term

From Middle English terme, borrowed from Old French terme, from Latin terminus (“a bound, boundary, limit, end; in Medieval Latin, also a time, period, word, covenant, etc.”).
Doublet of terminus and termon. Old English had termen, from the same source.

член

one of the addends in a sum or in another mathematical operation

A line is the term of a superficies, and a superficies is the term of a solid.

(geometry, archaic) A point, line, or superficies that limits.


cap

Inherited from Middle English cappe, from Old English cæppe, from Proto-West Germanic *kappā (“covering, hood, mantle”), from Late Latin cappa, itself from Latin caput. Ultimately from Proto-Indo-European *káput- and Proto-Indo-European *kap- (“head”). Doublet of cape, chape, and cope.

nalli

small amount of explosive used as detonator

(geometry) A portion of a spherical or other convex surface.


surface

From French surface. Doublet of superficies.

(mathematics, geometry) The locus of an equation (especially one with exactly two degrees of freedom) in a more-than-two-dimensional space.

سَطْح

locus of an equation in a more-than-two-dimensional space


folium

en-noun

folium (countable and uncountable, plural foliums or folia)

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From Latin folium (“leaf”). Doublet of foil and folio, distantly also with phyllo and phyllon.

These circular cubics are Newton's defective hyperbolae, with a diameter, species 39, 41, 45; the ampullate cubic represents the folium of the unipartite quartic, and the ampaniform the bipartite quartic.

1881, Henry M. Jeffery, “On Bicircular Quartics, with a Triple and Double Focus, and Three Single Foci, all of them Collinear.”, in Proceedings of the London Mathematical Society, volume 12, page 22:

I have argued that the real threat the Unruh effect poses to fundamental partical interpretation lies in its suggestion that physically reasonable states outrun the folium of any single irreducible Fock space representation.

2011, Laura Ruetsche, Interpreting Quantum Theories, page 222:

(geometry) A curve of the third order, consisting of two infinite branches having a common asymptote. The curve has a double point, and a leaf-shaped loop.


spiral

From Middle French spirale, from Medieval Latin spiralis, from Latin spīra, from Ancient Greek σπεῖρα (speîra, “wreath, coil, twist”).

der

(geometry) A curve that is the locus of a point that rotates about a fixed point while continuously increasing its distance from that point.


tesseract

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From tessara- (“four-”) + Ancient Greek ἀκτίς (aktís, “ray”).

af

Hence the cube determined by these axes is the face of the tesseract which we now have before us.

1906, Charles Howard Hinton, The Fourth Dimension, S. Sonnenschein & Company, page 239:

[…]then it would trace out a higher cube, or tesseract, and each of the six surrounding cubes, carried on in the same motion, would trace tesseracts also,[…].

1910, Henry Parker Manning, The Fourth Dimension Simply Explained, Munn, Incorporated, page 93:

(mathematics, geometry) The four-dimensional analogue of a cube; a 4D polytope bounded by eight cubes (analogously to the way a cube is bounded by six squares).


four-dimensional

(algebraic geometry) Having four dimensions; being measurable along four mutually perpendicular axes.


hypercube

(geometry) A geometric figure in four or more dimensions, which is analogous to a cube in three dimensions. Specifically, the n-dimensional equivalent of a cube for any non-negative integer n.

(geometry) Such a figure in four dimensions; a tesseract.


polytope

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From German Polytop, equivalent to poly- (“many”) + -tope (“surface”). Coined by Hoppe in 1882 and introduced to English by Alicia Boole Stott.

As is well known, the theory of linear inequalities is closely related to the study of convex polytopes.

1964, Victor Klee, On the Number of Vertices of a Convex Polytope: Canadian Journal of Mathematics, volume XVI, number 4, page 701:

This polytope is mapped into a Cartesian force polytope (resp. torque polytope) in the Cartesian space. Such a polytope represents the exact force (resp. torque) that can be produced on the vehicle main body.

1998, F. Pierrot, M. Benoit, P. Dauchez, “SamoS: A Pythagorean Solution for Omnidirectional Underwater Vehicles”, in Jadran Lenar I, Manfred L. Husty, editors, Advances in Robot Kinematics: Analysis and Control, page 220:

Verify the Hirsch conjecture for the 3-cube, 4-cube and any other polytope that takes your fancy.
The Steinitz theorem is a very satisfactory understanding of the graphs of three-dimensional polytopes.

2006, Rekha R. Thomas, Lectures in Geometric Combinatorics, page 27:

(geometry) A finite region of n-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence "point, line, polygon, polyhedron, ...".


acutangular

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perverse

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From Middle English perverse, pervers, from Old French pervers, from Latin perversum (“thoroughly turned”), past participle of pervertere, from per- (“thoroughly”) + vertere (“to turn”).

If two antipodal points move continuously on the sphere, they trace out what are called symmetric figures. These figures have corresponding elements equal, and are equal in area, but are not in general superposable. The one is, in fact, the perverse of the other.

1884, Robert Edgar Allardice, Spherical Geometry:

(geometry) A chiral opposite of something; a mirror image with opposite handedness.


evolution

en-noun

evolution (countable and uncountable, plural evolutions)

extinction

antonym(s) of “survival through adaptation”

/ɛvəˈlʉːʃən/

Borrowed from Latin ēvolūtiō, ēvolūtiōnis (“the act of unrolling, unfolding or opening (of a book)”), from ēvolūtus, perfect passive participle of ēvolvō (“unroll, unfold”), from ex + volvō (“roll”).

تَطَوُّر

general: a gradual process of development

(geometry) The opening out of a curve; now more generally, the gradual transformation of a curve by a change of the conditions generating it.


trapezium

en-noun

trapezium (plural trapeziums or trapezia)

Recorded since 1570, learned borrowing from Late Latin trapezium, from Ancient Greek τραπέζιον (trapézion, “irregular quadrilateral”, literally “a little table”), diminutive of τράπεζα (trápeza, “table”). Doublet of trapeze.

uder

(geometry, British, Australia, New Zealand) A quadrilateral with two sides parallel.

(restrictively) A quadrilateral with two sides parallel and two sides non-parallel.

(geometry, US, dated) A four-sided polygon with no parallel sides and no sides equal; a simple convex irregular quadrilateral.

شِبْهُ مُنْحَرِفٍ

polygon with no parallel sides and no equal sides

trapezoid

four-sided polygon with two parallel sides

trapezoid

four-sided polygon with no sides parallel and no equal sides


circumference

From Latin circumferentia, from circum (“around”) + ferō (“I carry”). Displaced native Old English ymbgang.

(geometry) The line that bounds a circle or other two-dimensional figure.

مُحِيط

line that bounds a circle or other two-dimensional object


transversal

From Middle French transversal, from Medieval Latin trānsversālis, from Latin trānsversus.

Let l and m be two hyperparallel lines. All the transversals to l and m that form congruent corresponding angles with l and m lie in a pencil.

2012, G. E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, page 357:

A line which traverses or intersects any system of other lines transversely.

(geometry) A line intersecting a pair of parallel lines.


eccentric

From Middle French excentrique, from Medieval Latin eccentricus, from Ancient Greek ἔκκεντρος (ékkentros, “not having the earth as the center of an orbit”), from ἐκ (ek, “out”) + κέντρον (kéntron, “point”). Equivalent to ex- + -centric.

der

(geometry, astronomy) A circle not having the same centre as another.


z-axis

(algebraic geometry) The axis on a graph of at least three dimensions that is usually drawn vertically and usually shows the range of values of a variable dependent on two other variables or the third independent variable.

z-as

axis on a graph that is usually drawn vertically


y-axis

independent variable
independent variable

(algebraic geometry) The axis on a graph that is usually drawn from bottom to top and usually shows the range of values of variable dependent on one other variable, or the second of two independent variables.


axle

From Middle English axil, in turn a combination of Old English eax and Old Norse ǫxull.

Axle in the Encyclopædia Britannica (11th edition, 1911)

the Sun’s axle


Cartesian coordinates

perpendicular distance
perpendicular distance

(algebraic geometry) The coordinates of a point measured as its perpendicular distance to the right of a vertical axis (the y-axis) and its perpendicular distance above a horizontal axis (the x-axis).


Cartesian distance

en-noun

Cartesian distance (plural Cartesian distances)

(algebraic geometry) Euclidean distance.


Euclidean distance

Euclidean distance (countable and uncountable, plural Euclidean distances)

euklidinen etäisyys

(geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:

The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:
 d( textbf a, textbf b)=√


Cartesian coordinate

Cartesian coordinate (plural Cartesian coordinates)

(geometry) The coordinates of a point measured from an origin along a horizontal axis from left to right (the x-axis) and along a vertical axis from bottom to top (the y-axis). This can be extended to three-dimensions by the z-axis perpendicular to the x- and y-axes.


discriminant

(geometry) The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in Pⁿ⁻¹ is singular.


hoof

From Middle English hoof, hof, from Old English hōf, from Proto-Germanic *hōfaz (compare West Frisian hoef, Dutch hoef, German Huf, Danish hov, Norwegian hov, Swedish hov), from Proto-Indo-European *ḱoph₂ós (compare Sanskrit शफ (śaphá, “hoof, claw”), Avestan 𐬯𐬀𐬟𐬀 (safa, “hoof”), possibly Czech, Polish kopyto).


diameter

From Old French diametre (French diamètre), from Latin diametrus, from Ancient Greek διάμετρος (diámetros) (γραμμή (grammḗ)) (diametros grammē, “line measuring across”), from διά (diá, “across”) + μέτρον (métron, “measure”). By surface analysis, dia- + -meter.

(geometry) Any straight line between two points on the circumference of a circle that passes through the centre/center of the circle; a chord that passes through the center of the circle.

In cases without good face contact, the diameter of the toolholder at the front of the flange or the tool itself should not be any larger than the gage diameter of the toolholder shank from a bending stiffness viewpoint.

2005, David A. Stephenson, John S. Agapiou, Metal Cutting Theory and Practice, page 280:

Viable non-malformed singleton pregnancies were selected for cerebellar measurements; transcerebellar diameter, (TCD), left and right cerebellar diameters (LCD, RCD).

2015 October 23, “Periconception Maternal Folate Status and Human Embryonic Cerebellum Growth Trajectories: The Rotterdam Predict Study”, in PLOS ONE, →DOI:

(geometry) The maximum distance between any two points in a metric space.


oblique

From Middle French oblique, from Latin oblīquus (also spelled oblīcus) (“slanting, sideways, indirect, envious”).


skeleton

From New Latin sceleton, from Ancient Greek σκελετόν (skeletón), the neuter of σκελετός (skeletós, “dried up, withered, dried body, parched, mummy”), from σκέλλω (skéllō, “dry, dry up, make dry, parch”), from Proto-Indo-European *(s)kelh₁- (“to parch, wither”); compare Ancient Greek σκληρός (sklērós, “hard”).

der

(geometry) The vertices and edges of a polyhedron, taken collectively.

luuranko

geometry: vertices and edges of a polyhedron


affinity

en-noun

affinity (countable and uncountable, plural affinities)

From Middle English affinite, from Old French affinité. Ostensibly equivalent to affine + -ity.

(geometry) An automorphism of affine space.


acnode

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(geometry) An isolated point not upon a curve, but whose coordinates satisfy the equation of the curve so that it is considered as belonging to the curve.


normal

en-adj

normal (comparative normaler or more normal, superlative normalest or most normal)

normaler (comparative)
more normal (comparative)
normalest (superlative)
most normal (superlative)

From Latin normālis (“made according to a carpenter's square; later: according to a rule”), from nōrma (“carpenter's square”), of uncertain origin; doublet of normale. The earliest meaning of the word in English was "perpendicular; forming a right angle" like something normālis (“made according to a carpenter's square”), but by Late Latin normālis had also come to mean "according to a rule", from which modern English senses of the word derive: in the 1800s, as people began to quantitatively study things like height, weight and blood pressure, the usual or most common values came to be called "normal", and by extension values regarded as healthy or desirable came to be called "normal" regardless of their usuality.

der

According to norms or rules or to a regular pattern.

(mathematics) Adhering to or being what is considered natural or regular in a particular field or context:

(algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.

The interior normal vector of a perfect sphere always point toward the center, and the exterior normal vector directly away, and both are always collinear with the ray whose tip ends at the point of intersection, which is the intersection of all three sets of points.

(geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.


normal

en-noun

normal (countable and uncountable, plural normals)

(geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.

նորմալ

mathematics: a line perpendicular to another


cleaver

From Middle English clevere, equivalent to cleave + -er.

Coordinate term: splitter

(geometry) A line segment that bisects the perimeter of a triangle and has one endpoint at the midpoint of one of the triangle's three sides.


lituus

(geometry) A curve with polar equation r²θ=a², where a is a constant.


kite

The noun is from Middle English kyte, kīte, kete (“a kite endemic to Europe, especially the red kite (Milvus milvus)”), from Old English cȳta (“kite; bittern”), from Proto-West Germanic *kūtijō, diminutive of Proto-Germanic *kūts (“bird of prey”), from Proto-Indo-European *gewH-d- (“to cry, screech”). The English word is cognate with Scots kyt, kyte (“kite; bird of prey”), Middle High German kiuzelīn, kützlīn (“owling”) (modern German Kauz (“owl”)). Possibly a doublet of coot.
Sense 3 (“lightweight toy”) is from the fact that it hovers in the air like the bird.
The verb is derived from the noun.

leko

military aviation, slang: aircraft — see also aircraft

leija

sailing, slang: spinnaker — see also spinnaker

Four-sided figures without parallel sides include trapezoids and kites.

A kite is a quadrilateral with exactly two pairs of adjacent congruent sides. Note that a parallelogram has opposite congruent sides, whereas the congruent sides of kites are adjacent. Therefore, a kite is also a parallelogram only when both pairs of adjacent congruent sides of the kite are congruent to each other, making the kite a rhombus.

2011, W. Michael Kelley, “Quadrilaterals”, in The Humongous Book of Geometry Problems: Translated for People Who Don’t Speak Math!!, New York, N.Y.: Alpha Books, →ISBN, page 216:

(geometry) A polygon resembling the shape of a traditional toy kite (sense 3): a quadrilateral having two pairs of edges of equal length, the edges of each pair touching each other at one end.

鷂形 /鹞形

geometry: a polygon resembling the shape of a traditional toy kite; a quadrilateral having two pairs of edges of equal length, the edges of each pair touching each other at one end


salient

en-adj

salient (comparative more salient, superlative most salient)

more salient (comparative)
most salient (superlative)

The heraldic sense “leaping” and the sense “projecting outward” are borrowed from Latin salientem, the accusative form of saliēns (“springing, leaping”), present participle of saliō (“leap, spring”, verb). The senses “prominent” and “pertinent” are relatively recent, and derive from the phrase salient point, which is a calque of the Latin punctum saliēns, a translation of Aristotle's term for the embryonal heart visible in (opened) eggs, which he thought seemed to move already. Compare also the German calque der springende Punkt.

(geometry) Denoting any angle less than two right angles.


roll

en-verb

roll (third-person singular simple present rolls, present participle rolling, simple past and past participle rolled)

rolls (present singular third-person)
rolling (participle present)
rolled (participle past)
rolled (past)

From Middle English rollen, partly from Old French roller, roler, röeler, röoler, from Medieval Latin rotulāre (“to roll; to revolve”), from Latin rotula (“a little wheel”), diminutive of rota (“a wheel”); partly from Anglo-Latin rollāre, from the same ultimate source.

rol

to cause something to revolve by turning over and over

rol

to move, or cause to be moved, upon rollers or small wheels

(geometry) To apply (one line or surface) to another without slipping; to bring all the parts of (one line or surface) into successive contact with another, in such a manner that at every instant the parts that have been in contact are equal.

rol

geometry: to apply (one line or surface) to another without slipping


semiregular tessellation

en-noun

semiregular tessellation (plural semiregular tessellations)

(geometry) A tessellation of the plane by two or more different convex regular polygons.

Mathworld article on regular tessellation


regular tessellation

regular tessellation (plural regular tessellations)

(geometry) A tessellation of the plane by a convex regular polygon.


tessellate

en-verb

tessellate (third-person singular simple present tessellates, present participle tessellating, simple past and past participle tessellated)

tessellates (present singular third-person)
tessellating (participle present)
tessellated (participle past)
tessellated (past)

Etymology tree
Proto-Indo-European *kʷetwóres
Proto-Hellenic *kʷétwores
Ancient Greek τέσσαρες (téssares)bor.
Latin tessera
Proto-Indo-European *-lós
Proto-Italic *-elos
Latin -lus
Latin tessella
Latin -ātus
Latin tessellātuslbor.
English tessellate
Learned borrowing from Latin tessellātus, from tessella, diminutive of tessera; from Ancient Greek τέσσαρες (téssares), from Proto-Indo-European *kʷetwóres.

tessellieren

to completely fill with multiple copies of a two-dimensional shape edge to edge

Regular hexagons tessellate.

(intransitive, geometry) to cover a two-dimensional shape, such that multiple copies of itself placed edge to edge cover an area leaving no space between the shapes.

It is possible to tessellate the plane with equilateral triangles and regular hexagons.

(transitive, geometry) To completely fill (an area) when multiple copies of one or more two-dimensional shapes are placed edge to edge.


tomahawk

From an Eastern Algonquian word, most likely Powhatan tumahák; compare also Malecite-Passamaquoddy tomhikon (“ax”), Abenaki temahigan, demahigan (“ax”).

(geometry) A geometric construction consisting of a semicircle and two line segments that serves as a tool for trisecting an angle; so called from its resemblance to the American Indian axe.


orthogonal

/ɔːˈθɒɡ.ə.nəl/

/ɔɹˈθɑɡ.ə.nəl/

By surface analysis, ortho- + -gon + -al. From French orthogonal, in turn from Medieval Latin orthogōnālis and Latin orthogōnius (“right-angled”), ultimately from Ancient Greek ὀρθογώνιος (orthogṓnios, “rectangular”).

der

A chord and the radius that bisects it are orthogonal.

(geometry) Of two objects, at right angles; perpendicular to each other.


bisect

en-verb

bisect (third-person singular simple present bisects, present participle bisecting, simple past and past participle bisected)

bisects (present singular third-person)
bisecting (participle present)
bisected (participle past)
bisected (past)

From bi- (“bi-, two”) + Latin secāre (“to cut”).

affix

(transitive) To cut or divide into two parts.

(transitive, geometry) To divide an angle, line segment, or other figure into two equal parts.

puolittaa

geometry: to divide an angle, line segment or other figure into two equal parts


bisect

(geometry) A bisector, which divides into two equal parts.


affine

en-adj

affine (comparative more affine, superlative most affine)

more affine (comparative)
most affine (superlative)

Now, let P, Q, and R be three noncollinear points that are left fixed by an affine transformation T.

1986, Patrick J. Ryan, Euclidean and Non-Euclidean Geometry: An Analytic Approach, Cambridge University Press, page 44:

In our example of the affine cryptosystem family, deciphering is also accomplished by an affine map, namely P#92;equiva#123;-1#125;C-a#123;-1#125;b#92;bmodN, and so the deciphering transformation uses the same algorithm as the enciphering transformation, except with a different key, namely, the pair (a#123;-1#125;,-a#123;-1#125;b).

1987, Neal Koblitz, A Course in Number Theory and Cryptography, Springer, page 81:

Clearly every linear functional is affine, and every affine function is both convex and concave.

2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edition, Springer, page 256:

linear transformation
linear transformation

(not comparable, geometry) Of or pertaining to a function expressible as f(⃑x)=A⃑x+⃑b (where A is a linear transformation and ⃑b is a constant), which, regarded as a transformation, maps parallel lines to parallel lines and finite points to finite points.

仿射

pertaining to a kind of function that generalises a linear transformation


cusp

From Latin cuspis (“a point, spear, pointed end”); first used in astrology. Doublet of cuspid and cuspis.

bor

(geometry) A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.

cúspide

point of a curve where it has no tangent


focal

Learned borrowing from New Latin focālis. By surface analysis, focus + -al.

lbor

Again, if the plane of the impressed couple intersects the mean plane between N and C, it will envelope the cone whose focals are ON, ON′, and whose internal axis is therefore OA.

1877, James Booth, A Treatise on Some New Geometrical Methods, page 209:

(geometry, obsolete) One of two lines perpendicular to the axis of a cone such that the cosine of the angle between the line and the axis is equal to the ratio of the cosines o the semiangles of the cone.


octant

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(geometry) The eighth part of a disc; a sector of 45 degrees; half a quadrant.


mitre

From Middle English mytre, from Old French mitre, from Ancient Greek μίτρα (mítra, “headband, turban”). Its use in reference to a counterfeit coin derived from the bishop's mitre stamped upon it. Doublet of Mithras, Mithra, Mitra, and Mehr.

doublet

(geometry, rare) A square with one triangular quarter missing from the outside.


secant

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From Latin secāns, present participle of secō (“to cut”).

(geometry) A straight line that intersects a curve at two or more points.


oblique line

(geometry) A line that, meeting or tending to meet another, makes oblique angles with it.


oblique system of coordinates

(analytic geometry) A system in which the coordinate axes are oblique to each other.


elation

en-noun

elation (countable and uncountable, plural elations)

From Middle English elacioun, from Old French elacion, from Latin ēlātiōnem, accusative singular of ēlātiō (“exaltation, elevation; pride, elation”), from ēlātus, perfect passive participle of efferō (“bring forth or out; raise; exalt”), from ē (“out of”), short form of ex, + ferō (“carry, bear”).

(geometry) A collineation that fixes all points on a line (called its axis) and all lines though a point on the axis (called its center).


exceptional

en-adj

exceptional (comparative more exceptional, superlative most exceptional)

more exceptional (comparative)
most exceptional (superlative)

ordinary

antonym(s) of “superior due to exception or rarity”

an exceptional curve; an exceptional divisor

(geometry) Corresponding to something of lower dimension under a birational correspondence.


node

→ Irish: nód

From Middle English node, borrowed from Latin nōdus. Doublet of knot, knout, and nodus.

(geometry) The point at which a curve crosses itself, being a double point of the curve. See crunode and acnode.

duaalipiste

geometry: point at which a curve crosses itself

(geometry) A similar point on a surface, where there is more than one tangent-plane.


roulette

en-noun

roulette (countable and uncountable, plural roulettes)

Borrowed from French roulette (“roulette, little wheel”). The sense "situation with a random chance of incurring serious harm" may be abstracted from Russian roulette.

bor

(countable, geometry) The locus of a point on a plane curve that rolls without slipping along another fixed plane curve.


splitter

lumper

antonym(s) of “one who prefers to split categories”

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

Coordinate term: cleaver

(geometry) A line segment through one of the vertices of a triangle that bisects the perimeter of the triangle.


trapeze

From French trapèze, from Latin trapezium. Doublet of trapezium.


spire

(geometry) The part of a spiral generated in one revolution of the straight line about the pole.


nonic

(algebraic geometry) Describing a curve the equation of which is nonic.


trope

Japanese: トロープ (torōpu)

Korean: 트로프 (teuropeu)

From Latin tropus, from Ancient Greek τρόπος (trópos, “a manner, style, turn, way; a trope or figure of speech; a mode in music; a mode or mood in logic”), related to τροπή (tropḗ, “solstice; trope; turn”) and τρέπειν (trépein, “to turn”); compare turn of phrase. The verb is derived from the noun.

der

Hence the section must be a conic passing through six nodes, that is, the plane touches the surface all along a conic, and is therefore a trope. The complete section of the surface by a trope is a conic counted twice; since this passes through six nodes, the trope must touch the six quadric tangent cones along generators which are tangents to the singular conic.

1905, R[onald] W[illiam] H[enry] T[urnbull] Hudson, “The Quartic Surface”, in Kummer’s Quartic Surface, Cambridge: At the University Press, →OCLC; republished Cambridge: Cambridge University Press, 2001, →ISBN, page 15:

A tangent space meeting a quartic surface in a conic.

troop

music, Roman Catholicism: phrase or verse added to the Mass

I take account of conical and biplanar nodes, or, as I call them, cnicnodes, and binodes; of pinch-points on the nodal curve; and of close-points and off-points on the cuspidal curve: viz. I assume that there are / C, cnicnodes, / B, binodes, / j, pinch-points, / #92;chi, close points, / #92;theta, off-points, / deferring for the present the explanation of these singularities. The same letters, accented, refer to the reciprocal singularities. Or using "trope" as the reciprocal term to node, these will be / C', cnictropes, / B', bitropes, / j', pinch-planes, / #92;chi', close-planes, / #92;theta', off-planes; / but these present themselves, not in the equations above referred to, but in the reciprocal equations.

1868 November 12, [Arthur] Cayley, “VI. A Memoir on the Theory of Reciprocal Surfaces”, in Philosophical Transactions of the Royal Society of London, volume 159, part I, London: Printed by Taylor and Francis, Red Lion Court, Fleet Street, published 1869, →OCLC, page 202:

(archaic) The reciprocal of a node on a surface.

Mathematical senses.
The reciprocal of a node on a surface.


equilateral triangle

en-noun

equilateral triangle (plural equilateral triangles)

(geometry) A triangle having all three sides equal.


isosceles triangle

isosceles triangle (plural isosceles triangles)

(geometry) A triangle having at least two sides equal.


hypotenuse

From Latin hypotenusa, from Ancient Greek ὑποτείνουσα πλευρά (hupoteínousa pleurá, “side subtending [the right angle]”), from ὑποτείνουσα (hupoteínousa, “stretching, extending, subtending”), active participle of ὑποτείνω (hupoteínō, “subtend, stretch under”).

uder

ὑποτείνουσα πλευρά

Coordinate term: cathetus

(geometry) The side of a right triangle opposite the right angle.

وَتَر

the side of a right triangle opposite the right angle


indivisible

PIE word
 *dwóh₁
From Middle French indivisible, from Late Latin indivisibilis.

(geometry) An infinitely small quantity which is assumed to admit of no further division.


equivalent

en-adj

equivalent (comparative more equivalent, superlative most equivalent)

more equivalent (comparative)
most equivalent (superlative)

From equi- + -valent.
From Latin aequivalentem, accusative singular of aequivalēns, present active participle of aequivaleō (“I am equivalent, have equal power”).

A square may be equivalent to a triangle.

(geometry) Equal in measure but not admitting of superposition; applied to magnitudes.


variety

en-noun

variety (countable and uncountable, plural varieties)

From Middle French varieté (“variety”) (modern French variété (“variety; genre, type”)) or directly from its etymon Latin varietās (“difference; diversity, variety”) + English -ty (suffix forming abstract nouns from adjectives). Varietās is derived from varius (“different, diverse, various; variegated”) (possibly ultimately from Proto-Indo-European *h₁weh₂- (“to abandon; to give out; to leave”)) + -tās (suffix forming feminine abstract nouns indicating a state of being). The English word displaced the native Old English mislīcnes.
Sense 1.3.2 (“total number of distinct states of a system; logarithm to the base 2 of the total number of distinct states of a system”) was coined by the English psychiatrist William Ross Ashby (1903–1972) in his work An Introduction to Cybernetics (1956).
cognates
* Galician variedade (“variety”)
* Italian varietà (“difference; variety”)
* Portuguese variedade (“variety”)
* Spanish variedad (“breed; variety”)

der

A collection or number of different things.

(algebraic geometry) Ellipsis of algebraic variety (“the set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition”).

algebraic variety
algebraic variety#English


concentric

en-adj

concentric (comparative more concentric, superlative most concentric)

more concentric (comparative)
most concentric (superlative)

Japanese: コンセント (konsento)

Korean: 콘센트 (konsenteu)

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From Middle English concentrik, from Middle French concentrique, from Medieval Latin concentricus, from Latin con- (“with, together”) + centrum (“circle, center”). Equivalent to con- + -centric.

Seven huge concentric semi-circular rings of stone surround the northern end, and quite rightly are Grade 2-listed by conservation body Historic England.

2020 August 26, Tim Dunn, “Great railway bores of our time!”, in Rail, page 45:


concave

concave (comparative more concave, superlative most concave)

more concave (comparative)
most concave (superlative)

From Middle English concave, from Old French concave, from Latin concavus.

(geometry, not comparable, of a polygon) Not convex; having at least one internal angle greater than 180 degrees.


convex

convex (comparative more convex, superlative most convex)

more convex (comparative)
most convex (superlative)

Borrowed from Middle French convexe, from Latin convexus (“arched”).

(geometry, not comparable, of a polygon) having no internal angles greater than 180 degrees.


noble

noble (comparative nobler or more noble, superlative noblest or most noble)

nobler (comparative)
more noble (comparative)
noblest (superlative)
most noble (superlative)

From Middle English, from Old French noble, from Latin nōbilis (“knowable, known, well-known, famous, celebrated, high-born, of noble birth, excellent”), from nōscere, gnōscere (“to know”).
False cognate of Arabic نبيل (nabīl). Displaced native Middle English athel, from Old English æþele.

der

(geometry, of a polyhedron) Both isohedral and isogonal.


geometry

en-noun

geometry (countable and uncountable, plural geometries)

From Middle English gemetry, geometrie, from Old French geometrie (modern French géométrie), from Latin geōmetria, from Ancient Greek γεωμετρία (geōmetría, “geometry, land-survey”), from γεωμέτρης (geōmétrēs, “land measurer”), from γῆ (gê, “earth, land, country”) + -μετρία (-metría, “measurement”), from μέτρον (métron, “a measure”). By surface analysis, geo- + -metry. Doublet of gematria.

der

(algebraic geometry, countable) A mathematical object comprising representations of a space and of its spatial relationships.


parallelogram

/ˌpæ.ɹəˈlɛl.əˌɡɹæm/

From Latin parallelogrammum, from Ancient Greek παράλληλος (parállēlos, “parallel”) + γραμμή (grammḗ, “line”).

uder

(geometry) A convex quadrilateral in which each pair of opposite edges are parallel and of equal length.


grade

→ Japanese: グレード (gurēdo)

→ Swahili: gredi

Borrowed from Middle French grade (“a grade, degree”), from Latin gradus (“a step, pace, degree”), from Proto-Italic *graðus, from Proto-Indo-European *gʰradʰ-, *gʰredʰ- (“to walk, go”). Doublet of gradus.
Cognate with Gothic 𐌲𐍂𐌹𐌸𐍃 (griþs, “step, grade”), Bavarian Gritt (“step, stride”), Lithuanian grìdiju (“to go, wander”).

(geometry) In a linear system of divisors on an n-dimensional variety, the number of free intersection points of n generic divisors.

aste

geometry: number of free intersection points of n generic divisors


conic section

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(geometry) Any of the four distinct shapes that are the intersections of a cone with a plane, namely the circle, ellipse, parabola and hyperbola.


proportional

It is almost superfluous to remark that the numbers attached to the elements of compounds are those of the proportionals in which they combine […]

1828, William Thomas Brande, Tables in Illustration of the Theory of Definite Proportionals, page xiii:

(mathematics, geometry, archaic) A proportion.


construction

en-noun

construction (countable and uncountable, plural constructions)

→ Mongolian: констракшн (konstrakšn)

From Middle English construccioun, construction, from Old French construction, from Latin cōnstructiō, from cōnstruere.
Morphologically construct + -ion.

(geometry) A geometric figure of arcs and line segments that is drawable with a straightedge and compass.


ellipse

From French ellipse. Doublet of ellipsis.

(geometry) A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone.


parabola

parabola (plural parabolas or parabolae or parabolæ)

parabolas (plural)
parabolae (plural)
parabolæ (plural)

Borrowed from New Latin parabola, from Ancient Greek παραβολή (parabolḗ), from παραβάλλω (parabállō, “I set side by side”), from παρά (pará, “beside”) + βάλλω (bállō, “I throw”). Doublet of parable, parole, and palaver.

(geometry) The conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix).


radiant

From Middle English radyant, from Latin radiāns, radiantis, present participle of radiāre (“to emit rays or beams”).

(geometry) A straight line proceeding from a given point, or fixed pole, about which it is conceived to revolve.


cone

From Middle English cone (“corner, angle”) and conoun (“cone”), from Medieval Latin cōnus, cōnon (“cone, wedge, peak”), from Ancient Greek κῶνος (kônos, “cone, spinning top, pine cone”). Reinforced by Middle French cone, from the same Graeco-Latin source.

der

surface of revolution
surface of revolution

(geometry) A surface of revolution formed by rotating a segment of a line around another line that intersects the first line.

(geometry) A solid of revolution formed by rotating a triangle around one of its altitudes.


similitude

en-noun

similitude (countable and uncountable, plural similitudes)

From Old French similitude. By surface analysis, similar + -itude.

(countable, geometry) A similarity: a transformation of Euclidean space that preserves angles and the ratios of distances.


excess

excess (countable and uncountable, plural excesses)

From Middle English exces (“excess, ecstasy”), from Old French exces, from Latin excessus (“a going out, loss of self-possession”), from excedere, excessum (“to go out, go beyond”). See exceed.

der

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


vector space

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A vector space is a set of vectors which can be linearly combined.

Each vector space has a basis and dimension.

scalar multiplication
scalar multiplication

(algebra, geometry, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.


chiral

From Ancient Greek χείρ (kheír, “hand”) + -al.

suf

In the close vicinity of a chiral nanostructure, the circular dichroism of a biomolecule could be greatly enhanced, due to the interaction with the local superchiral fields.

2016, S. Hamed Shams Mousavi, Sajanlal R. Panikkanvalappil, Mostafa A. El-Sayed, Ali A. Eftekhar, Ali Adibi, “Large Enhancement of Circular Dichroism Using an Embossed Chiral Metamaterial”, in arXiv:

(geometry, physical chemistry) that exhibits chirality; as in the left-handed and right-handed versions of a helix, or a molecule with L- and D- stereoisomers.


construct

en-verb

construct (third-person singular simple present constructs, present participle constructing, simple past and past participle constructed)

constructs (present singular third-person)
constructing (participle present)
constructed (participle past)
constructed (past)

Borrowed from Latin cōnstrūctus, from cōnstruō (“to heap together”), from com- (“together”) + struō (“I heap up, pile”). Doublet of construe.

Construct a circle that touches each vertex of the given triangle.

(transitive, geometry) To draw (a geometric figure) by following precise specifications and using geometric tools and techniques.


great circle

(geometry) A circle defined as the intersection of the surface of a sphere and a plane which passes through the centre of the sphere.


effective

en-adj

effective (comparative more effective, superlative most effective)

more effective (comparative)
most effective (superlative)

From French effectif, from Latin effectīvus (“productive; effective”), from efficiō (“I make; I bring about”), equivalent to effect + -ive.

der

(geometry, of a cycle or divisor) Having no negative coefficients.


uniform

en-adj

uniform (comparative more uniform, superlative most uniform)

more uniform (comparative)
most uniform (superlative)

Borrowed from Middle French uniforme, from Latin uniformis.

(geometry) (of a polyhedron) That is isogonal and whose faces are regular polygons; (of an n-dimensional (n>3) polytope) that is isogonal and whose bounding (n-1)-dimensional facets are uniform polytopes.


sextant

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(geometry) One sixth of a circle or disc; a sector with an angle of 60°.


catenary

From Late Latin catenaria, in turn from Latin catēna (“chain”). Attested since 1788.

/ˈkætəˌnɛɹi/

(geometry) The curve described by a flexible chain or a rope if it is supported at each end and is acted upon by no other forces than a uniform gravitational force due to its own weight and variations involving additional and non-uniform forces. It is described by the hyperbolic cosine function.


zone

→ Korean: 존 (jon)

→ Punjabi: ਜ਼ੋਨ (zon)

From Latin zōna, from Ancient Greek ζώνη (zṓnē, “girdle, belt”).

der

1835, Charles Davies, David Brewster (editors and translators), Adrien-Marie Legendre, Elements of Geometry and Trigonometry, [1794, Eléments de géométrie], page 293,
To find the surface of a spherical zone.
Rule.—Multiply the altitude of the zone by the circumference of a great circle of the sphere, and the product will be the surface (Book VIII. Prop. X. Sch. 1).

A zone of a sphere is the curved surface of a frustum.[…]Determine, correct to 3 significant figures (a) the volume of the frustum of the sphere, (b) the radius of the sphere and (c) the area of the zone formed.

2014, John Bird, Engineering Mathematics, page 183:

(geometry) The curved surface of a frustum of a sphere, the portion of surface of a sphere delimited by parallel planes.

(geometry, loosely, perhaps by meronymy) A frustum of a sphere.


ecliptic

Borrowed from Latin eclīptica. So named because an eclipse can occur only when the Moon lies on this plane.

(geometry) A great circle drawn on a terrestrial globe, used for illustrating and solving astronomical problems.


inclination

en-noun

inclination (countable and uncountable, plural inclinations)

From Middle English inclinacioun, inclinacyon, from Old French inclination and Latin inclīnātiō.
Morphologically incline + -ation

The astronomer calculated the inclination of the equator or ecliptic of Earth and the orbital planes of each visible heavenly body.

Artillery must take account of a weapon's precise inclination.

(geometry) The angle of intersection of a reference plane


incircle

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To construct the incircle of ΔABC, we need the center of the circle and a pass-through point.

2003, Clark Kimberling, Geometry in Action: A Discovery Approach Using the Geometer's Sketchpad, page 16:

Having constructed K, the incircle of the quadrilateral can be easily constructed since it is tangent to BA and BC.

2005, István Reiman, International Mathematical Olympiad: 1959-1975, page 51:

For example, in Figure 4.2a only two edges of the polygon are tangent to the incircle. The other four edges do not even touch the incircle, but their extensions, shown by dotted lines, are tangent to the incircle.

2012, Tom M. Apostol, Mamikon A. Mnatsakanian, New Horizons in Geometry, Mathematical Association of America, page 106:

(geometry) A circle within a polygon, especially a triangle, that is tangent to each side.

вписана окръжност

the circle within a polygon that is tangent to each side


cyclic

en-adj

cyclic (comparative more cyclic, superlative most cyclic)

more cyclic (comparative)
most cyclic (superlative)

From Ancient Greek κυκλικός (kuklikós). Possibly from cycle + -ic.

(geometry, of a polygon) Able to be inscribed in a circle.


spindle

From Middle English spyndel, spindle, spyndylle, from Old English spindle, spindel, alteration of earlier spinel, spinil, spinl (“spindle”), from Proto-West Germanic *spinnilu (“spindle”), equivalent to spin + -le. Cognate with Scots spindil, spinnell (“spindle”), Dutch spindel ("spindle"; < Middle Dutch spille, spinle), German Spindel (“spindle”), Danish spindel (“spindle”), Swedish spindel (“spindle”).

gloss

(geometry) A solid generated by the revolution of a curved line about its base or double ordinate or chord.


petal

From Ancient Greek πέταλον (pétalon), from πέταλος (pétalos, “broad, flat”), from Proto-Hellenic *pétalos, from Proto-Indo-European *peth₂- (“to spread out”), whence Latin pandō and Proto-Germanic *faþmaz (“embrace”) (English fathom).

der

(geometry) A lobe of a rose (geometric shape).


orthogon

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orthodrome

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Coordinate term: rhumb line (loxodrome)

(geometry) A great circle, or part of one.


insist

en-verb

insist (third-person singular simple present insists, present participle insisting, simple past and past participle insisted)

insists (present singular third-person)
insisting (participle present)
insisted (participle past)
insisted (past)

Partly from Middle French insister, from Latin īnsistere; and partly from a back-formation from insistence.

Angles likewise which insist on the Diameter, are all Right Angles.

1709, Venturus Mandey, Synopsis Mathematica Universalis:

(obsolete, chiefly geometry) To stand (on); to rest (upon); to lean (upon).


orthonormal

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(functional analysis, geometry, linear algebra) Of a set of vectors, both orthogonal and normalized.

(functional analysis, geometry, linear algebra) Of a linear transformation: that preserves both angles and lengths.


deficiency

en-noun

deficiency (countable and uncountable, plural deficiencies)

From deficient + -cy. Compare Latin dēficientia.

(geometry) The amount by which the number of double points on a curve is short of the maximum for curves of the same degree.

(geometry) The codimension of a linear system in the corresponding complete linear system.


octagonal

The sundials range in shape from octagonal to the usual round. Prices range from $75 to $375.

1985 April 4, Daryln Brewer, “HELPFUL HARDWARE; AN ARRAY OF SUNDIALS”, in The New York Times:

(geometry) Shaped like an octagon, in having eight sides and eight angles.


apothem

From Ancient Greek ἀπόθεμα (apóthema, “deposit”), from ἀπό (apó, “off, away”) + θέμα (théma, “that which is laid down”).

uder

(geometry) The perpendicular distance from the center of a circle to a chord of the same circle.

apoteema

(geometry) The distance from the center of a regular polygon perpendicular to one of its sides (a special case of the above).

апотема

the distance from the center of a polygon to a side


concurrent

en-adj

concurrent (comparative more concurrent, superlative most concurrent)

more concurrent (comparative)
most concurrent (superlative)

/kəŋˈkʌɹənt/

/kɒŋˈkʌɹənt/

/kəŋˈkɝɹənt/

From Middle English concurrent, from Old French concurrent, from Latin concurrēns, present active participle of concurrō (“happen at the same time”), from con- (“with”) + currō (“run”).


hull

From Middle English holle, hoole (“hull, hold of a ship, ship”), of uncertain origin. Possibly a variant and special use of Etymology 1 above, conformed to hull. Alternatively, a variant of Middle English hole, hoole, holle (“hiding place, lair, den, shelter, compartment”, literally “hole, hollow”), related to Middle Dutch and Dutch hol (“hole, ship's cargo hold”). More at hole.

The orthogonal convex hull of an orthogonal polygon is the smallest orthogonally convex polygon that encloses the original polygon.

holomorphically convex hull; affine hull; injective hull

(mathematics, geometry, of a set A) The smallest set that possesses a particular property (such as convexity) and contains every point of A; slightly more formally, the intersection of all sets which possess the specified property and of which A is a subset.


orientation

en-noun

orientation (countable and uncountable, plural orientations)

/ˌɔɹiɛnˈteɪʃən/

From French orientation. By surface analysis, orient + -ation.

(analytic geometry, topology, countable) The designation of a parametrised curve as "positively" or "negatively" oriented; the analogous description of a surface or hypersurface.


solid angle

(geometry) The three-dimensional analog of an angle, equivalent to the area of that portion of the surface of a unit sphere that it subtends.


obround

(geometry) A plane shape consisting of two semicircles connected by parallel lines tangent to their endpoints.


curvilinear

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From curve + -i- + linear, compare curve, linear.

In early art rectilinear decoration marks an advance on curvilinear, which, in the long ages before pottery was thought of, would naturally be associated with the fibrous baskets that served as vessels.

1907, Ronald M. Burrows, The Discoveries In Crete, page 52:


geodesic

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(geometry) The shortest curve between two points on a specific surface.

geodèsica

mathematics: the shortest line between two points on a specific surface


intercept

Borrowed from Latin interceptum, past participle of intercipiō.

the y intercept ― point at which a line crosses the y-axis

Because the horizontal-axis intercept occurs when y=0 and the vertical-axis intercept occurs when x=0, we can find the intercepts algebraically.

2012, Alice Kaseberg, Greg Cripe, Peter Wildman, Introductory Algebra: Everyday Explorations, page 278:

(algebraic geometry) The coordinate of the point at which a curve intersects an axis.


groin

From earlier grine, from Middle English grinde, grynde, from Old English grynde (“abyss”) (perhaps also "depression, hollow"), probably related to Proto-Germanic *grunduz; see ground. Later altered under the influence of loin.

(geometry) The surface formed by two such vaults.


umbilicus

umbilicus (plural umbilici or umbilicuses)

Borrowed from Latin umbilīcus (“navel”).

(geometry, obsolete) One of the foci of an ellipse or other curve.

A sphere may be osculatory to the surface in every direction at an umbilicus.

(geometry) A point of a surface at which the curvatures of the normal sections are all equal to each other.


projection

projection (countable and uncountable, plural projections)

/pɹəˈd͡ʒɛkʃən/

From either the Middle French projection or its etymon, the Classical Latin prōiectiō (stem: prōiectiōn-), from prōiciō, equivalent to project + -ion. Compare the Modern French projection, the German Projektion, and the Italian proiezione.

(geometry) An image of an object on a surface of fewer dimensions.

проекция

geometry: image of an object on a surface of fewer dimensions


hypersphere

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The timing and location of these battles have not been established. “Sphere” in this context is a hypersphere made up of complexes of two and three-D surfaces, or membranes, shortened in this translation to “branes,” extending into higher dimensions that combine vectors of transit, but also scalar tactical probabilities—a difficult concept to grasp, but essential to understanding Forerunner warfare.

2013 March 19, Greg Bear, String 25, in Halo: Silentium (Forerunner Saga; 3), New York: Tor, →ISBN, page 211:

To prove that the hypersphere is a manifold we wish to divide it into polyhedral solids.

2014, Donald W. Blackett, Elementary Topology: A Combinatorial and Algebraic Approach, Academic Press, →ISBN, page 198:

(geometry) The set of all points in a given hyperspace that are at a given distance from a given point; a generalization of a sphere in four or more dimensions.

гиперсфера

the points of a hyperspace at the same distance from a given point


chiliahedron

chiliahedron (plural chiliahedra or chiliahedrons)

chiliahedra (plural)
chiliahedrons (plural)

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(geometry) A polyhedron bounded by one thousand plane surfaces.


cuboctahedron

cuboctahedron (plural cuboctahedrons or cuboctahedra)

cuboctahedrons (plural)
cuboctahedra (plural)

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Blend of cube + octahedron, reflecting the fact that it can be regarded both as a rectified cube and a rectified octahedron.

There are just two polyhedra that will fulfill these conditions: the cuboctahedron and the icosidodecahedron (Diagram 3.3).

1976, Hugh Kenner, Geodesic Math and how to Use it, page 21:

In the case of perfect, symmetric L1₀ cuboctahedra, two of the (001)-surfaces have to be terminated completely with either iron or platinum.

2008, M. E. Gruner, Georg Rollmann, Alfred Hucht, Peter Entel, “Structural and Magnetic Proprties of Transition Metal Nanoparticles from First Principles”, in Rolf Haug, editor, Advances in Solid State Physics 47, page 124:

Octahedra are also needed to make the packing of square-sharing cuboctahedra space filling (Fig. 2.4(c)).

2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 54:

2015, Ke Jiang, Antoliy O. Pinchuk, Chapter Two: Noble Metal Nanomaterials: Synthetic Routes, Fundamental Properties, and Promising Applications, Robert E. Camley, Robert L. Stamps (editors), Solid State Physics, Volume 66, Elsevier, page 151,
Yang and coworkers have prepared Pt cuboctahedrons and cubes by reducing K₂PtCl₄ with H₂ generated in situ from the hydrolysis of NaBH₄ in the presence of tetradecyltrimethylammonium bromide as a surfactant [157,158].

(geometry) An Archimedean solid that has fourteen faces (eight triangular and six square) and is both isogonal and isotoxal.

kuboktaedri

polyhedron with 8 triangular and 6 square faces


spherical

en-adj

spherical (comparative more spherical, superlative most spherical)

more spherical (comparative)
most spherical (superlative)

English spheric [from Latin sphaericus, from Ancient Greek σφαιρικός (sphairikós)] + -al.

The ability of a segment of a glass sphere to magnify whatever is placed before it was known around the year 1000, when the spherical segment was called a reading stone, essentially what today we might term a frameless magnifying glass or plain glass paperweight.

2013 September-October, Henry Petroski, “The Evolution of Eyeglasses”, in American Scientist:

(geometry, not comparable) Of, or pertaining to, spheres.


scroll

From Middle English scrowle, scrolle, from earlier scrowe, scrouwe (influenced by Middle English rolle), from Old French escroe, escrowe, escrouwe (“scroll, strip of parchment”), from Frankish *skrōda (“a shred”), from Proto-Germanic *skraudō, from *skrew- (“to cut; cutting tool”), extension of *(s)ker- (“to cut”). Doublet of shred and escrow.


transverse

Late Middle English, from Latin trānsversus (“turned across; going or lying across or crosswise”). Doublet of transversal.

der

(geometry) (of an intersection) Not tangent, so that a nondegenerate angle is formed between the two things intersecting. (For the general definition, see Transversality (mathematics).)


transverse

(geometry) The longer, or transverse, axis of an ellipse.


isotropy

en-noun

isotropy (countable and uncountable, plural isotropies)

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down this road, as they watched, came a wagon, then a couple of riders, then a coach and another wagon, in daylight which slowly lost its stark isotropy and was flowed into by clouds and chimney smoke and even episodes of weather

2006, Thomas Pynchon, Against the Day, Vintage, published 2007, page 478:

(geometry, physics) The property of being identical, or having the same physical properties, in all directions.


coordinate system

coordinate system (plural coordinate systems)

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1992, D. H. Maling, Coordinate Systems and Map Projections, 2nd Edition, Pergamon Press, page 27,
In this chapter we review some of the fundamental ideas about the plane coordinate systems which are used in surveying and mapping, both from the viewpoint of studying the mathematics of map projections and the practical tasks which arise in cartography.

Note that the orientation of Squire's coordinate system relative to the physical coordinate system is changing as a function of wavenumbervector.

2003, Vejapong Juttijudata, Proper Orthogonal Decomposition in Squire's Coordinate System and Its Low-dimensional Model of Channel Turbulence, Cornell University, page 22:

In Chapter 1 the choice of the origin and orientation of the analysis Cartesian coordinate system was made arbitrarily.[…]Note that nothing was said about the origins of the above two Cartesian coordinate systems.

2008, Bruce K. Donaldson, Analysis of Aircraft Structures, 2nd edition, Cambridge University Press, page 38:

mathematical analysis
mathematical analysis

(geometry, mathematical analysis) A method of representing the position of any individual point in a space of given dimensionality as a tuple of numerical coordinates.

نِظَامُ إِحْدَاثِيَّاتٍ

method of representing points in a space


rotation

rotation (countable and uncountable, plural rotations)

/ɹoʊˈteɪʃən/

Borrowed from Latin rotatiō. By surface analysis, rotate + -ion.

The function mapping (x,y) to (−y,x) is a rotation.

(mathematics, geometry) An operation on a metric space that is a continuous isometry and fixes at least one point.


astroid

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From Ancient Greek ἄστρον (ástron, “a star”) + εἶδος (eîdos, “form, likeness”).

(geometry) A hypocycloid with four cusps.


hypocycloid

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From hypo- (“below or inside”) + cycloid.

(geometry) The locus of a point on the circumference of a circle that rolls without slipping inside the circumference of another circle.


epicycloid

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From epi- (“above or outside”) + cycloid.

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.


cycloid

In the firſt Courſe there was a Shoulder of Mutton, cut into an Æquilateral Triangle, a Piece of Beef into a Rhomboides, and a Pudding into a Cycloid.

1726 October 28, [Jonathan Swift], “The Humours and Dispositions of the Laputians Described. […]”, in Travels into Several Remote Nations of the World. […] [Gulliver’s Travels], volume II, London: […] Benj[amin] Motte, […], →OCLC, part III (A Voyage to Laputa, Balnibarbi, Glubbdubdribb, Luggnagg, and Japan), page 20:

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on a fixed straight line.

cicloide

geometry: locus of a point on the circumference of a rolling circle


trident

PIE word
 *tréyes
From Latin tridēns, from tri- (“three”) + dēns (“tooth”).

(geometry) A curve of third order of the form:


icosasphere

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(geometry) A geometric figure with twenty or more triangular faces producing a semi-spherical solid.


equivalence

equivalence (countable and uncountable, plural equivalences)

From French équivalence, from Medieval Latin aequivalentia.

(geometry) A number in intersection theory. A positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this number is its equivalence.


enclosing

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(geometry) Of a region, containing all points of a given set within its bounds.


latus rectum

latus rectum (plural latera recta or latus rectums)

latera recta (plural)
latus rectums (plural)

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(geometry) The line drawn through a focus of a conic section parallel to the directrix and terminated both ways by the curve. It is the parameter of the principal axis.


divisor

divisor

integer that divides another integer an integral number of times

(mathematics, algebraic geometry) Any of several kinds of formal object associated to an algebraic variety, scheme, etc., which play a role similar to that of homology or cohomology groups in the study of topological spaces.

(in the study of Riemann surfaces) An element of the free abelian group on the points of the space.

(on a variety (or integral locally Noetherian scheme)) A Weil divisor: an element of the free abelian group on the codimension-1 subvarieties (or subschemes).

(on a variety (or integral Noetherian scheme)) A Cartier divisor; see Cartier divisors on Wikipedia.Wikipedia


perigon

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(geometry) A round angle; a full circle.


round angle

Two angles whose sum is a straight angle are called supplemental; two angles whose sum is a round angle we may call explemental.

1893, William Benjamin Smith, Introductory Modern Geometry of Point, Ray, and Circle, MacMillan, page 31:

(geometry) An angle of 360 degrees; a full circle.


obtuse-angled

(geometry) Of a triangle, having an obtuse angle.


conical

en-adj

conical (comparative more conical, superlative most conical)

more conical (comparative)
most conical (superlative)

He anſwers, That this Motion is Conical; and judgeth, that by the Conick path all the Phænomena of Comets can, without any inconveniency, be readily ſolved; even of that, which (by Hiſtory) in fifty days, paſſed through more then the 12 Signs of the Zodiack; And of that, which in two days run through eight Signs: and of another, which in 48 days poſted through all the Signs, contra ſeriem.

1665 November 6, “An Account of Hevelius his Prodromus Cometicus, together with some Animadversions made upon it by a French Philosopher”, in Henry Oldenburg, editor, Philosophical Transactions, volume I, number 6:

(geometry) Of or relating to a cone or cones.


SSA

en-noun

SSA (countable and uncountable, plural SSAs)

(geometry) Initialism of side side angle (a geometric proof reason)


circle segment

circular segment
circular segment#English


homothetic

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homoteettinen

economics: depending on the ratio of prices

(mathematics, geometry) for a geometric figure that is the image of another figure under an homothety.


polyhedral

en-adj

polyhedral (comparative more polyhedral, superlative most polyhedral)

more polyhedral (comparative)
most polyhedral (superlative)

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(mathematics, geometry) Of, pertaining to or derived from a polyhedron.

(geometry, of a solid or surface) Having multiple planar faces or facets.

poliedrico

(geometry) having multiple planar faces or facets


flex

en-noun

flex (countable and uncountable, plural flexes)

From Latin flexus, past participle of flecto (“to bend”).

(countable, geometry) A point of inflection.


supplement

From Latin supplementum (“that which is added to supply a shortage”), from supplere (“to provide something”).

der

(geometry) An angle that, when added to a given angle, makes 180°; a supplementary angle.


AAS

en-noun

AAS (countable and uncountable, plural AASs)

(geometry) Initialism of angle-angle-side triangular congruency.


domino

1801, borrowed from French domino (1771), originally the term for a hooded garment, itself from Medieval Latin domino, oblique case of dominus (“lord, master”); compare Medieval Latin dominicale (“a kind of veil”).

cog

(geometry) A polyomino made up of two squares.


sphericon

(geometry) A solid constructed by slicing a bicone with 90-degree apices through a plane containing both of them, rotating one half by 90 degrees, and reconnecting them; the resulting shape has a single continuous face, and two edges.

esfericón

(geometry) a solid constructed by slicing a bicone


taxicab geometry

From the distance travelled by a taxicab in a grid of streets that cross at right angles to each other.

non-Euclidean geometry
non-Euclidean geometry

(geometry) A non-Euclidean geometry in which the distance between two points is the sum of the absolute differences between their corresponding coordinates.


nef

Short for numerically effective; introduced by Miles Reid.

[…] this condition is the numerical consequence of the condition that for some mgt;0, the linear system #124;mD#124; is effective and free; thus nef = "numerically (effective and free)".

1983, Miles Reid, “Minimal Models of Canonical 3-Folds”, in Advanced Studies in Pure Mathematics, volume 1, page 131:

(algebraic geometry) Of a line bundle on a complete algebraic variety over a field: such that the degree of its restriction to every algebraic curve in the variety is non-negative.


epicycle

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From Latin epicyclus, from Ancient Greek ἐπίκυκλος (epíkuklos), from ἐπί (epí, “upon”) + κύκλος (kúklos, “circle”).

(geometry) Any circle whose circumference rolls around that of another circle, thus creating a hypocycloid or epicycloid.

episykli

any circle whose circumference rolls around that of another circle


non-Euclidean geometry

en-noun

non-Euclidean geometry (countable and uncountable, plural non-Euclidean geometries)

(geometry) Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience.


Euclidean

Named after Euclid, who established the principles of plane geometry.

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(geometry) Adhering to the principles of traditional geometry, in which parallel lines are equidistant.


Euclidean geometry

Euclidean geometry (countable and uncountable, plural Euclidean geometries)

(geometry) The familiar geometry of the real world, based on the parallel postulate.

歐幾里德幾何 /欧几里德几何

Ōujǐlǐdé jǐhé


limaçon of Pascal

limaçon of Pascal (plural limaçons of Pascal)


cardioid

(geometry) An epicycloid with exactly one cusp; the plane curve with polar equation ρ=1+ cos ,θ - approximately heart-shaped


limaçon

From French limaçon, ultimately from Latin limax (“snail”).

(geometry) A plane curve with polar equation ρ=a+b, sin ,θ or ρ=a+b, cos ,θ, of which the cardioid is a special case.


octomino

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(geometry) A polyomino made up of eight squares.


n-omino

(geometry) A polyomino made up of n squares.


heptomino

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(geometry) A polyomino made up of seven squares.


hexomino

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(geometry) A polyomino made up of six squares.


monomino

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(geometry) The polyomino made up of one square.


nonomino

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(geometry) A polyomino made up of nine squares.


pentomino

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PIE word
 *pénkʷe
pent(a)- + (poly)omino

(geometry) A polyomino made up of five square units. When packing pentominoes into three-dimensional shapes, the square units commonly are expanded into cubes instead of being flattened.


tetromino

/tɛˈtɹɒmɪnəʊ/

/tɛˈtɹɑːmɪnoʊ/

(geometry) A polyomino made up of four squares connected edge to edge.


decomino

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(geometry) A polyomino made up of ten squares.


tromino

/ˈtɹɑmɪˌnoʊ/

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(geometry) A polyomino made up of three squares connected edge to edge.


polyform

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(geometry) A plane or solid figure constructed by joining together identical polygons edge to edge.


triomino

triomino (plural triominoes or triominos)

/tɹaɪˈɒmɪnəʊ/

/tɹaɪˈɑmɪˌnoʊ/

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A polyomino made up of three squares connected edge to edge.


polytan

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polyabolo

polyabolo (plural polyabolos or polyaboloes)

polyabolos (plural)
polyaboloes (plural)

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Blend of poly- + diabolo, from the resemblance of a diabolo in cross-section to two right isosceles triangles joined at the vertices of their right angles.

(geometry) A polyform made by joining right isosceles triangles edge to edge in various arrangements.


polystick

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(geometry) A figure made by joining line segments of equal length end to end at right angles.


polycube

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(geometry) A polyform made by joining one or more cubes face to face in various arrangements.


polydrafter

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From poly- + draft + -er, from drafting triangle.

(geometry) A polyform made by joining N-2 triangles edge to edge in various arrangements, each of these triangles being a right triangle with angles 30°, 60° and 90°.


polyhex

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(geometry) A polyform made by joining one or more regular hexagons edge to edge in various arrangements.


polyiamond

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Blend of poly- + diamond, the polyiamond made up of two triangles being a diamond or rhombus.

equilateral triangle
equilateral triangle

(geometry) A polyform made by joining one or more equilateral triangles edge to edge in various arrangements. Every polyiamond corresponds to a polyhex,


polyomino

polyomino (plural polyominos or polyominoes)

polyominos (plural)
polyominoes (plural)

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poly- + (d)omino, as if the d were for di-, two, a domino being made up of two squares

(geometry) A plane polyform made by joining one or more squares edge to edge in various arrangements; a similar polyform made from triangles or hexagons (or any polygon that can tile a plane)


n-iamond

(geometry) A polyiamond made up of n triangles.


pentiamond

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(geometry) A polyiamond made up of five triangles.


tetriamond

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(geometry) A polyiamond made up of four triangles.


hexiamond

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(geometry) A polyiamond made up of six triangles.


triamond

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(geometry) A polyiamond made up of three triangles.


moniamond

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(geometry) The polyiamond made up of a single triangle.


prism

→ Japanese: プリズム (purizumu)

→ Korean: 프리즘 (peurijeum)

→ Thai: ปริซึม (bprí-sʉ̂m)

[ˈpʰɹ̠̊ɪzm̩]

Learned borrowing from Late Latin prisma (“(geometry) prism”), from Ancient Greek πρίσμᾰ (prísmă, “anything sawn; sawdust; (Koine, geometry) prism”), from πρῐ́ζω (prĭ́zō) (a variant of πρῑ́ω (prī́ō, “to saw”), further etymology unknown) + -μᾰ (-mă, suffix forming neuter nouns denoting the effect or result of an action, etc.).

prizëm

transparent block used to reflect or refract light

(geometry) A polyhedron with parallel ends of the same polygonal shape and size, the other faces being parallelogram-shaped sides.

An object having the shape of a geometrical prism (sense 1).

(construction) A cutting (“open passage at a level lower than the surrounding terrain, dug for a canal, railway, or road to go through”) or an embankment shaped like a prism (sense 1) or a number of prisms, such that its volume can be easily calculated.

leikkaus

cutting or embankment shaped like a prism or number of prisms

(crystallography) A crystal in which the faces are parallel to the vertical axis.

prisma

[page 13] One of theſe Parts [of a piece of black paper] I painted vvith a red Colour and the other vvith a blevv. […] This Paper I vievved through a Priſm of ſolid Glaſs, vvhoſe tvvo Sides through vvhich the Light paſſed to the Eye vvere plane and vvell poliſhed, and contained an Angle of about Sixty Degrees: vvhich Angle I call the refracting Angle of the Priſm. […] [page 17] Theſe Experiments may ſuffice for the Colours of Natural Bodies. For in the Colours made by the Refraction of Priſms this Propoſition vvill appear by the Experiments vvhich are novv to follovv in the next Propoſition.

1704, I[saac] N[ewton], “[The First Book of Opticks. Part I.] Prop[osition] I. Theor[y] I. Lights which Differ in Colour, Differ also in Degrees of Refrangibility.”, in Opticks: Or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light. […], London: […] Sam[uel] Smith, and Benj[amin] Walford, printers to the Royal Society, […], →OCLC, pages 13 and 17:

Here, avvful [Isaac] Newton, the diſſolving clouds / Form, fronting on the ſun, thy ſhovvery priſm; / And to the ſage-inſtructed eye unfold / The various tvvine of light, by thee diſclos'd / From the vvhite mingling maze.

a. 1749 (date written), James Thomson, “Spring”, in The Seasons, London: […] A[ndrew] Millar, and sold by Thomas Cadell, […], published 1768, →OCLC, page 10, lines 207–211:

(optics) A transparent block in the shape of a prism (sense 1), typically with triangular ends, used to reflect or refract light.

The beams, that thro' the Oriel shine, / Make prisms in every carven glass, […]

1842, Alfred Tennyson, “The Day-Dream”, in Poems. […], volume II, London: Edward Moxon, […], →OCLC, page 151:

(archaic) A spectrum produced by light being refracted through a prism.


circumscribe

en-verb

circumscribe (third-person singular simple present circumscribes, present participle circumscribing, simple past and past participle circumscribed)

circumscribes (present singular third-person)
circumscribing (participle present)
circumscribed (participle past)
circumscribed (past)

From Latin circumscrībō, from circum (“around”) + scrībō (“write”). By surface analysis, circum- + scribe.

(geometry) To draw the smallest circle or higher-dimensional sphere that has (a polyhedron, polygon, etc.) in its interior.

описвам

to draw a circle, sphere, or higher-dimensional ball

piirtää ympyrä monikulmion kärkien kautta


annulus

Learned borrowing from Medieval Latin ānnulus, a misspelling of Latin ānulus (“ring, especially one worn on a finger”), from ānus (“ring”) (from Proto-Indo-European *h₁eh₂no- (“ring”)) + -ulus (diminutive suffix).
The plural form annuli is a learned borrowing from Medieval Latin ānnulī.

lbor

(geometry) The region in a plane between two concentric circles of different radii.


saddle

→ Japanese: サドル (sadoru)

Homer Tunnel
Milford Sound
Oxford English Dictionary

From Middle English sadel, from Old English sadol, from Proto-West Germanic *sadul, from Proto-Germanic *sadulaz (“saddle”). Further etymology uncertain, perhaps from Proto-Indo-European *sod-dʰlo-, from *sed- (“to sit”) + *-dʰlom (a variant of *-trom (suffix forming nouns denoting instruments or tools)), though the Oxford English Dictionary says this “presents formal difficulties”.
cognates
* Danish sadel
* Dutch zadel
* German Sattel
* Icelandic söðull
* Low German Sadel
* Russian седло́ (sedló)
* Saterland Frisian Soadel
* Scots sadil
* Swedish sadel
* West Frisian seal

saal

seat for a rider placed on the back of a horse or other animal

satula

something resembling a saddle in appearance or shape

satula

depression located along the axial trend of an anticline

Something resembling a saddle (sense 1) in appearance or shape.

(geometry) Synonym of saddle point (“a point in the range of a smooth function, every neighbourhood of which contains points on each side of its tangent plane”)


parallelepiped

/ˌpæɹəˌlɛləˈpaɪpɪd/

/ˌpæɹəlɛˈlɛpɪpɛd/

From Latin parallēlepipedum, from Ancient Greek παραλληλεπίπεδος (parallēlepípedos, “with parallel surfaces”), from παράλληλος (parállēlos, “parallel”) + ἐπίπεδος (epípedos, “plane”).

der

παραλληλεπίπεδος

A cuboid is a rectangular parallelepiped.

(geometry) A solid figure, having six faces, all parallelograms, all opposite faces being similar and parallel.


sector

Sector (Star Trek)
Sector (instrument)
sector

(geometry) Part of a circle, extending to the center; circular sector.


linear pair

(geometry) The two supplementary adjacent angles formed by two intersecting lines


line of centers

en-noun

line of centers (plural lines of centers)

(geometry) A line joining centers of figures.


polar

/ˈpəʊ̯lə(ɹ)/

[ˈpʰəʊ̯lə(ɹ)]

From Late Latin polāris, equivalent to pole + -ar.

(geometry) The line joining the points of contact of tangents drawn to meet a curve from a point called the pole of the line.


alternate angles

(geometry) the internal angles made by two (parallel) lines with a third, on opposite sides of it.

the internal angles made by two (parallel) lines with a third, on opposite sides of it.
If the parallels AB, CD, are cut by the line EF, intersecting at points G and H, then the angles AGH, GHD, are called alternate angles (as also are the angles BGH and GHC).


antiparallel

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(geometry) A line that forms equal angles with two other lines, but in opposite directions.


anharmonic

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(geometry) Describing the section of a line by four points, A, B, C, D, when their mutual distances are such that AB divided by CB is not equal to AD divided by CD.


cupola

Borrowed from Italian cupola, from Latin cūpula (“little tub”); from Latin cūpa, cuppa (“cup”); named for its resemblance to a cup turned over.

(geometry) A solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles.


quadrangle

/ˈkwɒdˌɹæŋ.ɡəl/

From Old French quadrangle, from Late Latin quadrangulum.

(geometry) A geometric shape with four angles and four straight sides; a four-sided polygon.


coincidence

coincidence (countable and uncountable, plural coincidences)

From French coïncidence. By surface analysis, coincide + -ence.

(geometry) A fixed point of a correspondence; a point of a variety corresponding to itself under a correspondence.


rotunda

Learned borrowing from Latin rotunda, from rotundus (“round”). In the architectural sense, from Sancta Maria Rotunda (the name for a church in the Pantheon).

(geometry) A form of cupola that has pentagons rather than squares or rectangles.


trapezohedron

trapezohedron (plural trapezohedra or trapezohedrons)

trapezohedra (plural)
trapezohedrons (plural)

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From trapezium + -hedron, with trapezium used in the US sense of a convex irregular quadrilateral.

The general form is called the tetragonal trapezohedron. In this case also there are both left- (Fig. 97) and right-handed (Fig. 98) forms.

1969, Carl W. Correns, translated by William D. Johns, Introduction to Mineralogy: Crystallography and Petrology, 2nd edition, page 40:

This trapezohedron, or antidiamond, is composed of ten quadrilaterals. In each quadrilateral, three of the angles are 108° and one is 36°.

2002, John Montroll, A Plethora of Polyhedra in Origami, page 105:

(geometry, crystallography) Any of a class of polyhedra that have kite-shaped faces and are dual polyhedra of antiprisms.

trapezopluredro

any of several forms of crystal with trapezia as faces


reflex

en-adj

reflex (comparative more reflex, superlative most reflex)

more reflex (comparative)
most reflex (superlative)

From Late Latin reflexus, past participle of reflectere (“to bend back”), equivalent to re- + flex. Photography sense is from noun sense meaning “reflection”. Compare English reflect.

A polygon is said to be convex when no one of its angles is reflex.

1878, James Maurice Wilson, Elementary Geometry, MacMillan, page 10:

An angle less than a right angle is said to be acute; one greater than a right angle but less than a straight angle is said to be obtuse; one greater than a straight angle but less than a perigon is said to be reflex or convex.

1895, David Eugen Smith, Wooster Woodruff Bernan, New Plane and Solid Geometry, page 7:

If the reflex region is the interior of the angle, the dihedral angle is reflex.

1958, Howard Fehr, “On Teaching Dihedral Angle and Steradian” in The Mathematics Teacher, v 51, National Council of Teachers of Mathematics, page 275

A reflex edge of a polyhedron is an edge where the inner dihedral angle subtended by two incident faces is greater than 180°.

1991, B. Falcidieno et al., “Configurable Representations in Feature-based Modelling”, in Eurographics '91: Proceedings, North-Holland, page 145:

We say that an angle is convex if it is not reflex.

2001, Esther M. Arkin et al., “On the Reflexivity of Point Sets”, in Algorithms and data structures: 7th International Workshop, WADS 2001: Proceedings, Springer, page 195:

P denotes a polygon and r the number of reflex vertices.

2004, Ana Paula Tomás and António Leslie Bajuelos, “Quadratic-Time Linear-Space Algorithms Generating Orthogonal Polygons with a Given Number of Vertices”, in Computational Science and Its Applications – ICCSA 2004 Proceedings, part 3, Springer, page 117

(geometry, of an angle) Having greater than 180 degrees but less than 360 degrees.


icosihemidodecahedron

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small icosihemidodecahedron
small icosihemidodecahedron

great icosihemidodecahedron
great icosihemidodecahedron

(geometry) Either of two polyhedra, the small icosihemidodecahedron and the great icosihemidodecahedron.


great icosihemidodecahedron

(geometry) A polyhedron having 26 faces, 30 vertices, 60 edges, six self-intersected faces, and six nonconvex faces.

大二十面半十二面体

だいにじゅうめんはんじゅうにめんたい


triangulate

en-verb

triangulate (third-person singular simple present triangulates, present participle triangulating, simple past and past participle triangulated)

triangulates (present singular third-person)
triangulating (participle present)
triangulated (participle past)
triangulated (past)

/tɹaɪˈæŋɡjəleɪt/

(geometry, computer graphics) To divide into triangles.


isosceles

Borrowed from Latin īsoscelēs, from Ancient Greek ἰσοσκελής (isoskelḗs, “equal-legged”), from ἴσος (ísos, “equal”) + σκέλος (skélos, “leg”) + -ής (-ḗs, adjective suffix).

affix

Upon each exterior side draw an Isosceles Triangle of 480 Fathoms.

1693, Abel Swall, transl., The New Method of Fortification, as Practised by Monsieur de Vavban, Engineer General of France, 2nd edition, "A New Treatise of Fortification", page 96:

A right double pyramid is isosceles when the extremities of the vertex-edge are at the same distance from the plane of the base.

1914, Henry Parker Manning, Geometry of Four Dimensions, page 204:

To prepare for the application of his method, Saccheri made use of a figure with which we are already acquainted. This is the isosceles quadrilateral with the two base angles right angles.

1945, Harold E. Wolfe, Introduction to Non-Euclidean Geometry, page 31:

The polygon advantageously is an isosceles trapezoid or rectangle with the pivotal connections between the deck or superstructure and four hulls respectively at its corners.

1965 April 8, Newton B. Dismukes, “Multihull vessels (Patent US3316873A)”, in Google Patents:

The flowers were stuck inside a flower pot that was shaped like an isosceles polygon with a rectangular "edge."

2019 January 23, Altered Book Lover, “Funky Flowers”, in Blogspot:

(geometry) Having (at least) two sides of equal length, used especially of a triangle or trapezoid.

հավասարասրուն

having two sides of equal length, used especially of an isosceles triangle or trapezoid


hexagonal

Nuts in engineering are generally hexagonal.

(geometry) Having six edges, or having a cross-section in the form of a hexagon.

ষড়ভুজাকৃতি

geometry: having six edges, or having a cross-section in the form of a hexagon


deltoid

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From Latin deltoideus, which was in turn from Ancient Greek adjective δελτοειδής (deltoeidḗs). See also: δέλτα (délta), the fourth letter of the Greek alphabet.

(geometry) A kite (quadrilateral having two pairs of edges of equal length, the edges of each pair touching each other at one end).

(geometry) A deltoid curve (hypocycloid with three cusps).


triangulation

en-noun

triangulation (countable and uncountable, plural triangulations)

/tɹʌɪaŋɡjʊˈleɪʃn̩/

/ˌtɹaɪˌæŋɡjəˈleɪʃən/

From Medieval Latin triangulātiōnem (“triangulation”), from triangulāre (“to triangulate”) + -tiōnem (suffix forming nouns relating to some actions or the results of actions). Triangulāre is derived from triangulāris (“triangular”), from triangulus (“triangular; triangle”), from trēs (“three”) + angulus (“angle; corner”). The English word is analysable as triangulate + -ion, and is cognate with French triangulation.

refn

An engraving from a 16th-century treatise by Levinus Hulsius (1546–1606).

Regular triangulations are a class in-between lifting and lexicographic triangulations. Their main draw-back in the context of this paper is that regularity depends on the specific realization and not only on the oriented matroid.

2002 March, Francisco Santos, “Triangulations of Oriented Matroids”, in Memoirs of the American Mathematical Society, volume 156, number 741, Providence, R.I.: American Mathematical Society, →ISSN, →OCLC, chapter 5 (Lifting Triangulations), page 59:

A triangulation of a point configuration #92;mathbf#123;A#125;#92;in#92;mathbb#123;R#125;ᵈ is a collection of d-simplices all of whose vertices are points in #92;mathbf#123;A#125; that satisfies the following two properties: 1. The union of all these simplices equals conv(#92;mathbf#123;A#125;). (Union Property) 2. Any pair of these simplices intersects in a common face (possibly empty). (Intersection Property)

2010, Jésus A[ntonio] De Loera, Jörg Rambau, Francisco Santos, “Triangulations in Mathematics”, in Triangulations: Structures for Algorithms and Applications (Algorithms and Computation in Mathematics; 25), Heidelberg, Dordrecht: Springer Verlag, →DOI, →ISBN, →ISSN, definition 1.0.1, page 1:

(countable, geometry) A subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices.


star polygon

(geometry) A geometric figure formed by connecting, with straight lines, every vertex of a p-sided regular polygon to the qth vertex beyond it (proceeding, consistently, either clockwise or anticlockwise).


ruled

(geometry, of a surface) Being a scroll; being such that through every point of S there is a straight line that lies on S.


hyperbolic

hyperbolic partial differential equation

A hyperbolic isometry f has two (distinct) fixed points on ∂ℋ.

2001, A. F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A. F. Costa, and E. Martínez, editors, Topics on Riemann Surfaces and Fuchsian Groups, Cambridge, page 6 http://books.google.com/books?id=RjbQdcP7DgwC&pg=PA6&dq=hyperbolic

(geometry, topology, of an automorphism) Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.


verf

The regular polyhedra include the five Platonic solids and the four Kepler-Poinsot solids. Their faces are all regular and congruent as well as their vertices and edges. Their verfs are regular also.

2012, Jonathan Bowers, Uniform Polyhedra and Other Three Dimensional Shapes:


perversion

en-noun

perversion (countable and uncountable, plural perversions)

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From Latin perversio, from pervertere (“corrupt”).


collinear

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(geometry, of three or more points) Lying on the same straight line.


truncate

en-verb

truncate (third-person singular simple present truncates, present participle truncating, simple past and past participle truncated)

truncates (present singular third-person)
truncating (participle present)
truncated (participle past)
truncated (past)

/ˈtɹʌŋˌkeɪt/

From Latin truncātus, perfect passive participle of truncō (“maim, reduce to a trunk”); see trunk as a verb.

بَتَرَ

shorten something as if by cutting off part of it

(geometry) To replace a corner by a plane (or to make a similar change to a crystal).


gree

From Middle English gre, from Old French gré, from Latin gradum (“step”). Compare degree. Doublet of grade.


affine transformation

en-noun

affine transformation (plural affine transformations)

An affine transformation does not in general preserve angles between lines or distances between points, but it does preserve ratios of distances between points lying on a straight line.

Given an affine space X, every affine transformation on X can be represented as the composition of a linear transformation on X and a translation of X.

Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation, shear and compositions of them in any combination and sequence.

Just as for plane transformations, we may show that the set of all affine transformations of space form a group.
Under an affine transformation of space, the image of a line is a line, and the image of a plane is a plane.

1965, P. S. Modenov, A. S. Parkhomenko, translated by Michael B. P. Slater, Geometric Transformations, Volume 1: Euclidean and Affine Transformations, Academic Press, page 145:

Theorem 15.2 A transformation such that the images of every three collinear points are themselves collinear is an affine transformation.
Are the affine transformations the same as those transformations for which the images of any three noncollinear points are themselves noncollinear? We shall see the answer is "Yes."

1982, George E. Martin, Transformation Geometry, Springer, page 169:

2004, Solomon Khmelnik, Computer Arithmetic of Geometrical Figures: Algorithms and Hardware Design, Mathematics in Computer Comp., page 8,
Most striking and well-known examples of affine transformation applications are computer tomography (see for instance [1]) and information compression for telecommunication systems (see [2]).
This book describes affine transformations (displacements, turns, scaling, shifts) of n-dimensional figures, where n=1,2,3,4.

(geometry, linear algebra) A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of an affine space: a mapping of an affine space onto itself that preserves both the dimension of any affine subspace and the ratio of the lengths of any pair of parallel line segments.

affine homomorphism

mappings from one space to a (generally) different one


affine geometry

affine geometry (countable and uncountable, plural affine geometries)

As an alternative to the axiomatic approach, affine geometry can be studied via the properties of affine transformations, which do not, in general, preserve distances or angles, but do preserve alignment of points and parallelism of lines.

The notion of parallelism remains central to affine geometry, in which the parallel postulate is replaced by Playfair's axiom, a version of the postulate that relies on neither distance nor angle size.

1940 [McGraw-Hill], E. T. Bell, The Development of Mathematics, 2017 [1992], Dover, page 265,
To include affine geometry, Menger (1935) imposed on lattices a reasonable axiom of parallelism.

1953 [Addison-Wesley], Dirk J. Struik, Lectures on Analytic and Projective Geometry, 2014, Dover, page 108,
And affine geometry itself can be considered as the geometry of all projective transformations which leave a line invariant.

Affine geometry is the geometry of an n-dimensional vector space together with its inhomogeneous linear structure.[…]Arbitrary affine linear maps take affine linear subspaces into one another, and also preserve collinearity of points, parallels and ratios of distances along parallel lines; all these are thus well defined notions of affine geometry.

2005, Miles Reid, Balazs Szendroi, Geometry and Topology, Cambridge University Press, page 62:

(geometry, uncountable) The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored.


truncation

truncation (countable and uncountable, plural truncations)

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From Late Latin truncātiō, from Latin truncāre, past participle truncātus (“to cut off”). See truncate.

(geometry) The replacement of a solid angle by a plane, or a similar operation in other dimensions.


toric

en-adj

toric (comparative more toric, superlative most toric)

more toric (comparative)
most toric (superlative)

Pertaining to or shaped like a torus, or a section of a torus; toroidal.

(geometry and algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.

(algebraic geometry, of a variety) Containing an algebraic torus as a dense subset, such that the group action of the torus on itself extends to the whole space; or, the embedding map taking the torus into the space. See Toric variety on Wikipedia.Wikipedia

(geometry, of a manifold, generalizing the case of toric varieties) (Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group.

(algebraic geometry, of a stack) Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus.

(commutative algebra, of an ideal) Generated by differences of monomials.


inscribe

en-verb

inscribe (third-person singular simple present inscribes, present participle inscribing, simple past and past participle inscribed)

inscribes (present singular third-person)
inscribing (participle present)
inscribed (participle past)
inscribed (past)

Borrowed from Latin īnscrībō, from in- (“upon”) and scrībō (“to write”).

(geometry) To draw a circle, sphere, etc. inside a polygon, polyhedron, etc. and tangent to all its sides.


tet

(geometry, engineering) A tetrahedron; a tetrahedral finite element.


superellipsoid

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(algebra, geometry) A closed surface, of which the sphere and ellipsoid are special cases, whose parametric equation is x = a.cos^(2/r)t, y = b.cos^(2/r)t, z = c.cos^(2/r)t.


superellipse

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(algebra, geometry) a geometric shape constituting a transition between a rectangle and a circle; a closed curve, of which the circle and ellipse are special cases, whose parametric equation is x = a.cos^(2/r)t, y = b.cos^(2/r)t


radical center

(geometry) A point at which the radical lines of three circles meet.


radial

en-adj

radial (comparative more radial, superlative most radial)

more radial (comparative)
most radial (superlative)

From Medieval Latin radiālis (“radial”), from Latin radius.

What is the relationship between arc length and radial length?

(geometry) Of, or relating to a radius (line joining to a geometric centre).

radial velocity


facultative

facultative (comparative more facultative, superlative most facultative)

more facultative (comparative)
most facultative (superlative)

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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.


gon

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

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


agonic

International Geomagnetic Reference Field

From Ancient Greek ᾰ̓- (ă-, 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

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(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

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(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.


interior angle

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


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


Archimedean solid

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.

sòlid arquimedià

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