

(geometry) A four-dimensional polytope whose twenty-four bounding facets are octahedra and which has no three-dimensional analogue.

hyper-diamond

4-dimensional polytope with 24 octahedral facets


The remaining 8, as before, are the vertices of the complementary 16-cell (see Figure 9). In Figure 7, these 8 points have been blackened, but not joined, because the 16-cell has longer edges; diameters of octahedral facets of the 24-cell.

1995, Harold Scott Macdonald Coxeter, “Paper Three: Two Aspects Of The Regular 24-Cell In Four Dimensions”, in F. Arthur Sherk, editor, Kaleidoscopes: Selected Writings of H.S.M. Coxeter, page 32:

This polytope has 16 tetrahedral cells, and for this reason it is called the 16-cell.[…]The 16-cell has 24 edges that are the diagonals of the 24 square faces of the hypercube. (Since we are selecting alternate vertices of the hypercube, we only get one diagonal for each square face.)

We will now consider the dual 16-cell. In some ways the 16-cell is a bit easier because it has fewer vertices and edges. But on the other hand the hypercube is perhaps easier to understand intuitively because we can readily (perhaps) see the various cubes of which it is composed.

2012, John Barnes, Gems of Geometry, 2nd edition, page 76:

(geometry) A four-dimensional polytope, analogous to an octahedron, whose sixteen bounding facets are tetrahedra.

4-dimensional polytope analogous to an octahedron


The triacontagonal projection of the 120-cell was first drawn by W. A. Wythoff, but not in reproducible form.

1964, Canadian Mathematical Bulletin, page 394:

In dimension four there are ten star polytopes which together with the 120-cell and 600-cell form the family of pentagonal polytopes (those regular 4-polytopes possessing axes of fivefold symmetry); all twelve have the same symmetry group.

1987, Jeffrey Hurst Butler, Hyperplane sections of regular star polytopes, page 28:

In 1985, M. Davis [3] gave the first explicit geometric construction of a closed hyperbolic 4-manifold by gluing together the opposite sides of a regular hyperbolic 120-cell P with dihedral angle 72°.

2006, John G. Radcliffe, “The Geometry of Hyperbolic Manifolds of Dimension a least 4”, in András Prékopa, Emil Molnár, editors, Non-Euclidean Geometries: János Bolyai Memorial Volume, page 270:

(geometry) A four-dimensional polytope, analogous to a dodecahedron, whose 120 bounding facets are dodecahedra.

正百二十胞体

せいひゃくにじゅうほうたい

Davis 120-cell (4-dimensional manifold in hyperbolic geometry constructed from a hyperbolic 120-cell)


apeirohedron

apeirohedron (plural apeirohedrons or apeirohedra)

apeirohedrons (plural)
apeirohedra (plural)

/əˌpiːɹɵˈhiːdɹən/

/əˌpeɪ̯ɹɵˈhiːdɹən/

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 polyhedron with an infinite number of faces.


logistic growth

(ecology) A pattern of growth that can be represented by a logistic function.


antimedial

(geometry) Being a triangle formed by three lines parallel to the sides of an original triangle ABC: the parallel to AB through C, the parallel to AC through B, and the parallel to BC through A.


coordinate axis

coordinate axis (plural coordinate axes)

(mathematics, geometry) One of the lines in the coordinate system that represents one of the dimensions.


isoptic

(geometry) The set of points for which two tangents of a given curve meet at a given angle.


orthoptic

(geometry) The isoptic whose given angle is a right angle.


indicator function

indicator function (plural indicator functions)

A function which is equal to 1 for all points in its domain which belong to a given set, and is equal to 0 for all points in the domain which do not belong to that given set.

indikaattorifunktio

function equal to 1 on elements of a given set


Pythagorean trigonometric identity

Pythagorean trigonometric identity (plural Pythagorean trigonometric identities)

Pythagorean trigonometric identities (plural)

(trigonometry) The equality sin (x)²+ cos (x)²=1, holding for all real and complex x, equivalent to the application of the Pythagorean theorem to the unit circle.

jedynka trygonometryczna

statement that sum of squares of sine and cosine equals one


digit

From Middle English digit, from Latin digitus (“a fingerbreadth; a number”). Doublet of digitus and toe .

bit

position in a sequence of numerals, symbol in a positional number system

(geometry, rare, obsolete) Synonym of degree: ¹⁄₃₆₀ of a circle.


hypercell

(geometry) A four-dimensional face of a polytope.


nephroid

From nephro- + -oid, i.e. "kidney-shaped".

(geometry) A plane curve resembling two intersecting ellipses


alysoid

Ancient Greek ἅλυσις (hálusis, “chain”).


anguinea

(mathematics) A cubic curve of the form xy² + ey = ax³ + bx² + cx + d


azygetic

azygetic triad; azygetic tetrad; azygetic set


cubo-cubic

Cremona transformation
Cremona transformation

(geometry, of a transformation) Being a Cremona transformation such that the homaloids of the transformation and its inverse all have degree 3.


antipoint

(geometry) One of a pair of points constructed from two foci of a curve.


biscribed

a biscribed triangle

(geometry) Both circumscribed and inscribed, i.e. having vertices that lie on a curve and sides that are tangent to the curve.


bitangential

(geometry) Meeting a curve at the tangency points of its bitangents.


binode

(geometry) A double point of a surface whose tangent cone consists of two different planes.


Aronhold set

Named after Siegfried Heinrich Aronhold.

(geometry) One of the 288 sets of seven of the 28 bitangents of a quartic curve corresponding to the seven odd theta characteristics of a normal set.


bigenus

(geometry) The second plurigenus P₂ of a surface.


biregular

(geometry, of a map) Being a regular map with regular inverse.

(geometry, of two varieties) Having a biregular map from one to the other, i.e. isomorphic as abstract varieties.


Brianchon hexagon

en-noun

Brianchon hexagon (plural Brianchon hexagons)

Named after Charles Julien Brianchon (1783–1864).

(geometry) A nonplanar hexagon whose three diagonals meet.


bielliptic

(geometry, of a curve) Being a branched double cover of an elliptic curve.


tacnode

A tacnode is defined to be a singularity equivalent to the origin in the curve y²-x²#x3D;0, that is, the union of two smooth arcs meeting with contact of order two. Similarly, an oscnode is a singularity equivalent to y²-x⁶#x3D;0, i.e., consisting of two smooth branched with contact of order three, and so on.

2012, Joe Harris, Algebraic Geometry: A First Course, page 262:

(geometry) A point of a curve where two or more osculating circles to the curve at that point are tangent, so that two branches of the curve have ordinary tangency at the double point.


Zeuthen-Segre invariant

Zeuthen-Segre invariant (plural Zeuthen-Segre invariants)

Introduced by Zeuthen (1871) and rediscovered by Corrado Segre (1896).

(geometry) A certain invariant of complex projective surfaces.


orbiform

(geometry) A plane for which the distance between the points of contact of two nonequal parallel tangents at a circle is the same everywhere.


S-shaped

en-adj

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

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

an S-shaped hook

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


hypercylindrical

hypercylindrical (comparative more hypercylindrical, superlative most hypercylindrical)

more hypercylindrical (comparative)
most hypercylindrical (superlative)


integral transform

en-noun

integral transform (plural integral transforms)

(Tf)(u)=∫ limits _(t_1)K(t,u),f(t),dt

(mathematics) Any transform of the form:


anabelian

From an- (“not”) + abelian (“commutative”); coined to imply a nuancedly stronger condition than "merely" noncommutative (see an-).

We end up this section with the following remarks, both for the sake of completeness, but mostly because of the relevance of the facts we want to mention for the anabelian phenomena.

2000, Florian Pop, “Alterations and Birational Anabelian Geometry”, in H. Hauser, J. Lipman, F. Oort, A. Quirós, editors, Resolution of Singularities, Birkhäuser, page 522:

We will formulate Grothendieck's anabelian conjectures in a more general context later, after having presented the basic facts about ́etale fundamental groups.

2012, Florian Pop, “Lectures on anabelian phenomena in geometry and arithmetic”, in John Coates, Minhyong Kim, Florian Pop, Mohamed Saïdi, Peter Schneider, editors, Non-abelian Fundamental Groups and Iwasawa Theory, Cambridge University Press, page 5:

But the interplay between those two parts remains mysterious and is at the source of some of the most standard conjectures about fundamental groups such as anabelian conjectures or the section conjecture.

2013, Anna Cadoret, “Galois Categories”, in Pierre Dèbes, Michel Emsalem, Matthieu Romagny, A. Muhammed Uludağ, editors, Arithmetic and Geometry Around Galois Theory, Springer (Birkhäuser), page 172:

algebraic fundamental group
algebraic fundamental group

(mathematics, algebraic geometry, arithmetic geometry) Of or relating to anabelian geometry, a proposed theory describing the way the algebraic fundamental group G of an algebraic variety (or some related geometric object) V determines how V can be mapped into another geometric object W, under the assumption that G is very far from being an abelian group, in a sense to be made more precise.


ellipsoid of revolution

ellipsoid of revolution (plural ellipsoids of revolution)

An ellipsoid of revolution may be either prolate or oblate.

(geometry) A spheroid; a solid of revolution generated by rotating an ellipse about one of its axes.


spherical excess

(geometry) The amount by which the sum of the three angles of a spherical triangle exceeds two right angles. The spherical excess is proportional to the area of the triangle.


strophoid

(geometry) The locus of a point that has a certain relationship with a given curve


logocyclic curve

logocyclic curve (plural logocyclic curves)


googolgon

(geometry) A polygon with a googol number of sides (virtually indistinguishable from a circle)


ultraparallel

(geometry, of lines in hyperbolic geometry) Sharing a common perpendicular.


boat conformation

boat conformation (plural boat conformations)

(organic chemistry) an unstable chemical conformation of a six-member single bonded carbon ring such as cyclohexane


minimoon

Coordinate term: quasi-satellite

This photo of Earth's newest minimoon was taken by the 8-meter Gemini North telescope on Hawaii's Maunakea.

2020 March 4, Theresa Machemer, “Earth's New Mini-Moon Is Leaving Soon”, in Smithsonian Magazine, archived from the original on 2022-08-20:

Earth has only had two minimoons on record – one in February 2020 and the other in 2006.

2020 September 22, Stacy Liberatore, “Earth is set to capture a minimoon in October that may stay until May 2021 – but some experts say the object could be man-made space junk”, in The Daily Mail, archived from the original on 2021-07-26:

These included a rare 'minimoon' named 2020 CD3, a tiny asteroid less than 3 metres in diameter that had been temporarily captured by Earth's gravity. The minimoon broke away from Earth's pull last April.

2021 March 11, Alexandra Witze, “Record number of asteroids seen whizzing past Earth in 2020”, in Nature, archived from the original on 2022-09-09:

(astronomy) A small asteroid captured by the Earth's gravity and temporarily acting as a second moon of Earth.


closed curve

(topology) A map from the circle, S¹, to a topological space.^((McLarty, p. 4))


quadrisecant

(geometry) A line that passes through four points of the curve.


homaloid

(geometry) An element of a homaloidal system, in particular the image of a hyperplane under a Cremona transformation.


flecnode

(geometry) A double point that is also a point of inflexion of one branch.


fleflecnode

(geometry) A double point that is also a point of inflexion of both branches.


hyperosculate

en-verb

hyperosculate (third-person singular simple present hyperosculates, present participle hyperosculating, simple past and past participle hyperosculated)

hyperosculates (present singular third-person)
hyperosculating (participle present)
hyperosculated (participle past)
hyperosculated (past)

A hyperosculating point is one where the tangent space meets with order higher than normal.

(geometry) To osculate at multiple points.


hypercusp

(geometry) A singularity of a curve of some multiplicity r whose tangent cone is a single line meeting the curve with order r+1.


hyperflex

(geometry) A point of a curve where the tangent line has contact of order at least 4.


equianharmonic

(geometry) A set of four points whose cross ratio (or anharmonic ratio) is a cube root of 1.


neusis

(geometry) A line segment of prescribed length, fitted between two given curves, part of a line that passes through a given point.


theta function

(mathematics) Any of a group of special functions of several complex variables, important in many areas, including the theories of abelian varieties and moduli spaces, and of quadratic forms.


hemihelix

en-noun

hemihelix (plural hemihelixes or hemihelices)

hemihelixes (plural)
hemihelices (plural)

a three-dimensional geometric shape similar to a helix, but with one or more perversions causing changes in chirality along its run


tendril perversion

tendril perversion (countable and uncountable, plural tendril perversions)

(geometry) A reversal of handedness in helical curves.


ball-and-stick model

ball-and-stick model (plural ball-and-stick models)

(physical chemistry) A molecular model of a chemical substance, displaying the three-dimensional position of the atoms (as spheres) and the bonds between them (as connecting rods).


Newton's method

(algebra, calculus) A method for finding successively better approximations to the roots (or zeroes) of a real-valued function.


visual angle

(geometry) The angle formed by two rays of light, or two straight lines drawn from the extreme points of an object to the center of the eye.


winding number

mathematical analysis
mathematical analysis

(geometry, topology, mathematical analysis) The total number of times a given curve travels counterclockwise around a specified point.

indeks

the number of times a curve travels counterclockwise around a point


sedenion

(mathematics) A 16-dimensional nonalternative extension of an octonion with one real part and 15 imaginary parts, each a real multiple of a distinct, independent square root of −1.

十六元數

nonassociative, nonalternative extension of an octonion


pulse wave

A kind of non-sinusoidal waveform that is similar to a square wave but lacks the perfectly symmetrical shape.


Bravais lattice

Bravais lattice (plural Bravais lattices)

(geometry, crystallography) An infinite array of discrete points generated by a set of discrete translation operations mathbf R=n_1 mathbf a₁+n_2 mathbf a₂+n_3 mathbf a₃, where nᵢ are any integers and aᵢ are known as the primitive vectors which lie in different directions and span the lattice.


geometrography

(geometry) The study of geometrical constructions.


lensoidal

en-adj

lensoidal (comparative more lensoidal, superlative most lensoidal)

more lensoidal (comparative)
most lensoidal (superlative)

(geometry) Of a lenticular shaped geometry.


excenter

(US, geometry) The center of an excircle.


long line

(mathematics) A topological space, constructed by stringing together an uncountable number of intervals, which is "longer" than the real line.


Dirac delta

Named after English theoretical physicist Paul Dirac (1902–1984); the notation was chosen because the symbol behaves analogously to the Kronecker delta.

named-after

(mathematics) A function-like symbol denoted as δ, with the property ∫f(t)δ(x-t)dt=f(x), informally understood as a function with an infinite value at 0 and zero elsewhere, and formally as a distribution or a measure.


Zariski-Riemann space

en-noun

Zariski-Riemann space (plural Zariski-Riemann spaces)

Named by Nagata (1962) after Oscar Zariski and Bernhard Riemann.

(algebraic geometry) A locally ringed space of a subring k of a field K, whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve.

Bernhard Riemann
Oscar Zariski
Zariski-Riemann space


Coxeter-Dynkin diagram

Coxeter-Dynkin diagram (plural Coxeter-Dynkin diagrams)

After mathematicians H. S. M. Coxeter and Eugene Dynkin.

A Coxeter-Dynkin diagram encodes the information in a Coxeter matrix, which in turn encodes the presentation of a Coxeter group.

Vertices of a Coxeter-Dynkin diagram represent generators of the corresponding Coxeter group. The generators (algebraic) in turn correspond to the reflecting hyperplanes (geometric). A pair of vertices which are not linked by an edge correspond to a pair of commuting generators. An unnumbered edge between a pair of vertices means that the braid relation between the corresponding generators has length three (e.g., aba = bab if the generators are a and b). An edge numbered ≥4 means that the braid relation between the corresponding generators has a length equal to that number. For example, if the edge is numbered 4 then the braid relation is cdcd = dcdc if the generators are c and d. If a set of edges form a cycle then the Coxeter group can be shown to be infinite. If a tree in a Coxeter-Dynkin diagram has more than one numbered edge then the Coxeter group can be shown to be infinite. There are a few more such rules, which ensure that finite Coxeter groups have Coxeter-Dynkin diagrams with relatively simple shapes.

Let 𝒬 be an indecomposable root lattice and let Γ denote the Coxeter-Dynkin diagram of the underlying root system Δ.

1995 June, R. V. Moody, J. Patera, “Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices”, in Canadian Journal of Mathematics, page 597:

There is a deep and only partially understood connection between the classification and structure of singularities and the Coxeter-Dynkin diagrams introduced by H. S .M. Coxeter for classification of reflection-generated groups and by E. B. Dynkin for classification of semisimple Lie algebras.

2000, Andrei Gabrielov, “Coxeter-Dynkin diagrams and singularities”, in Evgeniĭ Borisovich Dynkin, A. A. Yushkevich, Gary M. Seitz, A. L. Onishchik, editors, Selected Papers of E. B. Dynkin with Commentary, page 367:

For 3 ≤ n ≤ 5, we will use Eₙ to denote the Coxeter-Dynkin diagrams of types A₁ + A₂(N = 3), A₄(N = 4) and D₅(N = 5).

2012, Igor V. Dolgachev, Classical Algebraic Geometry: A Modern View, page 363:

(geometry, algebra) A graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

Coxeter-Dynkin diagram
Eugene Dynkin
Harold Scott MacDonald Coxeter


J-curve

From the shape, which resembles the letter J.

exponential growth, or a graph detailing it.


S-curve

From the shape, which resembles a vertically compressed letter S.

The current S-curve includes much gentler bends starting around Randolph Street and ending just before Monroe Street.

2016 March 15, Justin Breen, “Remember The Old Lake Shore Drive 'S' Curve? It's Been Gone For 30 Years”, in DNAinfo, archived from the original on 2023-07-29:

The so-called “S-curve” on I-25 is a notoriously dangerous stretch of freeway just south of the Big-I.

2024 April 17, Curtis Segarra, “NMDOT hosting public meeting on ‘S-curve’ portion of Albuquerque I-25”, in KRQE:


hosohedron

A tessellation of lunes on a spherical surface, such that each lune shares the same two vertices.


tricylinder

(geometry) A solid formed by three intersecting cylinders.


demihypercube

(geometry) Any of a class of n-polytopes constructed from alternation of an n-hypercube.


bicylinder

(geometry) A solid formed by two intersecting cylinders.


Steinmetz solid

Steinmetz solid (plural Steinmetz solids)

Named after Charles Proteus Steinmetz, though these solids were known long before Steinmetz studied them.

(geometry) The solid body generated by the intersection of two or three cylinders of equal radius at right angles.


Venus zone

Venus (planet) + zone, from being the zone where a Venus-like planet will acquire a Venus-like climate.

A theoretical orbital zone around a star that will result in an Earth-like planet existing in an orbit in the zone having a runaway greenhouse effect, similar to that found on Venus in our Solar System. The inner edge of the zone is where solar radiation is intense enough to strip the atmosphere of a planet away. The outer edge is where solar radiation is insufficient to power a runaway greenhouse.


golygon

(geometry) A serial isogon of 90 degrees; any polygon with all right angles, whose sides are consecutive integer lengths.


obtuse angle

(mathematics, geometry) An angle that is greater than 90 degrees and less than 180 degrees.


acute angle

(mathematics, geometry) An angle measuring less than ninety degrees.


reflex angle

(geometry) An angle greater than 180 degrees but less than 360 degrees.


parallel postulate

parallel postulate (plural parallel postulates)

From the reference to parallel lines in the definition as formulated below, following Scottish mathematician John Playfair; this wording leads to a convenient basic categorisation of Euclidean and non-Euclidean geometries. The original formulation in Euclid's Elements makes no mention of parallels.

Before we examine the particulars of the parallel postulates of Hyperbolic and Elliptical geometries, we must see their logic.

1962, Mary Irene Solon, The Parallel Postulates of Non-Euclidean Geometry: The Pentagon: A Mathematics Magazine for Students, Volumes 22-25, page 28:

The earliest known attempt to prove the parallel postulates from the other axioms was by Ptolemy in about 150 A.D.

1969, John B. Fraleigh, Mainstreams of Mathematics, Addison-Wesley, page 95:

Euclid's parallel postulate may not have seemed so important when you studied geometry in high school, since it is used only once in order to derive the basic result 1 on alternate interior angles, which is then constantly used to derive further results.

1989, Walter Prenowitz, Meyer Jordan, Basic Concepts of Geometry, Ardsley House Publishers, published 1965, page 28:

In order to understand this section, it is vital to keep in mind an important fact: The "proof" of the parallel postulate presented here is not correct. In fact, there can be no proof of the parallel postulate that relies only on the other axioms and postulates of Euclid.

1998, David A. Singer, Geometry: Plane and Fancy, Springer, page 16:

After enduring twenty centuries of criticism, Euclid's theory of parallels was fully vindicated in 1868 when Eugenio Beltrami proved the independence of Euclid's parallel postulate by constructing a Euclidean model of the hyperbolic plane.

2006, John Ratcliffe, Foundations of Hyperbolic Manifolds, Springer, page 7:

(geometry) An axiom of Euclidean geometry equivalent to the statement that, given a straight line L and a point P not on the line, there exists exactly one straight line parallel to L that passes through P; a variant of this axiom, such that the number of lines parallel to L that pass through P may be zero or more than one.

American Mathematical Society
Euclid's Elements
John M. Lee
John Playfair
parallel postulate


trans-Mars injection

trans-Mars injection (plural trans-Mars injections)

(astrodynamics) an orbital burn (rocket firing) used to change orbit from local orbit, to a Mars transfer orbit (a Solar orbit that will intercept the planet Mars).


blobular

en-adj

blobular (comparative more blobular, superlative most blobular)

more blobular (comparative)
most blobular (superlative)

The catfish fillet is hot and flaky inside, a hot blobular doughnut.

1998, Frank Chin, Bulletproof Buddhists and Other Essays, University of Hawaii Press, page 21:

However, on the unusual occasions that a sting mark is observed, it is generally blobular rather than linear, leading to a hypothesis that the bell is responsible for the sting.

2013, Lisa-Ann Gershwin et al., Advances in Marine Biology, Volume 66, Academic Press, page 64:


sphenomegacorona

From spheno- + mega- + corona. Coined by Norman W. Johnson in 1969.

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 16 triangles and 2 squares.


triangular hebesphenorotunda

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 13 triangles, 3 squares, 3 pentagons, and 1 hexagon.


augmented sphenocorona

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 16 equilateral triangles and one square.


sphenocorona

Blend of sphenoid + corona or from spheno- + corona. Coined by Norman W. Johnson in 1969.

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 12 equilateral triangles and 2 squares.


equiaffine

(geometry) Being an affine transformation that preserves area.


evectant

(geometry) A contravariant constructed from an invariant by acting on it with a differential operator called an evector.


equiaffinity

(geometry) An affine transformation that preserves area.


Eckardt point

(geometry) A point of intersection of three lines on a cubic surface.


Schläfli double six

en-noun

Schläfli double six (plural Schläfli double sixes)

(geometry) A configuration of 30 points and 12 lines. The lines can be partitioned into two subsets of six: each line is disjoint from (skew with) the lines in its own subset of six lines, and intersects all but one of the lines in the other subset of six lines. Each of the 12 lines of the configuration contains five intersection points, and each of these 30 intersection points belongs to exactly two lines, one from each subset.


evector

(geometry) A differential operator that allows a contravariant to be constructed from an invariant.


desmic

(geometry, of polyhedra) Related such that each edge of one cuts a pair of opposite edges of the other.


Desargues configuration

Desargues configuration (plural Desargues configurations)

(geometry) A configuration of ten points and ten lines, with three points per line and three lines per point, whose existence is proven by Desargues' theorem.


perspectivity

(geometry) The formation of an image in a picture plane of a scene viewed from a fixed point.


pmf

probability mass function
probability mass function#English

Initialism of probability mass function.


cumulative distribution function

cumulative distribution function (plural cumulative distribution functions)

cumulative distribution functions (plural)

A function which at each point t of the sample space has as its value the probability that a given random variable is less than (or equal) t. In symbols, F_X(t)=Pr(X<t).


pdf

probability density function
probability density function#English

Initialism of probability density function.


Jordan curve

Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem.

When μ is small and positive, the locus (1) consists of a Jordan curve near each of the Jordan curves belonging to B.

1950, Joseph Leonard Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, page 242:

If fis a closed curve that is one-one on [0,1] except for f(0) = f(I), then we say that f is a Jordan curve. A Jordan curve can be seen as a homeomorphism from the circle C onto a subset of the given space.

1992, Konrad Jacobs, Invitation to Mathematics, page 164:

The most general Jordan curves, like the triangle, have the property of dividing the plane into two regions.

2001, Constantin Carathéodory, Theory of Functions of a Complex Variable, volume 1, page 100:

(topology) A non-self-intersecting continuous loop in the plane; a simple closed curve.


orthoplex

Coined in 1991 by John Horton Conway and Neil Sloane. Blend of orthant + complex, since it has one facet for each orthant.

We made use of another way of considering the 120 cells, starting with the eight at the vertices of an orthoplex, that is, in the cells of a hypercube.

1990, Mathematica Journal, volumes 1-2, page 84:

It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.

1991, J. H. Conway, N. J. A. Sloane, “The Cell Structures of Certain Lattices”, in Peter Hilton, Friedrich Hirzebruch, Reinhold Remmert, editors, Miscellanea Mathematica, page 90:

The combinatorics of this case apply to all members of the Gosset series; in every case, their cells are simplexes and orthoplexes, the latter appearing with only half symmetry.

2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 412:

(geometry) A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions).

Cross-polytope
John Horton Conway
Neil Sloane


CPCTC

(geometry) Initialism of corresponding parts of congruent triangles are congruent, a theorem regarding congruent triangles, stating that if two or more triangles are proven congruent by any method, then all of their corresponding angles and sides are congruent as well.


CPCFC

(geometry) Initialism of corresponding parts of congruent forms are congruent.


HEO

highly elliptical orbit
highly elliptical orbit#English

(space science) Initialism of highly elliptical orbit.

GEO

geostationary orbit / geostationary Earth orbit

GSO

geosynchronous orbit / geosynchronous Earth orbit


DRO

distant retrograde orbit
distant retrograde orbit#English

(space science) Abbreviation of distant retrograde orbit.


tridiminished

(geometry) Having had three cupolae removed.


bidiminished

(geometry) Having had two cupolae removed.


triaugmented

(geometry) Having a square pyramid attached to each of three equatorial faces.


deltahedron

deltahedron (plural deltahedrons or deltahedra)

deltahedrons (plural)
deltahedra (plural)

From delta (Greek letter) + -hedron referring to the triangular shape of the letter.

There are infinitely many deltahedra, but only eight that are convex.

equilateral triangle
equilateral triangle

(geometry) A polyhedron whose faces are all equilateral triangles.


straight angle

(mathematics, geometry) An angle that is equal to 180° (pi radians or two right angles).


K-function

(mathematical analysis) A generalization of the hyperfactorial function in mathematics to real and complex numbers.


hyperfactorial

(mathematics) The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power.

The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power.
For example, the hyperfactorial of 3 is 1¹ * 2² * 3³ = 1 * 4 * 27 = 108


beta function

Considering the equation of the binomial coefficient n choose k described in terms of the factorial, replacing n with p + q and k with p, turning the RHS upside-down and replacing factorials with the Gamma function, then replacing (p + q) choose p with Β(p, q) yields Euler's equation for the Beta function.

Euler integral of the first kind
Euler integral of the first kind

(mathematical analysis) A mathematical function that is also called the Euler integral of the first kind; it is a symmetric special function.

Betafunktion

function which generalizes the notion of a factorial


convex function

convex function (plural convex functions)

(computer science) A mathematical function where the line segment between any two points on the graph of the function lies above the graph in a vector space of at least two dimensions.


concave function

concave function (plural concave functions)

(computer science) The negative of the convex function.


set function

(computer science) A mathematical function whose input is a set (usually of real numbers or a set of points in the Euclidean or some measure space), and whose output is usually a number.


density function

density function (plural density functions)

(probability theory) Clipping of probability density function.


Pi Day

pi + day, from the date March 14th in the month/day format (that is, 3/14), 3, 1 and 4 being the first three significant digits of the mathematical constant π.

Did you know that March 14 is Pi Day (no, π is not misspelled). Pi Day is celebrated on 3/14 or 3.14! To commemorate this remarkable ratio, we have a few circular activities. The first is the Pizza Survey. What are the students' favorite toppings on pizza? What do you like best?

1997, Louise Bock, Susan Guengerich, Hope Martin, “March Celebrations”, in Multicultural Math Fun: Holidays around the Year, Portland, Me.: J. Weston Walch Publisher, →ISBN, page 83:

As Quakers, we do not as a matter of religion celebrate any holidays (more accurately, all days are to be considered holidays because they have equal potential for revealing the Divine to us), but as a cultural matter we celebrate all kinds: Hindu, Christian, Jewish, ethnic, birthdays of famous composers, artists, writers, and scientists, π Day (March 14th – we bake several pies and divide them into fractions before eating), even some we just make up ourselves.

1999, David H. Albert, “Exits and Entrances”, in And the Skylark Sings with Me: Adventures in Homeschooling and Community-based Education, Gabriola Island, B.C.: New Society Publishers in cooperation with Holt Associates/Growing Without Schooling, →ISBN, page 128:

Of all known mathematical constants, however, pi continues to attract the most attention. […] The Exploratorium in San Francisco continues to celebrate Pi Day on March 14 each year, starting at 1:59 pm.

2002, Ivan Peterson, “A Passion for Pi”, in Mathematical Treks: From Surreal Numbers to Magic Circles (Spectrum Series; a Science News Book), [Washington, D.C.]: Mathematical Association of America, →ISBN, page 17:

Whereas Pi can be approximated as 3.14, and thus March 14, 2009, is an appropriate day for "National Pi Day": Now, therefore, be it / Resolved, That the [United States] House of Representatives— / (1) supports the designation of a "Pi Day" and its celebration around the world; […]

2009 March 12, H. Res. 224 Supporting the Designation of Pi Day, and for Other Purposes, [Washington, D.C.]: United States Government Publishing Office, archived from the original on 2016-12-28, page 2:

Likewise, March 14 in North America has been π Day, since in the USA the month is written before the day ('314'). In schools throughout North America, it has become a reason for mathematical projects, especially focussing on π.

2012 June 19, Jonathan M[ichael] Borwein, “The Life of Pi: From Archimedes to Eniac and Beyond”, in David H[arold] Bailey, Jonathan M. Borwein, Pi: The Next Generation: A Sourcebook on the Recent History of Pi and Its Computation, Switzerland: Springer Nature, published 2016, →DOI, →ISBN, page 446:

March 14, or 3/14, is recognized by math geeks as Pi day. That happens every year. But as UBS’s Art Cashin notes, next year’s Pi day will be a once-in-a-century Pi day. “At 9:26:53 a.m., they can write 3/14/15; 9:26:53, which you should also recall are the first ten digits of Pi in perfect order,” said Cashin.

2015 March 14, Sam Ro, “March 14, 2015 will be a once-in-a-century thrill for math geeks”, in Business Insider, archived from the original on 2016-03-04:

Pi lovers like to celebrate Pi Day every year. In the US, they write the date with the month first, then the day and year. So in 2015, 14th March was 3 14 15, the first five digits of π. So that was a really special Pi Day when, of course, they sang their special song, Pi, Pi, Mathematical Pi, to the tune of that great song everyone danced to in the 1970s, 'Bye-bye, Miss American Pie' by Don McLean.

2016, Liz Strachan, “A Little More Pi”, in Easy as Pi: Maths Made Simple, London: Robinson, →ISBN:

March 14th, an annual celebration of the mathematical constant π (pi).


octadecagon

A regular octadecagon cannot be constructed using a compass and straightedge.

(geometry, rare) A polygon with 18 sides and 18 vertices.


omega point

To begin, let AB be a given segment, and l and m be sensed parallel lines with shared omega point Ω.

2018, Maureen T. Carroll, Elyn Rykken, Geometry: The Line and the Circle, page 319:

(geometry) A well-defined point outside the hyperbolic plane.


number-theoretic function

number-theoretic function (plural number-theoretic functions)

(mathematics) a real or complex valued function of n defined on the set of natural numbers that expresses some arithmetical property of n.


stress function

stress function (plural stress functions)

(physics) A function that finds a more tractable method for the elastic equations that describe the deformation of an elastic body subject only to boundary surface forces.


mass function

(astronomy, mathematics) A relationship that describes the mass distribution.


unit function

multiplicative function
multiplicative function

(mathematics) a completely multiplicative function on the positive integers that is defined as equal to one for a special value and zero otherwise:


correlation function

correlation function (plural correlation functions)

(mathematics) function giving the statistical correlation between random variables at two different points in space or time


partition function

partition function (plural partition functions)

(mathematics) generalization of the definition of a partition function in statistical mechanics


stream function

stream function (plural stream functions)

(mathematics) A function used to plot streamlines that represent the trajectories of particles in a steady flow.


discriminant function

discriminant function (plural discriminant functions)

(mathematics) A function used to predict a categorical dependent variable by one or more continuous or binary independent variables.


zeta function

(mathematics) function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1.


distance function

distance function (plural distance functions)

(mathematics) a function used to calculate the distance between two points.


Hankel function

Hankel function (plural Hankel functions)

(mathematics) Either of two functions that are solutions to Bessel's equation.


distribution function

distribution function (plural distribution functions)

(mathematics, physics) A function of seven variables of the form f(x,y,z,t;v_x,v_y,v_z) that gives the number of particles per unit volume in single-particle phase space.


gorge circle

(gearing) The outline of the smallest cross section of a hyperboloid of revolution.


galactic habitable zone

galactic habitable zone (plural galactic habitable zones)

(astrobiology, astronomy) the zone in a disk galaxy lying within the disk which is neither too far from the core so as to be lacking in heavier elements, nor too close to the core as to experience excessive exposures to supernovae, where intelligent life may develop


decic

(mathematics) Of the tenth degree or order; e.g. for a polynomial


octogram

(geometry) A regular eight-pointed star shape.


nonagram

(geometry) A regular nine-pointed star shape.


Dirac comb

Named after English physicist Paul Dirac. The functions, when plotted visually, resemble the teeth of a comb.

named-after

tempered distribution
tempered distribution

Dirac delta function
Dirac delta function

(mathematics) A periodic tempered distribution constructed from Dirac delta functions for some given period. It allows both continuous and discrete phenomena to be represented in a single framework.


quadrilinear

(geometry) Having, or bounded by, four lines.


modular form

analytic function
analytic function#English

functional equation
functional equation#English

(mathematics) A complex analytic function satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.


Hadwiger's theorem

(geometry) A theorem asserting that every valuation on convex bodies in Rⁿ that is continuous and invariant under rigid motions of Rⁿ is a linear combination of the quermassintegrals (or, equivalently, of the intrinsic volumes).


hypertorus

(geometry, topology) An N-dimensional equivalent of a torus, where N is a positive integer greater than 3.


diffeology

In this case, A and f(A) are both D-open and f#x3A;A#x5C;rightarrowf(A) is a diffeomorphism where A and f(A) are equipped with their subset diffeology.

2007, Jan Kubarski, Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann; on the Occasion of the Hundredth Anniversary of His Birthday, page 358:

And, for #x5C;mathcal#x7B;G#x7D;#x2A;#x2F;#x5C;Gamma and #x5C;mathcal#x7B;G#x7D;'#x2A;#x2F;#x5C;Gamma' equipped with the quotient diffeologies, h#x2A;#x5F;#x5C;Gamma is naturally smooth.

2010, Patrick Iglesias-Zemmour, The Moment Maps in Diffeology, American Mathematical Society, page 32:

differential geometry
differential geometry

(differential geometry) The set of smooth parametrizations of a given set X; the set of smooth maps S→X, where S is any open set ⊆ℝⁿ; the theory of such constructs.


JOI

orbital insertion
orbital insertion#English

(astronautics) Initialism of Jupiter orbital insertion.


Iitaka dimension

en-noun

Iitaka dimension (plural Iitaka dimensions)

(algebraic geometry) The Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by L.


polydisc

(mathematics) A Cartesian product of discs.


isocrystal

(algebraic geometry) A kind of p-adic analogue of a sheaf.


Fano plane

Named after Gino Fano (1871–1952), an Italian mathematician.

(geometry) The finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point.


Dickman function

(number theory) A function, denoted by ρ, used to estimate the proportion of smooth numbers up to a given bound.


Catalan surface

Catalan surface (plural Catalan surfaces)

Named after the Belgian mathematician Eugène Charles Catalan.

(geometry) A ruled surface whose rulings are all parallel to a fixed plane.


hyperpath

(mathematics) Any path that is longer than the shortest path possible


needle-shaped

en-adj

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

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


Brocard point

Named after Henri Brocard (1845–1922), French mathematician.

(geometry) The point inside a triangle at the intersection of the lines through each vertex such that the angle between the line and the side of the triangle when moving clockwise is the same for each vertex.


Brocard triangle

en-noun

Brocard triangle (plural Brocard triangles)

(geometry) The triangle formed by joining the points of intersection of the lines from each vertex of a triangle to its Brocard points.


parallelohedron

parallelohedron (plural parallelohedrons or parallelohedra)

parallelohedrons (plural)
parallelohedra (plural)

(geometry) A polyhedron that can tessellate three-dimensional spaces with face-to-face contacts via translations.