facultative

facultative (comparative more facultative, superlative most facultative)

more facultative (comparative)
most facultative (superlative)

From French facultatif. By surface analysis, faculty + -ative.

For then it is seen, as before, that it is the points outside the two sheets which are facultative, and not the points between the surface and the touching plane.

1866, George Salmon, Lessons Introductory to the Modern Higher Algebra, Dublin: Hodges, Smith, and Co., page 197:

(geometry, of a point) At which a given function is positive.


quadrature of the circle

(geometry) The problem, proposed by ancient Greek geometers, of using a finite ruler-and-compass construction to make a square with the same area as a given circle.


point cloud

A series of points in three-dimensional space that collectively describe the geometry of a physical object.


gon

From Ancient Greek γωνία (gōnía, “angle”).

(geometry, trigonometry) One hundredth of a right angle; a gradian.


level set

mathematical analysis
mathematical analysis

(mathematical analysis) The set of values x for which a real-valued function f(x) is equal to a given constant.


logistic curve

Calque of French courbe logistique, coined by Belgian mathematician Pierre François Verhulst in 1845. Verhulst did not explain his choice of the name logistique; see discussion at logistic.

coined

(mathematics, biology) An S-shaped curve that models the growth of many ecosystems.


logistic function

en-noun

logistic function (plural logistic functions)

Calque of French fonction logistique; see discussion at logistic.

exponential function
exponential function

(mathematics) A function, the result of the division of two exponential functions, that gives rise to the logistic curve.


agonic

International Geomagnetic Reference Field

From Ancient Greek ᾰ̓- (a-, the alpha privativum, a prefix forming words having a sense opposite to the word or stem to which it is attached) + γωνία (gōnía, “angle”) + -ic.


involute

(geometry) A curve that cuts all tangents of another curve at right angles; traced by a point on a string that unwinds from a curved object.

involuutta

a curve that cuts all tangents of another curve at right angles; traced by a point on a string that unwinds from a curved object


solidity

en-noun

solidity (countable and uncountable, plural solidities)

From solid + -ity, from Middle French solidité, from Latin soliditās.

(geometry) The solid contents of a body; volume; amount of enclosed space.


regular polygon

regular polygon (plural regular polygons)

(geometry) A polygon which is both equiangular and equilateral (i.e. having all sides the same length and all interior angles the same).


equiangular

(geometry) Of a polygon, having all interior angles equal. This is not necessarily a regular polygon, since that would also be equilateral; a rectangle is equiangular but not equilateral, unless it is a square.

роўнаку́тны

geometry: having all internal angles equal


equilateral

ewesydig

referring to a polygon all of whose sides are of equal length

(geometry, of a polygon) Having all the sides equal.

(geometry, of a polyhedron) Having all the faces equal.


Langevin function

Langevin function (plural Langevin functions)

(physics) a mathematical function that describes the behaviour of paramagnetic materials and the dielectric properties of insulators


Lagrangian function

Lagrangian function (plural Lagrangian functions)

From Joseph Louis Lagrange, French mathematician and astronomer.

Lagrange's equations
Lagrange's equations

(mathematics) A function of the generalized coordinates and velocities of a dynamic system from which Lagrange's equations may be derived.


interior angle

(geometry) The inner angle between two sides of a polygon.


lemniscate of Bernoulli

lemniscate of Bernoulli (plural lemniscates of Bernoulli)

From the name of Swiss mathematician Jakob Bernoulli.

(mathematics) Any closed curve described by a Cartesian equation of the form (x²+y²)²=2a²(x²-y²).


Lagrangian

/læˈɡɹɑ̃ʒi.ən/

Lagrangian point
Lagrangian point#English

(astrophysics) Ellipsis of Lagrangian point; a Lagrange point.


Cartesian plane

From the name of the French mathematician and philosopher René Descartes who is credited with developing the mathematics.

(geometry) A coordinate plane, with an applied Cartesian coordinate system.

karteesinen taso

coordinate plane with Cartesian coordinates


circularly

en-adv

circularly (comparative more circularly, superlative most circularly)

more circularly (comparative)
most circularly (superlative)

From Middle English circulerlich, equivalent to circular + -ly.


Lissajous figure

en-noun

Lissajous figure (plural Lissajous figures)

Named after French mathematician Jules Antoine Lissajous (1822–1880), who invented an apparatus that projected such figures onto a wall.

named-after

The Scope proved to be a haunt for electronics assembly people from Yoyodyne. The green neon sign outside ingeniously depicted the face of an oscilloscope tube, over which flowed an ever-changing dance of Lissajous figures.

1966 March, Thomas Pynchon, chapter 3, in The Crying of Lot 49, Philadelphia, Pa.; New York, N.Y.: J[oshua] B[allinger] Lippincott Company, →OCLC, page 30:

(mathematics) A plane curve traced by a point which executes two perpendicular independent harmonic motions, the frequencies of which are in a simple ratio.


Johnson solid

From Johnson (“a surname”) + solid, after American mathematician Norman Johnson, who listed them in 1966.

1986 April, Andrew Hume, Folding Regular Polyhedra, AUUGN: Australian Unix Users Group Newsletter, Volume 6, Number 5, page 40,
The Johnson solids, combined with the Archimedean polyhedra and five of the regular polyhedra, constitute all the possible convex polyhedra with regular faces..])

There are other possible models that we have not written about and for which we do not include pictures. namely the Johnson solids and their truncations [2]. (The egg^([truncated hexadecahedron]) is an approximation of a truncation of a Johnson solid.)

2003, Rona Gurkewitz, Bennett Arnstein, Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, page 2:

Students will be very unlikely to discover very many of the Johnson solids on their own. Someone may come up with the triangular and pentagonal dipyramids, but the others are just not very intuitive. Once students are convinced that there are no other possibilities than the ones they've come up with, then it is time to unveil some of the more complicated Johnson solids.

2012, Thomas Hull, Project Origami: Activities for Exploring Mathematics, 2nd edition, page 159:

(geometry) Any of a class of convex polyhedra that have regular faces but are not uniform (that is, not Platonic solids, Archimedean solids, prisms, or antiprisms).

solido di Johnson

convex non-uniform polyhedron that has regular faces


Archimedean solid

en-noun

Archimedean solid (plural Archimedean solids)

Named after ancient Greek mathematician and engineer Archimedes of Syracuse (c. 287 – c. 212 BCE).

(geometry) Any of a class of convex semiregular polyhedra, composed of two or more types of regular polygon meeting in identical vertices.

arĥimeda solido

any of a class of semi-regular convex polyhedra composed of two or more types of regular polygon meeting in identical vertices


small circle

a circle formed by a plane that cuts a sphere not through its centre


DMS

DMS (countable and uncountable, plural DMSs)

(uncountable, geometry) Initialism of degree-minute-second (a method of writing angles).


rhombicosidodecahedron

rhombicosidodecahedron (plural rhombicosidodecahedra or rhombicosidodecahedrons)

rhombicosidodecahedra (plural)
rhombicosidodecahedrons (plural)

/ˌɹɒmbaɪˌkəʊsidəʊˌdɛkəˈhiːdɹən/

/ˌɹɒmbaɪˌkəʊsidəʊˌdɛkəˈhiːdɹə/

PIE word
 *déḱm̥
Etymology tree
New Latin rhombicosidodecaēdronlbor.
English rhombicosidodecahedron
Learned borrowing from New Latin rhombicosidodecaēdron (coined by the German astronomer and mathematician Johannes Kepler (1571–1630) in his work Harmonices Mundi Libri V (The Harmony of the World in Five Books, 1619)), a blend of Latin rhomb(us) + īcos(aedron) + -i- + dodecaēdron. The English word is analysable as a blend of rhomb(ic) + icosidodecahedron, referring to the fact that the 30 square faces lie in the same planes as the 30 rhombic faces of the rhombic triacontahedron, which is dual to the icosidodecahedron.

coinage

Archimedean solid, one of the thirteen solids described by Archimedes, which, without being regular, have all their solid angles alike, all their faces regular, and not less than four faces of any one kind; […] They are […] the rhombicosidodecahedron, the truncated icosidodecahedron, and the snub-dodecahedron.

1889, “Archimedean, a.”, in William Dwight Whitney, editor, The Century Dictionary: An Encyclopedic Lexicon of the English Language […], volume I, New York, N.Y.: The Century Co., →OCLC, page 297, column 1:

The purpose of this article is to offer a method of approach for investigating the stellation pattern of the deltoidal hexecontahedron, the dual of the rhombicosidodecahedron.

1989, P. W. Messer, M[agnus] J[oseph] Wenninger, “Symmetry and Polyhedral Stellation—II”, in Computers & Mathematics with Applications, volume 17, numbers 1–3, Oxford, Oxfordshire: Pergamon Press, →DOI, →ISSN, →OCLC, page 195; reprinted in István Hargittai, editor, Symmetry 2: Unifying Human Understanding (International Series in Modern Applied Mathematics and Computer Science; 18), Oxford, Oxfordshire: Pergamon Press, 1989, →ISBN, part 1, page 195:

There are two distinct rhombicosidodecahedra, one bearing the unmodified name and the other called the great rhombicosidodecahedron. Like the rhombus, the icosahedron and the dodecahedron, all of the great rhombicosidodecahedron’s 62 faces are either [square] rhombi (30), equilateral triangles (20) or regular pentagons (12).

1994, Steven Schwartzman, “rhombicosidodecahedron”, in The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: 2:Mathematical Association of America, →DOI, →ISBN, page 189, column 1:

Next, the totality of 31 axes is illustrated in a rhombicosidodecahedron, an Archimedean solid composed of 30 squares, 20 triangles, and 12 pentagons[…], with a view to the inside of the model showing the center of the group, the point of invariancy O […] Finally, the other dihedral subgroups are also illustrated on a rhombicosidodecahedron: D#x5F;3 of order 6 and index 10 […] and D#x5F;5 of order 10 and index 6[…].

1996, Hugo F[rançois] Verheyen, “Groups of Isometries”, in Symmetry Orbits (Design Science Collection), Boston, Mass.; Basel, Basel-Stadt: Birkhäuser, →DOI, →ISBN, part I (Realization of Symmetry Groups), page 37:

[…] I noticed that the little balls (rhombicosidodecahedrons) had openings shaped in the form of triangles, rectangles, and pentagons.

2014, Thomasenia Lott Adams, Joanne LaFramenta, “Conclusion”, in Math Know-how: Answers to Your Most Persistent Teaching Issues, Grades 3–5, Thousand Oaks, Calif.; London: Corwin, SAGE Publications, →ISBN, page 172:

(geometry) An Archimedean solid with 62 regular faces (20 triangles, 30 squares, and 12 pentagons), 60 vertices and 120 edges.

斜方二十・十二面体

しゃほうにじゅうじゅうにめんたい

菱形二十・十二面体

りょうけいにじゅうじゅうにめんたい

小菱形二十・十二面体

しょうりょうけいにじゅうじゅうにめんたい

切頂菱形三十面体

せっちょうりょうけいさんじゅうめんたい


irreducible

en-adj

irreducible (comparative more irreducible, superlative most irreducible)

more irreducible (comparative)
most irreducible (superlative)

/ˌɪɹɪˈdjuːsɪbəl/

(algebraic geometry, of an algebraic variety) Inexpressible as the union of two proper algebraic subvarieties.


reniform

/ˈɹɛnəˌfɔɹm/

Learned borrowing from Latin rēnis (the genitive singular of rēn (“kidney”); see further at that entry) + English -form (suffix meaning ‘having the form or shape of’), modelled after New Latin rēnifōrmis (“of seeds: kidney-shaped”).

reniforme

synonym of kidney-shaped — see also kidney-shaped

intussusception with a reniform appearance

multiple reniform circumscribed fat-containing masses

The Bean […] is oval, and not at all reniform'd like the Kidney-Beans.

[1745, James Parsons, “Tab. V. Fig. 12. a. Cow-itch, Coughage, or Stinging-Beans.”, in The Microscopical Theatre of Seeds: […], volume I, London: […] F. Needham, […]; and sold by M. Cooper, […], →OCLC, page 201:

[T]he antheræ are reniform: the germen is oval, and obtuſely trigonal; […]

1751, John Hill, “Class the Sixth. Order the First. Division the First. Hexandria Monogynia, Having Corollæ Divided into Three Segments, and Cups to Them. [TRADESCANTIA.]”, in A General Natural History: Or, New and Accurate Descriptions of the Animals, Vegetables, and Minerals of the Different Parts of the World; […], volume II (A History of Plants), London: […] Thomas Osborne, […], →OCLC, part III (Plants Called the More Perfect Ones), page 364:

In one of the ſegments of the lovver portion of the kidney, there vvas a large reniform Papillæ, in the outer circumference of vvhich a ſmall part of the papillary fleſh vvas vvanting. […] In the oppoſite ſegment, there vvas a fourth reniform Papilla, reſembling the firſt; […]

1756, Albert Haller [i.e., Albrecht von Haller], “Observation LIX. A Coalition of the Kidnies.”, in Pathological Observations, Chiefly from Dissections of Morbid Bodies, London: […] D. Wilson and T. Durnam, […], →OCLC, page 178:

The oxyde of cobalt, […] is found either ſuperficial, interſperſed, or in lumps; ſometimes botryoidal or reniform or bearing particular impreſſions.

1799, William Babington, “[Class III. Metals. Order II. Fragile. Genus IV. Cobalt.] Species II. Native Oxyde of Cobalt.”, in A New System of Mineralogy, in the Form of a Catalogue, after the Manner of Baron Born’s Systematic Catalogue of the Collection of Fossils of Mlle. Élénore de Raab, London: […] T[homas] Bensley, […]; and sold by W. Phillips, […]; G. G. and J. Robinsons, […]; and T[homas] Cox, […], →OCLC, page 232:

Nothing could be more simple than the furniture. The chairs were either posts mounted on four legs spread out for a base, or three-legged stools with reniform seats.

1861, Richard F[rancis] Burton, “To Ruby Valley”, in The City of the Saints and across the Rocky Mountains to California, London: Longman, Green, Longman, and Roberts, →OCLC, page 570:

(chiefly biology, mineralogy) Synonym of kidney-shaped (“having an approximately circular or elongated ovoid shape with an inward curve or indentation on one side”)

kidney-shaped

(botany) Of a leaf: kidney-shaped, with the petiole attached at the notch.

munuaismainen

of a leaf: kidney-shaped, with the petiole attached at the notch


complementary function

en-noun

complementary function (plural complementary functions)

differential equation
differential equation

(mathematics) The general solution of a homogenous linear differential equation.


particular integral

particular integral (plural particular integrals)

(mathematics) Any solution to a differential equation.


quintic

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

From Latin quintus (“fifth”) + -ic (“of pertaining to”).

(mathematics) Of or relating to the fifth degree, such as a quintic polynomial which has the form ax⁵+bx⁴+cx³+dx²+ex+f=0 (containing a term with the independent variable raised to the fifth power).


polyacron

From Ancient Greek πολῠ- (polu-) and ᾰ̓́κρον (ákron).


arctan

tan (arctan 2/2)=1/ϕ


arccos

arccos (1/2ϕ)=2π/5

[…]with the appropriate constraint angles measured in terms of the arccoses and arctans.

1973, The Soviet Economy in Regional Perspective, Praeger Publishers, page 3:


Arrhenius equation

Arrhenius equation (plural Arrhenius equations)

(physical chemistry) An equation which approximates the dependence of the rate of any chemical reaction on the temperature.


Cartesian product

Cartesian product (plural Cartesian products)

From Cartesian + product, after French philosopher, mathematician, and scientist René Descartes (1596–1650), whose formulation of analytic geometry gave rise to the concept.

On the Cartesian product of two manifolds a differentiable structure can be constructed in the following way.

1987, M. Göckeler, T. Schücker, Differential Geometry, Gauge Theories, and Gravity, published 1989, page 98:

(geometry, of an m-dimensional space X and an n-dimensional space Y) An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from X and Y, but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. X and Y are vector spaces, the elements of X×Y are thought of as (m+n)-tuples instead of ordered pairs) and written X×Y.


spindle-shaped

en-adj

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

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

a spindle-shaped fibroblast


developable surface

en-noun

developable surface (plural developable surfaces)

(geometry) A surface (in more than two dimensions, a plane is trivially developable) that can be flattened into a plane without distortion.


bisector

South Street is the bisector of Broken Dreams Boulevard.

(geometry) A line or curve that bisects or divides a line segment, angle, or other figure into two equal parts.


buckyball

Blend of buckminsterfullerene + ball, used as an abbreviation for buckminsterfullerene

(chemistry, informal) A buckminsterfullerene molecule (C₆₀).

(by extension) The most common types of spheroidal fullerenes, C₆₀ and C₇₀ usually; with C₇₂ and C₇₆ sometimes also included.

(by extension) Any spheroidal fullerene, from C₂₀ on upwards.


straight line

(geometry) A line with no curvature; a line with constant direction. The path of shortest length between two points.


funicular

en-adj

funicular (comparative more funicular, superlative most funicular)

more funicular (comparative)
most funicular (superlative)

From Latin fūniculus (“cord”), diminutive from fūnis (“cord”) + -culus.


arccosh

/ˈɑː(ɹ)kˌkɒʃ/

(mathematics) Alternative form of arcosh (“the inverse hyperbolic cosine function”)


arcsinh

/ˈɑː(ɹ)kˌʃaɪn/

(trigonometry) Alternative form of arsinh (“the inverse hyperbolic sine function”)


arctanh

/ˈɑː(ɹ)kˌtænʃ/

(trigonometry) Alternative form of artanh (“the inverse hyberbolic tangent function”)


dendrimer

(graph theory) A graph formed of branches from a central core.


noneuclidean geometry

en-noun

noneuclidean geometry (plural noneuclidean geometries)

non-Euclidean geometry
non-Euclidean geometry

(geometry) A US spelling of non-Euclidean geometry.


spherical lune

(geometry) A portion of the surface of a sphere cut off by two vertical planes through the centre of the sphere.


spherical wedge

spherical wedge (plural spherical wedges)

(geometry) A volume of a sphere lying between two vertical planes through the centre of the sphere.


spherical cap

(geometry) A portion of the surface of a sphere cut off by a plane.


spherical geometry

spherical geometry (usually uncountable, plural spherical geometries)

The basic concepts of Euclidean geometry of the plane are the point and the (straight) line; in spherical geometry, the corresponding concepts are the point and the great circle.

Due to the way the geometry of a sphere's surface differs from that of the plane, spherical geometry has some features of a non-Euclidean geometry and is sometimes described as being one. Historically, however, spherical geometry was not considered a fully fledged (non-Euclidean) geometry capable of resolving the question of whether the parallel postulate is a logical consequence of the rest of Euclid's axioms of plane geometry.

1972, Morris Kline, Mathematical Thought from Ancient to Modern Times: Volume 1, Oxford University Press, 1990, paperback, page 119,
Spherical trigonometry presupposes spherical geometry, for example the properties of great circles and spherical triangles, much of which was already known; it had been investigated as soon as astronomy became mathematical, during the time of the later Pythagoreans.

We start with spherical geometries. The two geometries on spheres of radiuses R₁ and R₂ are obviously identical if R₁ = R₂; moreover, the converse also holds.

1994, Viacheslav V. Nikulin, Igor R. Shafarevich, translated by Miles Reid, Geometries and Groups, Springer, page 194:

To collect the boundary of the point set in the tree we pass a bounding box (for Euclidean geometries) or the universal set (for spherical geometries) to the root of the tree.

2008, Sherif Ghali, Introduction to Geometric Computing, Springer, page 272:

2020, Marshall A. Whittlesey, Spherical Geometry and Its Applications, Taylor & Francis (CRC Press), unnumbered page,
It has been at least fifty years since spherical geometry and spherical trigonometry have been a regular part of the high school or undergraduate curriculum.

(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;

The geometry of the 2-dimensional surface of a sphere;
(countable) a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres.


transdimensional

en-adj

transdimensional (comparative more transdimensional, superlative most transdimensional)

more transdimensional (comparative)
most transdimensional (superlative)

(statistics) Applicable to multiple dimensionalities; Having components or subspaces of different dimension


hexagonal prism

en-noun

hexagonal prism (plural hexagonal prisms)

(geometry) any prism, an octahedron, constructed on a hexagonal base

seslatera prismo

prism (an octahedron) made on a hexagonal base


algebraic geometry

algebraic geometry (countable and uncountable, plural algebraic geometries)

1977, Robin Hartshorne, Algebraic Geometry, Springer, Softcover Reprint, 1977, page xiii,
The author of an introductory book on algebraic geometry has the difficult task of providing geometrical insight and examples, while at the same time developing the modern technical language of the subject. For in algebraic geometry, a great gap appears to separate the intuitive ideas which form the point of departure from the technical methods used in modern research.
The first question is that of language. Algebraic geometry has developed in waves, each with its own language and point of view.

2003, Ian F. Blake, Curves with Many Points and Their Applications, Marc Fossorier, Hideki Imai, Shu Lin, Alain Poli (editors), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, Proceedings, Springer, LNCS 1719, page 55,
The use of curves in algebraic geometries, in applications such as coding and cryptography, now has an extensive literature and has been responsible for dramatic developments in both subjects.

For example, every high school mathematics student has studied a bit of algebraic geometry, in learning the basic properties of conic sections, such as parabolas and hyperbolas.

2013, Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves, An Invitation to Algebraic Geometry, Springer, page 1:

(mathematics) A branch of mathematics that studies algebraic varieties (solution sets of polynomial equations) and their generalisations, using techniques from both algebra (chiefly commutative algebra) and geometry.

հանրահաշվական երկրաչափություն

branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry


orthocenter

(geometry) The intersection of the three lines that can be drawn flowing from the three corners of a triangle to a point along the opposite side where each line intersects that side at a 90 degree angle; in an acute triangle, it is inside the triangle; in an obtuse triangle, it is outside the triangle.


Lemoine hexagon

Lemoine hexagon (plural Lemoine hexagons)

Named after the French mathematician Émile Lemoine.

(geometry) A cyclic hexagon with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.

Mathworld article on the Lemoine hexagon


fixed point

(computing) A fractional-number representation with a fixed number of digits after the decimal point. Compare floating point and integer.

(mathematics) A value which is unchanged by a function or other mapping. Formally: a value x for which f(x)=x.


fixed point

(computing) Pertaining to fixed point representations or operations.


heptahedron

heptahedron (plural heptahedrons or heptahedra)

heptahedrons (plural)
heptahedra (plural)

(geometry) A polyhedron with seven faces.


zero-dimensional

(geometry) Having zero dimensions; having no extent in any direction.


hectogon

(geometry) A polygon having a hundred sides.

(computing) An individual processor in some parallel processing systems.


myriagon

For it differs in no way from the representation I should form if I were thinking of a myriagon, or any figure with very many sides.

1998, Réné Descartes, translated by Desmond M. Clarke, Meditations, Penguin, published 2003, page 58:


chiliagon

From Ancient Greek χιλιάγωνος (khiliágōnos), from χίλιοι (khílioi, “thousand”) + γωνία (gōnía, “angle”). Equivalent to chilia- + -gon.

If Kant's claim is just that it is impossible to have a sensory experience of the absence of space, then by contrast it is not impossible to have a sensory experience of a chiliagon.

1995, Lorne Falkenstein, Kant's Intuitionism, Toronto, published 2004, page 198:

(geometry, rare) A polygon with a thousand vertices and a thousand edges.


icosagon

From Ancient Greek εἰκοσάγωνος (eikoságōnos, “having twenty sides”), from εἴκοσι (eíkosi, “twenty”) + γωνία (gōnía, “angle”). Equivalent to icosa- + -gon.

uder

1993 The upper half of a regular icosagon frame is folded. - author? - Space Structures 4

(geometry) A polygon with twenty sides and twenty angles.


heptadecagon

The regular 17-sided polygon (heptadecagon) can be constructed with the help of a compass and a ruler.

2001, Kunihiko Kasahara, Amazing Origami, New York, N.Y.: Sterling Publishing, →ISBN:

(geometry) A polygon with seventeen sides and seventeen angles.


pentadecagon

/ˌpɛntəˈdɛkəɡən/

In ⊙ O, draw chord AB equal to r. Draw chord AC equal to Vt (which is the side of a regular decagon). CB is now one side of the regular pentadecagon.

2003, Steven Atiyah, Essentials of Geometry, Trafford, published 2003, page 357:

(geometry) A polygon with fifteen sides.


biconical

consisting of two cones placed together apex to apex


geosynchronous

Refers to the orbit of a satellite whose rate of revolution is matched to the rotation period of the Earth. A special case is the geostationary orbit which is circular and equatorial, so that the satellite appears to be fixed over a particular point on Earth's sky.

geosynkroninen

orbit whose rate of revolution is matched with Earth


plane curve

(mathematics) The locus of points in the Euclidean plane that satisfies some geometric or algebraic definition; a curve in a plane (as opposed to higher-dimensional space).


Euclidean plane

en-noun

Euclidean plane (plural Euclidean planes)


cline

Let C₁ and C₂ be two nonintersecting clines. Prove that there is a unique pair of points that are simultaneously symmetric to both C₁ and C₂.

2001, Michael Henle, Modern Geometries: Non-Euclidean, Projective, and Discrete, page 77:

To visualize Möbius transformations, it is helpful to focus on fixed points and, in the case of two fixed points, on two families of clines with respect to these points.

2009, Michael P. Hitchman, Geometry with an Introduction to Cosmic Topology, page 64:

2011, Dominique Michelucci, What is a Line?, Pascal Schreck, Julien Narboux, Jürgen Richter-Gebert (editors), Automated Deduction in Geometry, 8th International Workshop, ADG 2010, Revised Selected Papers, LNAI 6877, page 139,
Let Ω be a fixed, arbitrary, point. Then circles (in the classical sense) through Ω can be considered as lines. For convenience, such circles are called clines in this section. Two distinct clines cut in one point (ignoring Ω and the two cyclic points); it can happen that Ω is a double intersection point; in this case, one may say that the two clines are parallel, and that they meet at a point at infinity, which is Ω.

(geometry, inversive geometry) A generalized circle.


oriented

en-adj

oriented (comparative more oriented, superlative most oriented)

more oriented (comparative)
most oriented (superlative)

(geometry, topology) In any of various technical senses, admitting or being equipped with a notion of handedness (i.e. of distinguishing clockwise and anticlockwise). See Orientability on Wikipedia.Wikipedia


pointlessness

en-noun

pointlessness (countable and uncountable, plural pointlessnesses)

(topology, geometry, uncountable) The quality of not mentioning points.


hypertoroid

An N-dimensional equivalent to a toroidal, given N being a positive integer greater than 3.

fourth dimension
fourth dimension#English

(by restriction) A toroid scaled up into the fourth dimension.


multidimensional

(mathematics) Having more than two dimensions.

Having multiple dimensions (aspects).
Having more than two dimensions.


havercosine

trigonometric function
trigonometric function

(trigonometry) the trigonometric function (1 + cos(x)) / 2, equal to half the vercosine


haversed sine

(trigonometry, rare) The trigonometric function defined as half the versed sine. Abbreviation: haversin


versine

The simplest method of calculating the radius of a curve in situ is to measure the versine; in railway practice this is done by extending a tape 66 ft. (1 ch.) long in a straight line or chord between two points on the periphery of a curve, and then measuring the maximum distance of the rail from the chord at the centre of the 66 ft. The radius in chains is found by dividing the versine in inches into 99. Thus if a versine measures 3 in., the radius will be 33 ch.

1941 September, “The Why and the Wherefore: Curves”, in Railway Magazine, page 430:


hacoversed sine

hacoversed sine (plural hacoversed sines)

(trigonometry) The trigonometric function equal to half the coversed sine. Abbreviation: hacoversin


coversed sine

From contraction of complement + versed sine.

The cosine of an arc is the sine of its complement.† In like manner, the coversed sine, cotangent, and cosecant of an arc, are respectively the versed sine, tangent, and secant of its complement.

1825, Jas Thomson, Elements of Plane and Spherical Trigonometry, page 2:

At the top of the page on the left-hand side is placed the number of degrees, and in the left-hand column each minute of the degree, opposite to which are arranged the numerical values of the sine, coversed sine, &c, of the corresponding angle in those columns, at the top of which those terms are placed.

1830, W. Hopkins, “Book II: Elements of Trigonometry”, in Geometry, Plane, Solid, and Spherical, page 46:

For the coversed sine; subtract the sine of the angle from 1. Thus, for the same angle we have the coversed sine,
1 — ·36650 = ·6335.

1838, William Grier, The Mechanic′s Pocket Dictionary, page 21:

Hence the cosines and versed sines of zenith distances are respectively equal to the sines and coversed sines of the corresponding angular elevations.

1871, Homersham Cox, The Law and Science of Ancient Lights, 2nd edition, page 109:

(trigonometry) The trigonometric function 1 − sin(x).


versed sine

From New Latin sinus versus (“flipped sine”); the sine function being sometimes called sinus rectus.

For the divisions, to be laid on this line, are the differences between the logarithm versed sine of 180°, and the logarithm versed sines of the successive arcs.

1753, John Robertson, “The Construction of the Logarithmic Lines on the Gunter′s Scale”, in Philosophical Transactions: 1750-1755, Great Britain: Royal Society, page 340:

But if the given arch exceed 90°, find the natural co-sine of its supplement, which add to 1000000, and the sum will be the natural versed sine required.

1805, John William Norie, A New and Complete Epitome of Practical Navigation, page xxii:

The Natural Sines in this table are fractions (radius being unit); and are particularly adapted to Dunthorne′s and other methods of clearing the moon′s distance from the effects of parallax and refraction, where natural sines or versed sines are used ;[…].

1806, John Garnett, Tables Requisite To Be Used with The Nautical Ephemeris, page 41:

(trigonometry) The trigonometric function 1 − cos(x).


unit circle

(trigonometry, the unit circle) The circle of radius 1 with centre at the origin, used in defining trigonometric functions.

jednotková kružnice

circle of radius 1 with centre at the origin, used in trigonometry


projective

en-adj

projective (comparative more projective, superlative most projective)

more projective (comparative)
most projective (superlative)

Formed by the suffixation of prōiect- (the perfect passive participial stem of the Classical Latin prōiciō, whence the English verb project) with the English -ive, forming project + -ive; however, compare the post-Classical Latin prōiectīvus (“relating to purging”).

cog

Hence the non-Euclidean angle is measured by one-half the logarithm of the cross-ratio of four rays. Although the Euclidean point of view has been adopted for simplicity, the final result, depending as it does only on the cross-ratio, is projective; it is therefore independent of the particular assumptions that the rays α and β are perpendicular and that the initial line bisects the angle between them.

1912 November 5, Edwin B. Wilson, Gillbert B. Lewis, “The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics”, in Proceedings of the American Academy of Arts and Sciences, volume 45, number 11, page 503:

(geometry) Of or related to projective geometry:

(now usually in set phrases, of a property of a geometric object, figure, etc.) Invariant under projective transformations.

now usually in set phrases; figure; now usually in set phrases; figure

(of a geometric object, figure, etc.) Defined in or inhabiting a projective space.


excosecant

(trigonometry) The trigonometric function csc(x) − 1. Abbreviation: excsc


exsecant

(trigonometry) The trigonometric function sec(x) − 1. Abbreviation: exsec


golden ratio

(geometry) The irrational number (approximately 1.618), usually denoted by the Greek letter φ (phi), which is equal to the sum of its own reciprocal and 1, or, equivalently, is the square root of the sum of itself and 1.

黄金比

おうごんひ ōgon hi


contour

Borrowed from French contour, from contourner, equivalent to con- + tour.

A line on a map or chart delineating those points which have the same altitude or other plotted quantity: a contour line or isopleth; (metonymically) the landform or its surface.


fano

A non-singular complete algebraic variety whose anticanonical bundle is ample.


Pythagorean theorem

Named after Pythagoras (from Ancient Greek Πυθαγόρας (Puthagóras)), the Greek mathematician and philosopher who by tradition is credited with the theorem’s discovery and proof.

The Pythagorean theorem only applies to right triangles.

(geometry) A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides.


adjoint

Adjoint representation
Adjoint representation of a Lie algebra
adjoint

/ˈæd͡ʒ.ɔɪnt/

From French adjoindre (“to join”), from late 19th C; see also adjoin. Doublet of adjunct.
In the case of category theory (which brings together concepts from numerous fields), the term is often confounded with adjunct and the relationship is called an adjunction. The origin of any particular usage may therefore be uncertain.

The sets A + A₀, B + B₀, together, form the complete intersection, with f = 0, of a composite adjoint curve of order m + k, consisting of the adjoint curve of order m through A + B, together with the non-adjoint curve ω = 0; and the set B + B₀ consists of p points, and lies on i + j adjoint φ-curves of f = 0.

1933, H. F. Baker, Principles of Geometry, volume 5, published 2010, page 103:

As we have stated before, a curve f' is adjoint to a curve f if it have at least the multiplicity r#x5F;i-1 at each point where f has the multiplicity r#x5F;i. A first polar #x5C;sum#x5F;iy#x5F;i#x5C;left(#x5C;partialf#x2F;#x5C;partialx#x5F;i#x5C;right)#x3D;0 is an example of an adjoint curve.

1963, Julian Lowell Coolidge, A History of Geometrical Methods, page 205:

This imposes n(n - 3)/2 conditions on the n-gon adjoint curve.

2016, Eugene Wachspress, Rational Bases and Generalized Barycentrics: Applications to Finite Elements and Graphics, page 216:

(geometry, of one curve to another curve) Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.


adjoint

/ˈæd͡ʒ.ɔɪnt/

(geometry, algebraic geometry) A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used.


polarity

en-noun

polarity (countable and uncountable, plural polarities)

polaritat

chemistry: dipole-dipole intermolecular force

(projective geometry) A duality that is an involution, i.e. has order two. ᵂᵖ

trilinear polarity
trilinear polarity#English

(geometry) Ellipsis of trilinear polarity.


one-dimensional

en-adj

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

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

Such one-dimensional characters have always existed in the theatre along with more recognizably human characters.

1972, Hardie Albright, Stage direction in transition:

In contrast to this are the flat, one-dimensional characters found in fables.

1999, Kimberly Kimbell-Lopez, Connecting with traditional literature:

(figuratively) Lacking depth or believability; flat.

ერთგანზომილებიანი

figuratively, lacking depth or believability


complex plane

(mathematics) a representation of the space of complex numbers


rose curve

(mathematics) Any plane curve that consists of loops (petals) emanating from a central point.


Riemann surface

en-noun

Riemann surface (plural Riemann surfaces)

From Bernhard Riemann, German mathematician.

(mathematics) A one-dimensional complex manifold; a generalization of the complex plane.


bounding

(geometry) Containing all points of a given set within it.


geostationary

The measurement is accomplished by observing the Faraday rotation angle of signals from geostationary satellites on a continuous basis.

1971, Thomas A. Croft, Measurement of a Solar Wind Plasma Stream which Endures Several Months But is Intermittent on a Time Scale of about One Day:

At a fixed distance in three dimensions relative to a particular point on the Earth's surface; generally only possible with orbital satellites.


angle bisector

(geometry) A ray that divides an angle into two equal parts.


foliate

en-adj

foliate (comparative more foliate, superlative most foliate)

more foliate (comparative)
most foliate (superlative)

From Latin foliātus (“having leaves, leafy, leaved”) + English -ate (suffix forming adjectives with the sense ‘having [the specified thing]’). Foliātus is derived from folium (“leaf; (Late Latin) leaf or sheet of paper”) (ultimately from Proto-Indo-European *bʰleh₃- (“blossom, flower”) or *dʰelh₁- (“to be green”)) + -ātus (suffix forming adjectives with the sense ‘having [the specified thing]’).

der

Shaped like or otherwise resembling a leaf; leaflike.

(geometry) Of a curve: having two infinite branches with a common asymptote, and a leaf-shaped loop.

lehti-

of a curve: having two infinite branches with a common asymptote, and a leaf-shaped loop


compass error

(geometry, geomagnetism) The combination of variation and deviation which is the horizontal angle between the direction indicated by a magnetic compass and true north.


exterior angle

(geometry) An angle formed between one side of a polygon and an extension of an adjacent side.

vnější úhel

an angle formed between one side of a polygon and an extension of an adjacent side


semidiameter

From Middle English semidiametre, semydiametre, from Medieval Latin sēmidiameter, equivalent to semi- + diameter.

(astronomy) The apparent radius of a star etc, when viewed from Earth.

[B]etweene the ſphere of Saturne and the Firmament, there is ſuch an incredible and vaſt ſpace or diſtance (7000000. ſemidiameters of the earth, as Tycho [Brahe] calculates) void of ſtarres: [...]

1638, Democritus Junior [pseudonym; Robert Burton], “Ayre Rectified. With a Digression of the Ayre.”, in The Anatomy of Melancholy. […], 5th edition, Oxford, Oxfordshire: […] [Robert Young, Miles Flesher, and Leonard Lichfield and William Turner] for Henry Cripps, →OCLC, partition 2, section 2, member 3, page 254:


function space

(mathematics) Any metric space whose elements are functions


space curve

(mathematics) Any curve in three-dimensional space; includes any plane curve as a subset.


space velocity

en-noun

space velocity (plural space velocities)

(astronomy) The velocity of a star relative to the Sun


alternating function

alternating function (plural alternating functions)

independent variable
independent variable

(mathematics) Any function in which the interchange of two independent variables changes the sign of the dependent variable.


antihyperbolic function

antihyperbolic function (plural antihyperbolic functions)

inverse hyperbolic function
inverse hyperbolic function

(mathematics) An inverse hyperbolic function


arc-hyperbolic function

arc-hyperbolic function (plural arc-hyperbolic functions)


inverse hyperbolic function

inverse hyperbolic function (plural inverse hyperbolic functions)


boxcar function

boxcar function (plural boxcar functions)

The graph resembles a rectangular boxcar on a railway line.

(mathematics) Any function whose value is zero except for a finite part of its argument for which it has a constant non-zero value


comparable function

comparable function (plural comparable functions)

(mathematics) Either of a pair of functions that have the same domain and that the values of one are equal to or greater than the other for all points in that domain.


composite function

composite function (plural composite functions)

(mathematics) A function of one or more independent variables, at least one of which is itself a function of one or more other independent variables; a function of function(s).


cofunction

Cosine and sine are each other's cofunctions.

(mathematics) The trigonometric function of the complement of the supplied angle.

(programming) A costatement that takes the form of a function and can accept parameters and return a value.


constant function

constant function (plural constant functions)

(mathematics) A function whose value is the same for all the elements of its domain.


inverse trigonometric function

inverse trigonometric function (plural inverse trigonometric functions)

inverse trigonometric functions (plural)

(mathematics) A function that is the inverse of an appropriate restriction of a trigonometric function.


circular function

circular function (plural circular functions)

trigonometric function
trigonometric function#English

(trigonometry) Synonym of trigonometric function


algebraic function

algebraic function (plural algebraic functions)

Quite often, algebraic functions are algebraic expressions using a finite number of terms and involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Some algebraic functions, however, cannot be expressed by such finite expressions.

The value of an algebraic function at an algebraic number is always an algebraic number.

1989, Manuel Bronstein, An Algorithm for the Integration of Elementary Functions, James H. Davenport (editor), EUROCAL '87: European Conference on Computer Algebra, Proceedings, Springer, LNCS 378, page 491,
Trager (1984) recently gave a new algorithm for the indefinite integration of algebraic functions.

1992, A. A. Goldberg, V. A. Pyana, Uniqueness Theorems for Algebraic Functions, A. B. Sossinsky (translation editor), Boris Yakovlevich Levin (editor), Entire and Subharmonic Functions, American Mathematical Society, page 199,
It is known that the algebraic function w=w(z) enables one to determine the polynomial P(z,w) up to a constant factor.

1993, Goro Kato (translator), Kenkichi Iwasawa, Algebraic Functions, American Mathematical Society, page xiv,
Riemann provided a clear picture of many difficult topics. His most significant contribution, rather than his construction of a Riemann surface from an algebraic function, was to derive the existence of algebraic functions as he built his theory based on the concept of a Riemann surface.

(algebraic geometry) Informally, any function expressible using (only) the operations of addition, subtraction, multiplication, division and raising to a rational power; more precisely, any continuous function definable as the root of some polynomial equation.


functor

In the category of categories, #x5C;mathbb#x7B;CAT#x7D;, the objects are categories and the morphisms are functors.

1991, Natalie Wadhwa (translator), Yu. A. Brudnyǐ, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, Volume I, Elsevier (North-Holland), page 143,
Choosing for U the operation of closure, regularization or relative completion, we obtain from a given functor ℱ∈𝒥ℱ the functors
◌̅F: overrightarrow X→◌̅F( overrightarrow X),F⁰: overrightarrow X→F( overrightarrow X)⁰,Fᶜ: overrightarrow X→F( overrightarrow X)ᶜ.

Given a homotopical category X and a functor u#x3A;A#x5C;rightarrowB, a homotopical u-colimit (resp. u-limit) functor on X will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor Xᵘ#x3A;Xᴮ#x5C;rightarrowXᴬ (47.1).

2004, William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, Jeffrey H. Smith, Homotopy Limit Functors on Model Categories and Homotopical Categories, American Mathematical Society, page 165:

2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,
In this chapter, we recall the definition of the category of Σ_*-objects and we review the relationship between Σ_*-objects and functors. In short, a Σ_*-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor S(M):X→S(M,X), defined by a formula of the form
S(M,X)=⨁ ᪲ᵣ₌₀(M(r)⊗X)_(Σᵣ).

(category theory) A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities.


critical function

critical function (plural critical functions)

calculus of variations
calculus of variations

(mathematics) Any function, in the calculus of variations, that satisfies the Euler equations


cost function

Any mathematical relationship between an activity and its cost.


decreasing function

decreasing function (plural decreasing functions)

(mathematics) Any function of a real variable whose value decreases (or is constant) as the variable increases.


cylinder function

cylinder function (plural cylinder functions)

(mathematics) Any function that is a solution of the Bessel equation


strictly decreasing function

strictly decreasing function (plural strictly decreasing functions)

(mathematics) Any function of a real variable whose value decreases as the variable increases.


dissipation function

dissipation function (plural dissipation functions)

(physics) The function governing the rate at which mechanical energy is converted to heat during viscous flow.


logarithmic function

logarithmic function (plural logarithmic functions)

(mathematics) Any function in which an independent variable appears in the form of a logarithm; they are the inverse functions of exponential functions


entire function

entire function (plural entire functions)

(mathematics) Any function of a complex variable that is holomorphic throughout the complex plane


definite integral

definite integral (plural definite integrals)

(mathematics) The integral of a function between an upper and lower limit


even function

(mathematics) Any function whose value is unchanged if the independent variable changes sign i.e. f(x) = f(-x)


elementary function

elementary function (plural elementary functions)

logarithmic function
logarithmic function

(mathematics) Any function that is composed of algebraic functions, trigonometric functions, exponential functions and/or logarithmic functions, combined using addition, subtraction, multiplication and/or division

elementary function (differential algebra)


function multiplier

function multiplier (plural function multipliers)

An electronic analog computing device that accepts as input two periodic functions and outputs their mathematical product


function table

(mathematics) A printed tabulation of selected values of a function corresponding to selected independent variables; e.g. a table of logarithms.


Heaviside unit function

Heaviside unit function (plural Heaviside unit functions)

(mathematics) The function whose value is zero if its independent variable is negative, and one otherwise.


exponential function

exponential function (plural exponential functions)

(mathematics) Any function in which an independent variable is in the form of an exponent; they are the inverse functions of logarithms


explicit function

explicit function (plural explicit functions)

(mathematics) Any function whose value may be directly calculated from the independent variable.


hypergeometric function

hypergeometric function (plural hypergeometric functions)

hypergeometric equation
hypergeometric equation

hypergeometric series
hypergeometric series

(mathematics) Any function that is a solution of the hypergeometric equation; usually an expansion of an hypergeometric series


harmonic function

harmonic function (plural harmonic functions)

(mathematics) A function of two, three or n variables which is a solution to any of Laplace's equations


identity function

identity function (plural identity functions)

(mathematics) A function whose value is always the same as its independent variable, and for which the codomain equals the domain.

funció identitat

a function whose value is always the same as its independent variable


elliptic function

elliptic function (plural elliptic functions)

(mathematics) Any function of a complex variable which is periodic in two directions.

椭圆函数

any function of a complex variable which is periodic in two directions


implicit function

implicit function (plural implicit functions)

An important class of implicit functions comprises those defined by equations of the form x-f(y)#x3D;0. Choosing y as the value means that the implicit function is the inverse of f. This type of implicit function is of particular interest when that inverse is not expressible as a closed-form expression, and thus is difficult to study directly.

Thus, in the equation,
#x5C;quad#x5C;quad#x5C;quaday²#x2B;bxy#x2B;cx²#x2B;d#x3D;0;
y is an implicit function of x. Implicit functions are generally connected with their variables by one or more equations. When these equations are solved the implicit equation becomes explicit.
[…]The differential of an implicit function may be found without first finding the function itself.

1871, William G. Peck, Practical Treatise on the Differential and Integral Calculus, A. S. Barnes & Company, page 50:

The process of evaluating the derivatives in the case of implicit functions is exemplified below.

1875, J. Minot Rice, W. Woolsey Johnson, The Elements of the Differential Calculus, Part 2, Washington: Government Printing Office, page 71:

In this section we discuss the analysis of implicit functions for addressing questions like this.

2002, Michael W. Klein, Mathematical Methods for Economics, Addison-Wesley, page 245:

(mathematical analysis, algebraic geometry) A function defined by a (multivariable) implicit equation when one of the variables is regarded as the value of the function, especially where said equation is such that the value is not directly calculable from the other variables.

неявна функция

function defined as the solution to an implicit equation


inverse function

inverse function (plural inverse functions)

Halving is the inverse function of doubling.

If an inverse function exists for a given function, then it is unique.

The inverse function of an inverse function is the original function.

In the context of linearization, we recall the reflective property of inverse functions; the ƒ curve contains the point (a,b) if and only if the ƒ⁻¹ curve contains the point (b,a).

1995, Nicholas M. Karayanakis, Advanced System Modelling and Simulation with Block Diagram Languages, CRC Press, page 217:

An example of another function that has an inverse function is f(x)#x3D;4x#x2B;5.
Its inverse is f#x7B;-1#x7D;(x)#x3D;#x5C;frac#x7B;x-5#x7D;#x7B;4#x7D;.

2014, Mary Jane Sterling, Trigonometry For Dummies, 2nd edition, Wiley, page 51:

In words, this formula says that the derivative of a function, f, with respect to x, is the reciprocal of the derivative of its inverse function with respect to f.

2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147, If f and g are inverse functions, then f'(x)=1/(g'(f(x)))

(mathematics) For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x.

funció inversa

function that reverses the mapping action of a given function


rectification

rectification (countable and uncountable, plural rectifications)

/ˌɹɛktɪfɪˈkeɪʃən/

From Middle English rectificacioun, from Old French rectificacion, from Late Latin rectificatio.

(geometry) The determination of a straight line whose length is equal to a portion of a curve.

(geometry) The truncation of a polyhedron by replacing each vertex with a face that passes though the midpoint of each edge connected to the vertex; an analogous procedure on a polytope of dimension higher than 3.


indefinite integral

indefinite integral (plural indefinite integrals)

(mathematics) A function whose derivative is a given function; an antiderivative


impulse function

impulse function (plural impulse functions)

(mathematics) Any generalized function which is defined by its behavior under integration.


incidence function

incidence function (plural incidence functions)

(mathematics) A function that assigns a pair of vertices to each edge of a graph.


increasing function

increasing function (plural increasing functions)

(mathematics) Any function of a real variable whose value increases (or is constant) as the variable increases.


strictly increasing function

strictly increasing function (plural strictly increasing functions)

(mathematics) Any function of a real variable whose value increases as the variable increases.


independent function

independent function (plural independent functions)

(mathematics) Any of a set of functions the value of which can not be deduced from that of all the others.


initial mass function

(astronomy) a relationship that specifies the mass distribution of a newly formed stellar population


integral function

integral function (plural integral functions)


integrable function

integrable function (plural integrable functions)

(mathematics) Any function that possesses a finite integral


elliptic

From Ancient Greek ἐλλειπτικός (elleiptikós), from ἐλλείπω (elleípō, “I leave out, omit”). By surface analysis, ellipse + -tic.

Novv ſince the Planets move in Elliptick Orbits, in one of vvhoſe foci the Sun is, and by a Radius from the Sun deſcribe equal Area's in equal Times, vvhich no other Lavv of a Circulating Fluid, but the Harmonical Circulation can Account for, vve muſt find out a Lavv for the Paracentrical Motion, that may make the Orbits Elliptick.

1705, George Cheyne, “Of the Physical Laws, and the Uniform Appearances of Nature. Law III.”, in Philosophical Principles of Natural Religion: […], London: […] George Strahan […], →OCLC, § XXIV, page 39:

In this chapter, the history of solving elliptic problems by direct marching methods is reviewed.

1995, Patrick J. Roache, Elliptic Marching Methods and Domain Decomposition, page 1:

(geometry) Of or pertaining to an ellipse.

эліптычны

relating to an ellipse or its mathematical definition


linear function

linear function (plural linear functions)

(mathematics) Any function whose graph is a straight line: f(x)=ax+b


natural function

natural function (plural natural functions)

(mathematics) An ordinary trigonometric function


point function

(mathematics) Any function whose values are points


nuclear response function

nuclear response function (plural nuclear response functions)

(physics) A relationship that describes the probability of a particle that collides with another being scattered in any particular manner


penalty function

penalty function (plural penalty functions)

(mathematics) Any function that applies constraints to a maximum or minimum problem


orthonormal function

orthonormal function (plural orthonormal functions)

(mathematics) An orthogonal function whose inner product with itself is unity


orthogonal function

orthogonal function (plural orthogonal functions)

(mathematics) Either of a pair of functions whose inner product is zero


membership function

membership function (plural membership functions)

(mathematics) A generalization of the indicator function for a fuzzy set which assigns a truth value (0 or 1) to each element.


periodic function

periodic function (plural periodic functions)

(mathematics) Any function whose value repeats after the regular addition of a period to its independent variable; i.e., a function ƒ such that, for some positive constant p, ƒ(x + p) = ƒ(x) for all x.


partial function

partial function (plural partial functions)

total function

1967 [John Wiley & Sons], Stephen Cole Kleene, Mathematical Logic, 2002, Dover, page 244,
The Church-Turing thesis applies to partial functions on the same grounds as to total functions (§ 41).

1991, Michel Bidoit, Hans-Jörg Kreowski, Pierre Lescanne, Fernando Orejas, Donald Sannella (editors), Algebraic System Specification and Development: A Survey and Annotated Bibliography, Springer, LNCS 501, page 15,
Nowadays it seems quite clear that if algebraic specifications are to be used as a powerful and realistic tool for the development of complex systems they should permit the specification of partial functions. […] There are essentially two ways of specifying partial functions.

2006, Paulo Oliva, Understanding and Using Spector's Bar Recursive Interpretation of Classical Analysis, Arnold Beckmann, Ulrich Berger, Benedikt Löwe, John V. Tucker (editors), Logical Approaches to Computational Barriers: 2nd Conference on Computability in Europe, Proceedings, Springer, LNCS 3988, page 432,
In the following σ and τ will denote finite partial functions from N to N , i.e. partial functions which are defined on a finite domain. A partial function which is everywhere undefined is denoted by ⟨⟩, whereas a partial function defined only at position k (with value n) is denoted by ⟨k,n⟩.

(mathematics) A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X.

hlutskilgreint fall

mathematics: a function whose domain is a subset of the set on which it is formally defined


odd function

(mathematics) Any function whose value changes sign if the independent variable changes sign i.e. f(-x) = -f(x)


measurable function

measurable function (plural measurable functions)

(mathematical analysis) A function whose codomain is a topological space and domain is a measurable space, with the property that the inverse image of every open set in its codomain is a measurable set in its domain.


probability density function

probability density function (plural probability density functions)

(probability theory) Any function whose integral over a set gives the probability that a random variable has a value in that set.


phase function

(astronomy) A function that describes the angular distribution of light reflected from a body when illuminated from a specific direction


probability mass function

probability mass function (plural probability mass functions)

(mathematics) A function that gives the relative probability that a discrete random variable is exactly equal to some value.


psi function

(mathematics) A function of a complex variable obtained by differentiating the logarithm of a gamma function; the digamma function


radial distribution function

radial distribution function (plural radial distribution functions)

(mathematics, physics) A function which specifies the average density of atoms, molecules etc in three dimensions from a given point.


regular function

regular function (plural regular functions)


quadratic function

quadratic function (plural quadratic functions)

(mathematics) Any function whose value is the solution of a quadratic polynomial


scattering function

scattering function (plural scattering functions)

(physics) A function which describes the intensity of scattered radiation in any given direction


sample function

sample function (plural sample functions)

(statistics) Any function used to obtain a set of samples from a given population


random function

random function (plural random functions)

(mathematics, computing) A function whose formula is always the same, but whose initial value is chosen at random from a set of possible values (its domain).

(mathematics) A function chosen at random from a set of functions.

probability distribution
probability distribution

(computing) A function that returns a random or pseudo-random value that is distributed according to a specific probability distribution associated with the function.


symmetric function

symmetric function (plural symmetric functions)

(mathematics) Any function, of multiple variables, whose value is independent of the order of the variables, i.e. f(a,b) = f(b,a).


scalar function

scalar function (plural scalar functions)

(mathematics) Any function whose domain is a vector space and whose value is its scalar field


single-valued function

single-valued function (plural single-valued functions)

(mathematics) Any function in which each point in the domain maps to just one point in the range


user-defined function

user-defined function (plural user-defined functions)

(computing) A program or subroutine, provided by the user rather than being built into the system, that may return a value and may take input parameters.


trigonometric cofunction

trigonometric cofunction (plural trigonometric cofunctions)

(mathematics) Either of a pair of trigonometric functions that have equal values when their arguments are complementary angles, e.g. sine and cosine.


truth function

(mathematics, logic) A Boolean function whose value is interpreted as truth or falsity


Turing computable function

Turing computable function (plural Turing computable functions)

From Alan Turing, English mathematician, logician, and cryptographer.

(mathematics) Any function whose value may be computed using a Turing machine.

Turing-reiknanlegt fall

any function whose value may be computer using a Turing machine


simple function

simple function (plural simple functions)

mathematical analysis
mathematical analysis

(mathematical analysis) Any complex-valued measurable function whose range is finite.


recursive function

recursive function (plural recursive functions)

Computable function
Recursion (computer science)

(computing) Any function that uses recursion and can call itself until a certain condition is met.


rational function

rational function (plural rational functions)

Our first problem is that of interpolation in prescribed points to a given function by a rational function whose poles are given.

1960, J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, 3rd edition, American Mathematical Society, page 184:

By Theorem 2.3.2., we have that the right-hand side of this equation can be equal to a rational function only if that rational function is equal to zero.

1970, Ellis Horowitz, Algorithms for Symbolic Integration of Rational Functions, University of Wisconsin-Madison, page 24:

Let #x5C;mathcal#x7B;C#x7D; be the class of continuous maps of #x5C;mathbb#x7B;C#x7D;#x5F;#x5C;infty into itself and let #x5C;mathcal#x7B;R#x7D; be the subclass of rational functions.[…]Now #x5C;mathcal#x7B;R#x7D; is a closed subset of #x5C;mathcal#x7B;C#x7D;#x5F;#x5C;infty because if the rational functions R#x5F;n converge uniformly to R on the complex sphere, then R is analytic on the sphere and so it too is rational.

2000, Alan F. Beardon, Iteration of Rational Functions: Complex Analytic Dynamical Systems, Springer, page 45:

(mathematics, complex analysis, algebraic geometry) Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which are the roots of the denominator).

rationaalifunktio

function expressible as the quotient of polynomials


cubical

en-adj

cubical (comparative more cubical, superlative most cubical)

more cubical (comparative)
most cubical (superlative)


squared

The children were taught to plot graphs on squared paper.

(geometry) Covered with a grid of squares.


escribe

en-verb

escribe (third-person singular simple present escribes, present participle escribing, simple past and past participle escribed)

escribes (present singular third-person)
escribing (participle present)
escribed (participle past)
escribed (past)

From Latin e (“out, out of”) + scribere (“to write”).

(transitive, geometry) To draw outside of; designating a circle that touches one of the sides of a given triangle, and also the other two sides produced.


segment

From Latin segmentum (“a piece cut off, a strip, segment of the earth, a strip of tinsel”), from secāre (“to cut”).

der

A straight path between two points that is the shortest distance between them; a line segment.

(geometry) The part of a circle between its circumference and a chord (usually other than the diameter).

(geometry) The part of a sphere cut off by a plane.

сегмент

geometry: part of a sphere cut off by a plane

(topology) Any of the pieces that constitute an order tree.


spherical harmonics

(mathematics) The solutions to Laplace's equation using spherical coordinates


squarely

en-adv

squarely (comparative more squarely, superlative most squarely)

more squarely (comparative)
most squarely (superlative)

From square + -ly. First use appears c. 1557 in the writings of Robert Recorde.

(geometry) In the shape of a square; at right angles.


double point

(geometry) A point on a curve at which there are two tangents (because it touches itself, or has a cusp).


Boolean function

en-noun

Boolean function (plural Boolean functions)

(algebra, logic, computing) Any function based on the operations AND, OR and NOT, and whose elements are from the domain of Boolean algebra

fonction booléenne

function based on AND, OR and NOT operations


antiderivative

(calculus) A function whose derivative is a given function; an indefinite integral


analytic function

analytic function (plural analytic functions)

There is a large and important literature concerned with the question of how to characterize precisely the boundary values of analytic functions. For example, when the analytic functions are of Hardy Class H#x2A; in a half plane, then their boundary values are attained in the L2 norm and, in fact, the analytic function can be reproduced by a Cauchy integral of the boundary value.

1966, E. J. Beltrami, M. R. Wohlers, Distributions and the Boundary Values of Analytic Functions, Academic Press, page vii:

2000, Vladimir V. Mityushev, Sergei V. Rogosin, Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions: Theory and Applications, Chapman & Hall / CRC, page v,
Thus we have limited ourselves by boundary value problems for analytic functions, and some related problems. The constructive ideas are always in our mind, so, the basic goal of this book is to be useful for experts in analytic function theory and for nonspecialists in it, and even for non-mathematicians who apply these methods in their research.

2010, Emmanuel Fricain, Andreas Hartmann, Regularity on the Boundary in Spaces of Holomorphic Functions on the Unit Disk, Javad Mashreghi, Thomas Ransford, Kristian Seip (editors, Hilbert Spaces of Analytic Functions, American Mathematical Society, page 91,
We review some results on regularity on the boundary in spaces of analytic functions on the unit disk connected with backward shift invariant subspaces in Hᵖ.

(mathematical analysis) Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ.


regression

regression (countable and uncountable, plural regressions)

/ɹɪˈɡɹɛʃ.ən/

/ɹiːˈɡɹɛʃ.ən/

/ɹɪˈɡɹɛʃ.ən/

/ɹəˈɡɹɛʃ.ən/

/ɹəˈɡɹeʃ.ən/

Learned borrowing from Latin regressio. Equivalent to regress + -ion.
The statistics sense comes from regression to the mean.

(statistics) An equation using specified and associated data for two or more variables such that one variable can be estimated from the remaining variable(s).


ellipsoid

Polarizability can be imagined as a three-dimensional ellipsoid centred on the centre of the molecule, as shown in Figure 10.4.

2002, John Michael Hollas, Basic Atomic and Molecular Spectroscopy, page 133:

Because only ellipsoids of rotation have been adopted in practical geodesy and surveying and triaxial ellipsoids have been limited to theoretical studies, we will use the term ellipsoid for brevity to mean ellipsoid of rotation.

2004, Alfred Leick, GPS Satellite Surveying, 3rd edition, page 367:

As mentioned before, modern geodetic datums rely on the surfaces of geocentric ellipsoids to approximate the surface of the earth.

2010, Jan Van Sickle, Basic GIS Coordinates, 2nd edition, page 73:

Cartesian coordinates
Cartesian coordinates

(mathematics, geometry) A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x²/a² + y²/b² + z²/c² = 1.

উপবৃত্তাকার

surface all of whose cross sections are elliptic or circular


Poisson distribution

Poisson distribution (plural Poisson distributions)

After French mathematician Siméon Denis Poisson (1781-1840), who introduced the distribution in his 1837 work Recherches sur la probabilité des jugements en matière criminelle et en matière civile ("Research on the Probability of Judgements in Criminal and Civil Matters"), although prior work had been done by Abraham de Moivre.

For the modeling of many phenomena there is a need for enlarging the family of Poisson distributions. One possibility of doing this is the use of mixed Poisson distributions (outlined above).

1993, Rolf-Dieter Reiss, A Course on Point Processes, Springer, page 62:

It is worth noting, therefore, that unlike the binomial distribution in which we are interested in observing both 'success' and 'failure', the application of the Poisson distribution is concerned only with occurrences rather than non-occurrences.

2000, Michael C. Fleming, Joseph G. Nellis, Principles of Applied Statistics: An Integrated Approach Using MINITAB and Excel, 2nd edition, Thomson, page 116:

A mixture of Poisson processes will have a spike count described by a mixture of Poisson distributions. A model allowing a mixture of a few Poisson distributions adds substantial flexibility, while keeping the calculations reasonably simple.

2007, “4: Order Statistics for Decoding of Spike Trains”, in Kenji Doya, Shin Ashii, Alexandre Pouget, Rajesh P. N. Rao, editors, Bayesian Brain: Probabilistic Approaches to Neural Coding, The MIT Press, page 83:

As indicated, problems involving the number of occurrences of independent, randomly occurring events per unit of space or time can often be modeled with the Poisson distribution.

2017, William Q. Meeker, Gerald J. Hahn, Luis A. Escobar, Statistical Intervals: A Guide for Practitioners and Researchers, 2nd edition, Wiley, page 128:

negative binomial distribution
negative binomial distribution

(statistics) Any of a class of discrete probability distributions that express the probability of a given number of events occurring in a fixed time interval, where the events occur independently and at a constant average rate; describable as a limit case of either binomial or negative binomial distributions.

Abraham de Moivre
Poisson distribution
Siméon Denis Poisson


low Earth orbit

low Earth orbit (plural low Earth orbits)

A satellite orbit around the Earth within the altitude range of ~ 200 - 2000 km, in which a satellite can communicate with Earth with a small time lag and energy consumption. Abbreviation: LEO.


plutino

From Plut(o) + -ino (“diminutive suffix”), meaning "little Pluto" (compare neutrino); coined by David C. Jewitt, et al.

We present a study of the dynamical evolution of plutinos recently escaped from the resonance through numerical simulations. It was shown in previous works the existence of weakly chaotic orbits in the plutino population that diffuse very slowly finally diving into a strong chaotic region.

2010, Romina P. Di Sisto, Adrián Brunini, Gonzalo C. de Elía, “The contribution of plutinos to the Centaur population”, in Julio A. Fernández, Daniela Lazzaro, Dina Prialnik, Rita Schulz, editors, Icy Bodies of the Solar System: IAU Symposium S263, Cambridge University Press, page 89:

This is dubbed a 3:2 resonance (with Neptune), Pluto being the largest Plutino.
About one fourth of the KBOs are Plutinos. Plutinos may be debris from the collision of another KBO with Pluto, resulting in the formation of Pluto's largest moon, Charon.

2018, C Sivaram, Kenath Arun, Kiren O V, Current Trends in Astrobiology, Cambridge Scholars Publishing, page 39:

(astronomy) Any planetoid in the Kuiper belt whose orbit, like that of Pluto, has a resonance of 3:2 with that of Neptune.

冥族小天體

planetoid in orbit with 3:2 resonance to that of Neptune


golden section

(geometry) the division of a whole into two parts such that the ratio of the smaller part to the larger is equal to the ratio of the larger part to the whole.


paraboloid

surface of revolution
surface of revolution

(mathematics) A surface having a parabolic cross section parallel to an axis, and circular or elliptical cross section perpendicular to the axis; especially the surface of revolution of a parabola.


parabolic

From Ancient Greek παραβολικός (parabolikós).

(mathematics) A parabolic function, equation etc.


radio-

radiosymmetrical


homology

homology (countable and uncountable, plural homologies)

Henri Poincaré
Homology
MathWorld
singular homology

From homo- + -logy.
In topology, first used by French polymath Henri Poincaré, in the sense (close to what is now called a bordism) of a relation between manifolds mapped into a reference manifold: that is, the property of such manifolds that they form the boundary of a higher-dimensional manifold inside the reference manifold. Poincaré's version was eventually replaced by the more general singular homology, which is what mathematicians now mean by homology.

homologia

biology, psychology: relationship of having a common evolutionary or developmental origin

1863, George Salmon, A Treatise on Conic Sections, Longman, Brown, Green, Longman, and Roberts, 4th Edition, page 61,
Two triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point [called the centre of homology].

1885, Charles Leudesdorf (translator), Luigi Cremona, Elements of Projective Geometry, Oxford University Press (Clarendon Press), page 11,
Two corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology.

The relationship of being homologous; a homologous relationship.

(geometry, projective geometry) specifically, such relationship in the context of the geometry of perspective.

If the homology centre lies on the homology axis, the homology is said to be singular or parabolic; otherwise, it is called non-singular or hyperbolic.

perspective projection
perspective projection

(geometry, projective geometry) An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves.

samankaltaisuus

geometry: automorphism representing a perspective projection


decahedron

decahedron (plural decahedrons or decahedra)


line segment

(geometry) A part of a straight line bounded by two points.


unknot

(mathematics) In knot theory, a loop that is not knotted.


incidence

incidence (countable and uncountable, plural incidences)

From Middle French incidence, from Medieval Latin incidentia (“a falling upon”), from Latin incidens, present participle of incidere (“to fall upon”), from in (“on”) + cadere (“to fall”).

der

(geometry) The falling of a point on a line, or a line on a plane.

kuuluminen

geometry: falling of a point on a line, or a line on a plane


suborbital

The first rocket test was suborbital; it didn't even get off the ground but rather exploded on the launchpad.

Not reaching orbit; having a trajectory that does not reach orbital velocity and so must return to ground eventually.


plane angle

(geometry) An angle formed by two intersecting straight lines.

rovinný úhel

(geometry) An angle formed by two intersecting planes, measured by the angle between two intersecting straight lines that are in respective planes and perpendicular to the intersection of the planes.


subnormal

w:Webster's Dictionary#Webster's New International Dictionary 1909

(geometry) That part of the axis of a curved line which is intercepted between the ordinate and the normal.


cathetus

From Latin cathetus, from Ancient Greek κάθετος (káthetos, “perpendicular”).

uder

(geometry) A line perpendicular to a surface (or line); in particular, either of the sides of a right triangle other than its hypotenuse.


primitive recursive

(mathematics) Of a function, capable of being constructed from the zero function, successor function, and projection functions, by a finite number of applications of composition and recursion.


dog bone

a bone that is given to a dog to chew on and play with, similar to a dog biscuit. They can be real bones, or they can be made of other materials like plastic or leather

"The First Nanochips", Scientific American, April 2004, p. 81.
If ... the pattern on the mask were designed to look more like a dog bone, the result would better approximate a rectangle with sharp corners.

a 2- or 3-dimensional compound shape, evocative of a dog biscuit or dog-bone toy with a central shaft and two lobes (analogous to femoral condyles) at each end

Me and D-Money keep smokin' that bomb
Need a little game, you better log on
Girls get naked
Lickin' on my dog bone

2003, “PimpandHo.com”, in Married to the Game, performed by Too $hort:

(slang, possibly African-American Vernacular) the penis


rhumb line

Coordinate term: orthodrome

On portolan maps rhumb lines were all the go long before Mercator's time. […] It's a different matter putting a straight rhumb line on a map made for a round world. And on a map made for the whole world.

1964, David Greenhood, Mapping, University of Chicago Press, →ISBN, page 128:

(nautical) A line that cuts all meridians at the same angle, the path of a vessel that maintains a constant compass direction.

loksodromio

a line cutting all meridians at a constant angle


incenter

(US, geometry) The point formed at the intersection of the three angle bisectors of a triangle; also the centre of the incircle.


homogeneous function

en-noun

homogeneous function (plural homogeneous functions)

homogeneous polynomials
homogeneous polynomials

(mathematics) the ratio of two homogeneous polynomials, such that the sum of the exponents in a term of the numerator is equal to the sum of the exponents in a term of the denominator.


homogeneous polynomial

homogeneous polynomial (plural homogeneous polynomials)

(mathematics) a polynomial such that the sum of the exponents of the variables is the same for every term.

齐次多项式

mathematics: polynomial such that the sum of the exponents of the variables is the same for every term


spheroidal

en-adj

spheroidal (comparative more spheroidal, superlative most spheroidal)

more spheroidal (comparative)
most spheroidal (superlative)

The buccal mass in milacids is spheroidal, and contains an oxygnathic jaw.

2004, G. M. Barker, Natural Enemies of Terrestrial Molluscs, page 299:


Euler's formula

Named after Swiss mathematician Leonhard Euler (1707–1783).

named-after

κₙ(θ)=κ₁ cos ²θ+κ₂ sin ²θ

differential geometry
differential geometry

(differential geometry) A formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures κ₁ and κ₂ and the angle θ which that direction makes with the first principal direction:


noetherian

(algebraic geometry, of a scheme) admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;


continuous function

en-noun

continuous function (plural continuous functions)

(mathematical analysis) a function whose value at any point in its domain is equal its limit at the same point

անընդհատ ֆունկցիա

function whose value changes only slightly when its input changes slightly


linear transformation

linear transformation (plural linear transformations)

(linear algebra) A map between vector spaces which preserves the operations of vector addition and scalar multiplication.

lineêre transformasie

a map between vector spaces preserving vector addition and scalar multiplication


homomorphism

Coordinate term: homology

A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving.

1954, Kuo-Tsai Chen, Iterated Integrals and Exponential Homomorphisms, Proceedings of the London Mathematical Society, Reprinted in 2001, Philippe Tondeur (editor), Collected Papers of K.-T. Chen, Birkhäuser, page 54,
This motivates a generalization, and exponential homomorphisms are now defined, in an algebraic fashion, from certain free products to formal power series rings with non-commutative indeterminates.

A homomorphism of presheaves h#x3A;A#x5C;rightarrowB is a collection of homomorphisms h#x5F;U#x3A;A(U)#x5C;rightarrowB(U) commuting with restrictions.

1997, Glen E. Bredon, Sheaf Theory, 2nd edition, Springer, page 8:

Definition 1.15. Let G and H be matrix Lie groups. A map #x5C;Phi from G to H is called a Lie group homomorphism if (1) #x5C;Phi is a group homomorphism and (2) #x5C;Phi is continuous.

2003, Brian C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Springer, page 17:

(algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.

automorphism

structure-preserving map between algebraic structures


morphism

1982, Israel Program for Scientific Translations (translator), Lev J. Leifman (editor of translation), N. N. Čencov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Translations of Mathematical Monographs, Volume 53, page 50,
1° The composition of two morphisms is defined if and only if the final object of the first morphism is the initial object of the second. This composition is also a morphism, whose initial object is the initial object of the first morphism and whose final object is the final object of the second.

1992, Terrance Brown (translator), Gil Henriques, Chapter 13: Morphisms and Transformations in the Construction of Invariants, Terrance Brown (translator), Jean Piaget, Gil Henriques, Edgar Ascher (editors), Morphisms and Categories: Comparing and Transforming, page 198,
In certain extreme cases in mathematics, the synthesis of morphisms and of transformations is so intimate that one can speak of a veritable fusion. […] Essentially, categories are sets of morphisms organized into operatory systems.

The proof of toroidalization of morphisms of 3-folds to surfaces in [C3] breaks up into two parts: a reduction to prepared morphisms and then a proof of toroidalization of prepared morphisms from n-folds to [surfaces] in [CK].

2007 November, Steven Dale Cutkosky, “Toroidalization of Dominant Morphisms of 3-Folds”, in Memoirs of the, volume 190, number 890, American Mathematical Society, page 3:

(mathematics, category theory) (formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises.


unit vector

(linear algebra, mathematical analysis) A vector with the length of 1, defined as mathbf ̂u=(mathbf u)/(‖ mathbf u‖).


convex hull

1994, David Eppstein, Chapter 10: Average Case Analysis of Dynamic Geometric Optimization, Association of Computing Machinery, Society for Industrial and Applied Mathematics, Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, page 83,
This problem can be solved in time O(nᶜ) by combining a weight-balanced tree of the convex hull vertices with a farthest neighbor data structure of Agarwal and Matoušek [2].

Thus, the polyhedron and the convex hull of the set of its vertices coincide, which was to be proved.
Since the convex hull of a set M is determined uniquely from M, Theorem 1 implies that a bounded solid polyhedron and its surface, i.e., a closed convex polyhedron, are determined uniquely from its vertices.

2005, A.D. Alexandrov, Convex Polyhedra, page 23:

The convex hull of a compact subset of an infinite dimensional topological vector space need not be a compact set.

2007, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, page 185:

(mathematics) The smallest convex set of points in which a given set of points is contained.

convex envelope

smallest convex set of points containing a given set


confluent

en-adj

confluent (comparative more confluent, superlative most confluent)

more confluent (comparative)
most confluent (superlative)

(geometry, of a triangle) Exactly the same size as another triangle.


coplanar

(geometry, of at least two things, usually lines or plane figures) Within the same plane.


supplementary angle

en-noun

supplementary angle (plural supplementary angles)

Angle A is 40°, and its supplementary angle, B, is 140°.

(geometry) An angle that, when added to another referenced angle, produces an angle of 180 degrees.


oblique angle

(geometry) Any angle that is not a right angle or multiple of right angles.

vino kulma

any angle that is not a right angle or multiple of right angles


right-angled

(not comparable, geometry) Having a right angle.


y-direction

(algebraic geometry) The direction aligned with the y-axis of a coordinate system.


x-direction

(algebraic geometry) The direction aligned with the x-axis of a coordinate system.


z-direction

(algebraic geometry) The direction aligned with the z-axis of a coordinate system.


heart-shaped

en-adj

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

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

[…] Passing, I leave thee lilac with heart-shaped leaves, / I leave thee there in the door-yard, blooming, returning with spring.

1865, Walt Whitman, “When Lilacs Last in the Dooryard Bloom’d”, in Sequel to Drum-Taps: When Lilacs Last in the Dooryard Bloom’d and other poems:

Having the traditional shape of a heart (♥), that is pointed at one end and indented at the opposite side.


icosihenagon

From Ancient Greek εἰκοσιέν (eikosién, “twenty-one”) + -gon.

uder

(geometry) A polygon with twenty-one edges and twenty-one angles.


sigmate

en-adj

sigmate (comparative more sigmate, superlative most sigmate)

more sigmate (comparative)
most sigmate (superlative)


Bessel function

en-noun

Bessel function (plural Bessel functions)

For Friedrich Bessel, German mathematician.

differential equation
differential equation

(mathematics) Any of a class of functions that are solutions to a particular form of differential equation (a Bessel equation) and are typically used to describe waves in a cylindrically symmetric system.


vector field

(differential geometry) a function which associates, to each point on a surface, a vector in the tangent plane of that point


Euclidian space

Euclidian space (countable and uncountable, plural Euclidian spaces)

(mathematics, geometry) A space where the principles of Euclidean geometry apply.


celestial equator

celestial equator (plural celestial equators)

(astronomy) A great circle on the celestial sphere, coincident with the plane of Earth's Equator.


first fundamental form

(differential geometry) the Riemannian metric for 2-dimensional manifolds, i.e. given a surface with regular parametrization x(u,v), the first fundamental form is a set of three functions, {E, F, G}, dependent on u and v, which give information about local intrinsic curvature of the surface. These functions are given by


Christoffel symbol

Christoffel symbol (plural Christoffel symbols)

Named for Elwin Bruno Christoffel (1829–1900).

⃑x_uu\⃑x_uv\⃑x_vv=ΓᵤᵤᵘΓᵤᵤᵛl\ΓᵤᵥᵘΓᵤᵥᵛm\ΓᵥᵥᵘΓᵥᵥᵛn⃑x_u\⃑x_v\⃑n

(differential geometry) For a surface with parametrization ⃑x(u,v), and letting i,j,k∈u,v, the Christoffel symbol Γᵢⱼᵏ is the component of the second derivative ⃑x_ij in the direction of the first derivative ⃑x_k, and it encodes information about the surface's curvature. Thus,


holonomy

(differential geometry) Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P.


surface normal

⃑n=±⃑x_u×⃑x_v/ lVert ⃑x_u×⃑x_v rVert

(differential geometry) A unit vector at any given point P of a surface M which is perpendicular to the tangent plane T_P(M) of M at P. For a surface with parametrization ⃑x(u,v), it is given by


surface of revolution

surface of revolution (plural surfaces of revolution)

A sphere is a surface of revolution of a circle around an axis which runs through the center of the circle.

A torus is a surface of revolution of a circle around an axis which is outside the circle.

(mathematics) A surface formed when a given curve is revolved around a given axis. If the resulting surface is a closed one, it also defines a solid of revolution.


tangent plane

(differential geometry) The plane passing through a given point which contains the tangent lines of all the curves on a surface passing through that same point.


centroid

From centre + -oid. From 1844, used as a replacement for the older terms "centre of gravity" and "centre of mass" in situations described in purely geometrical terms, and subsequently used for further generalisations.

形心

mean position of points in a geometrical figure — see also center of gravity, barycenter

barycentre

centre of gravity of a uniform, rigid object

The center of gravity of any body or geometrical magnitude is by definition the same as the centroid of a certain system of parallel forces. It will be convenient, therefore, to use the word centroid in most cases instead of center of gravity.[…]The centroid of any area may be found by the following method: Divide the area into parts such that the area and centroid of each part are known. Take the centroids of the partial areas as the points of application of forces proportional respectively to those areas. The centroid of this system of forces is the centroid of the total area, and may be found by the method of Art. 172.

1892, Leander Miller Hoskins, The Elements of Graphic Statics, MacMillan and Co., pages 151–152:

For example, if a postal code area (PCA) has 1000 distinct residences, we might suppose all 1000 residences are at the centroid of the PCA. Centroids are commonly used, for example, with geographic information systems and CD-ROM phone books (Francis, Lowe, Rushton and Rayco 1999).

2004, Richard L. Francis, Timothy J. Lowe, Arie Tamir, “7: Demand Point Aggregation for Local Models”, in Zvi Drezner, Horst W. Hamacher, editors, Facility Location: Applications and Theory, Springer-Verlag, page 207:

operatorname Centroid(𝒳)=(∫xg(x)dx)/(∫g(x)dx)      (6)
where the integrals are taken over the whole space ℝⁿ, and g is the characteristic function of the subset, which is 1 inside 𝒳 and 0 outside it [27].

2020, Cheng Zhang, Qiuchi Li, Lingyu Hua, Dawei Song, Assessing the Memory Ability of Recurrent Neural Networks, Giuseppe De Giacomo, et al. (editors), ECAI 2020: 24th European Conference on Artificial Intelligence, IOS Press, page 1660, In ℝⁿ, a centroid is the mean position of all the points in all of the coordinate directions. The centroid of a subset 𝒳 of ℝⁿ is computed as follows

(geometry, physics, engineering, of an object or a geometrical figure) The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.

(geometry, specifically, of a triangle) The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.


hyperdimensional

A game of tic-tac-toe in five dimensions is hyperdimensional.

Of or pertaining to a system having more dimensions than naturally observed in our universe.


axis of symmetry

axis of symmetry (plural axes of symmetry)

(geometry) Any of one or more lines about which a geometric figure is symmetric

о́с на симе́трия

a line about which a geometric figure is symmetric


square pyramid

Great Pyramid of Giza
Great Pyramid of Giza

(geometry) A three-dimensional geometric figure with a square base and four triangular sides that connect at one point. An example is the Great Pyramid of Giza.


central angle

(geometry) An angle positioned with its vertex at the center of a circle.

keskuskulma

an angle positioned with its vertex at the center of a circle


parallelepipedal

(geometry) Having the form of a parallelepiped


hyperspatial

Of or pertaining to multi-dimensional geometry.


fixed set

(mathematics) A set which is unchanged by a function or other mapping. Formally: a set, S, is a fixed set of a function, f, if and only if for all x in S, f(x)=x.


natural logarithm

natural logarithm (plural natural logarithms)

From New Latin logarithmus nātūrālis, coined in 1668 by Nicholas Mercator in his book Logarithmo-technica.

The natural logarithm can be used to integrate ¹⁄ₓ.

(mathematics) The logarithm in base e: either the function that given x returns y such that eʸ = x, or the value of y given by the function.


flatiron

a flatiron building

The street down which Warwick had come intersected Front Street at a sharp angle in front of the old hotel, forming a sort of flatiron block at the junction, known as Liberty Point

1900, Charles W. Chesnutt, chapter I, in The House Behind the Cedars:


flyby

The upcoming flyby of Halley's comet is expected to provide new information on the nature of the comet.

Farthest from the dim red dwarf Ondeste, the ice dwarf Maisuth has attracted no interest beyond a cursory flyby by automated probe in 1874. No significant resources were noted.

2010, BioWare, Mass Effect 2 (Science Fiction), Redwood City: Electronic Arts, →OCLC, PC, scene: Maisuth, Ondeste System:

A flight past a celestial object in order to make observations.


truncated icosahedron

truncated icosahedron (plural truncated icosahedra or truncated icosahedrons)

truncated icosahedra (plural)
truncated icosahedrons (plural)

From truncated + icosahedron.
Truncatedicosahedron.gif|regular truncated icosahedron
Buckminsterfullerene animated.gif|C₆₀: buckminsterfullerene
Comparison of truncated icosahedron and soccer ball.png|A soccer ball with a regular truncated icosahedron

A truncated icosahedron may be formed by truncating the vertices of an icosahedron. Each vertex of the icosahedron is replaced by a pentagonal face and each triangular face of the icosahedron is replaced by a hexagonal face, which is inscribed inside the triangular face of the original icosahedron. The entire resulting truncated icosahedron is thus fittingly inscribed inside the original icosahedron.

This is the truncated icosahedron. Where the five triangles meet to form a vertex is now a pentagon, and a hexagon now replaces each triangular face. Therefore, the truncated icosahedron is composed of twelve pentagons and twenty hexagons.

1989, Tony Rothman, Science a la Mode: Physical Fashions and Fictions, page 64:

In addition to the 20 lithium atoms in layer b, additional lithium atoms (layer e) are located above the twelve pentagonal faces of the peripheral truncated icosahedra which, because of the way that the truncated icosahedra are linked, simultaneously cap the pentagonal faces of two adjacent truncated icosahedra sharing an edge (sharing method 1 above).

1993, R. Bruce King, Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry, page 183:

Fullerenes are truncated icosahedrons with 90 edges of equal length, 60 vertices, 20 hexagonal faces, and 12 pentagonal faces that form a closed shell.

2001, Edward A. Rietman, Molecular Engineering of Nanosystems, page 130:

2008, Jill Vincent, Andy Edwards, David Tynan, Gloria Stillman (editors), MathsWorld Year Eight for Queensland, Teacher Edition, page 308,
Do you know which sport is played with a truncated icosahedron?

(geometry) A polyhedron that has thirty-two faces (12 regular pentagons and 20 regular hexagons) and 60 vertices and 90 edges, and is one of the Archimedean solids.


figure eight

/ˌfɪɡəɹˈeɪt/

The shape consisting of two circles or ovals joined together at one point, resembling the numeral 8.


bipyramid

Yet the perfect hexagonal bipyramids still in the test-tube must have had an internal order to produce those shapes.

1998, Georgina Ferry, Dorothy Hodgkin: A Life:


dipyramid

In geometry, any of a class of solids formed from two pyramids placed symmetrically base to base.