Hadwiger's theorem

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


hypertorus

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

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


geometria analítica

(geometry) analytic geometry (ranch of mathematics that investigates coordinates of figures)


покшолма

head

покшолма • (pokšolma)

покш (pokš) + -л (-l) + -ма (-ma)
First coined by bishop Damaskin in 1785.


τραπέζιον

grc-noun

τρᾰπέζῐον • (trăpézĭon) n (genitive τρᾰπεζίου); second declension

τρᾰπέζῐον (canonical)
trăpézĭon (romanization)
τρᾰπεζίου (genitive)
τὸ τρᾰπέζῐον (nominative singular)
τρᾰπεζῐ́ω (dual nominative)
τᾰ̀ τρᾰπέζῐᾰ (nominative plural)
τοῦ τρᾰπεζῐ́ου (genitive singular)
τρᾰπεζῐ́οιν (dual genitive)
τρᾰπεζῐ́ων (genitive plural)
τῷ τρᾰπεζῐ́ῳ (dative singular)
τρᾰπεζῐ́οιν (dative dual)
τοῖς τρᾰπεζῐ́οις (dative plural)
τὸ τρᾰπέζῐον (accusative singular)
τρᾰπεζῐ́ω (accusative dual)
τᾰ̀ τρᾰπέζῐᾰ (accusative plural)
τρᾰπέζῐον (singular vocative)
τρᾰπεζῐ́ω (dual vocative)
τρᾰπέζῐᾰ (plural vocative)

Greek: τραπέζι (trapézi)

desc

→ Assyrian Neo-Aramaic: ܛܲܪܦܹܙܝܘܿܢ (ṭarpēzyōn)

→ Latin: trapezium (see there for further descendants)

From τράπεζα (trápeza, “table”) + -ιον (-ion, diminutive suffix)


लम्ब

lamba (romanization)
लम्बः (nominative singular)
लम्बौ (dual nominative)
लम्बा1 (dual nominative)
लम्बाः (nominative plural)
लम्बासः1 (nominative plural)
लम्बम् (accusative singular)
लम्बौ (accusative dual)
लम्बा1 (accusative dual)
लम्बान् (accusative plural)
लम्बेन (instrumental singular)
लम्बाभ्याम् (dual instrumental)
लम्बैः (instrumental plural)
लम्बेभिः1 (instrumental plural)
लम्बाय (dative singular)
लम्बाभ्याम् (dative dual)
लम्बेभ्यः (dative plural)
लम्बात् (ablative singular)
लम्बाभ्याम् (ablative dual)
लम्बेभ्यः (ablative plural)
लम्बस्य (genitive singular)
लम्बयोः (dual genitive)
लम्बानाम् (genitive plural)
लम्बे (locative singular)
लम्बयोः (dual locative)
लम्बेषु (locative plural)
लम्ब (singular vocative)
लम्बौ (dual vocative)
लम्बा1 (dual vocative)
लम्बाः (plural vocative)
लम्बासः1 (plural vocative)

→ Telugu: లంబము (lambamu)


-ângulo

pt-adj

-ângulo (adjective-forming suffix, feminine -ângula, masculine plural -ângulos, feminine plural -ângulas)

-ângula (feminine)
-ângulos (masculine plural)
-ângulas (feminine plural)

(geometry) -angle; -angular (having the given number angles)


-ângulo

pt-noun

-ângulo m (noun-forming suffix, plural -ângulos)

(geometry) -angle (shape with the given number of internal angles)


cięciwa

cięciwa (nominative singular)
cięciwy (nominative plural)
cięciwy (genitive singular)
cięciw (genitive plural)
cięciwie (dative singular)
cięciwom (dative plural)
cięciwę (accusative singular)
cięciwy (accusative plural)
cięciwą (instrumental singular)
cięciwami (instrumental plural)
cięciwie (locative singular)
cięciwach (locative plural)
cięciwo (singular vocative)
cięciwy (plural vocative)


Iitaka dimension

en-noun

Iitaka dimension (plural Iitaka dimensions)

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


antipolo

(geometry) antipole (position directly opposite)


antiprismático

pt-adj

antiprismático (feminine antiprismática, masculine plural antiprismáticos, feminine plural antiprismáticas)

antiprismática (feminine)
antiprismáticos (masculine plural)
antiprismáticas (feminine plural)

(geometry) antiprismatic (relating to antiprisms)


antiprismatico

it-adj

antiprismatico (feminine antiprismatica, masculine plural antiprismatici, feminine plural antiprismatiche)

antiprismatica (feminine)
antiprismatici (masculine plural)
antiprismatiche (feminine plural)


łamana

łamana (nominative singular)
łamane (nominative plural)
łamanej (genitive singular)
łamanych (genitive plural)
łamanej (dative singular)
łamanym (dative plural)
łamaną (accusative singular)
łamane (accusative plural)
łamaną (instrumental singular)
łamanymi (instrumental plural)
łamanej (locative singular)
łamanych (locative plural)
łamana (singular vocative)
łamane (plural vocative)

(nominalized, geometry) polyline (sequence of line segments)


isocrystal

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


Fano plane

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

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


arcossegundo

(geometry) arcsecond (a unit of angle: ¹⁄₃₆₀₀ of a degree)


व्यास

hi-noun

व्यास • (vyās) m

vyās (romanization)
व्यास (direct singular)
व्यास (direct plural)
व्यास (oblique singular)
व्यासों (oblique plural)
व्यास (singular vocative)
व्यासो (plural vocative)

hi:व्यास (ज्यामिति)


व्यास

head

व्यास • (vyās) m

mr-noun

व्यास • (vyās) m

vyās (romanization)
व्यास
व्यासा
व्यासां-
व्यासाला
व्यासांना
व्यासाने (ergative)
व्यासानं (ergative)
व्यासांनी (ergative)
व्यासाशी (instrumental)
व्यासांशी (instrumental)
Locative Note: -त  is a postposition.
व्यासाचा
व्यासाचे
व्यासाची
व्यासाच्या
व्यासाचं
व्यासांचा
व्यासांचे
व्यासांची
व्यासांच्या
व्यासांचं
व्यासांच्या

mr-decl-noun

masc cons-stem

Learned borrowing from Sanskrit व्यास (vyāsa).


व्यास

Telugu: వ్యాసము (vyāsamu)

(geometry) width, breadth, the diameter of a circle


Catalan surface

en-noun

Catalan surface (plural Catalan surfaces)

Named after the Belgian mathematician Eugène Charles Catalan.

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


hipercubo

(geometry) hypercube (an analogue of a cube in four or more dimensions)


sólido de Arquimedes

pt-noun

sólido de Arquimedes m (plural sólidos de Arquimedes)

(geometry) Archimedean solid (any of a class of semi-regular convex polyhedra composed of two or more types of regular polygon meeting in identical vertices)


circunscrever

pt-verb

circunscrever (first-person singular present circunscrevo, first-person singular preterite circunscrevi, past participle circunscrito)

circunscrevo (first-person present singular)
circunscrevi (first-person preterite singular)
circunscrito (participle past)
circunscrever (impersonal infinitive)
circunscrever (first-person infinitive singular)
circunscreveres (infinitive second-person singular)
circunscrever (infinitive singular third-person)
circunscrevermos (first-person infinitive plural)
circunscreverdes (infinitive plural second-person)
circunscreverem (infinitive plural third-person)
circunscrevendo (gerund)
circunscrito (masculine participle past singular)
circunscritos (masculine participle past plural)
circunscrita (feminine participle past singular)
circunscritas (feminine participle past plural)
circunscrevo (first-person indicative present singular)
circunscreves (indicative present second-person singular)
circunscreve (indicative present singular third-person)
circunscrevemos (first-person indicative plural present)
circunscreveis (indicative plural present second-person)
circunscrevem (indicative plural present third-person)
circunscrevia (first-person imperfect indicative singular)
circunscrevias (imperfect indicative second-person singular)
circunscrevia (imperfect indicative singular third-person)
circunscrevíamos (first-person imperfect indicative plural)
circunscrevíeis (imperfect indicative plural second-person)
circunscreviam (imperfect indicative plural third-person)
circunscrevi (first-person indicative preterite singular)
circunscreveste (indicative preterite second-person singular)
circunscreveu (indicative preterite singular third-person)
circunscrevemos (first-person indicative plural preterite)
circunscrevestes (indicative plural preterite second-person)
circunscreveram (indicative plural preterite third-person)
circunscrevera (first-person indicative pluperfect singular)
circunscreveras (indicative pluperfect second-person singular)
circunscrevera (indicative pluperfect singular third-person)
circunscrevêramos (first-person indicative pluperfect plural)
circunscrevêreis (indicative pluperfect plural second-person)
circunscreveram (indicative pluperfect plural third-person)
circunscreverei (first-person future indicative singular)
circunscreverás (future indicative second-person singular)
circunscreverá (future indicative singular third-person)
circunscreveremos (first-person future indicative plural)
circunscrevereis (future indicative plural second-person)
circunscreverão (future indicative plural third-person)
circunscreveria (conditional first-person singular)
circunscreverias (conditional second-person singular)
circunscreveria (conditional singular third-person)
circunscreveríamos (conditional first-person plural)
circunscreveríeis (conditional plural second-person)
circunscreveriam (conditional plural third-person)
circunscreva (first-person present singular subjunctive)
circunscrevas (present second-person singular subjunctive)
circunscreva (present singular subjunctive third-person)
circunscrevamos (first-person plural present subjunctive)
circunscrevais (plural present second-person subjunctive)
circunscrevam (plural present subjunctive third-person)
circunscrevesse (first-person imperfect singular subjunctive)
circunscrevesses (imperfect second-person singular subjunctive)
circunscrevesse (imperfect singular subjunctive third-person)
circunscrevêssemos (first-person imperfect plural subjunctive)
circunscrevêsseis (imperfect plural second-person subjunctive)
circunscrevessem (imperfect plural subjunctive third-person)
circunscrever (first-person future singular subjunctive)
circunscreveres (future second-person singular subjunctive)
circunscrever (future singular subjunctive third-person)
circunscrevermos (first-person future plural subjunctive)
circunscreverdes (future plural second-person subjunctive)
circunscreverem (future plural subjunctive third-person)
circunscreve (imperative second-person singular)
circunscreva (imperative singular third-person)
circunscrevamos (first-person imperative plural)
circunscrevei (imperative plural second-person)
circunscrevam (imperative plural third-person)
não circunscrevas (imperative negative second-person singular)
não circunscreva (imperative negative singular third-person)
não circunscrevamos (first-person imperative negative plural)
não circunscrevais (imperative negative plural second-person)
não circunscrevam (imperative negative plural third-person)
circumscrever (alternative)

Semi-learned borrowing from Latin circumscrībere.

slbor

(transitive, geometry) to circumscribe (draw a circle, sphere, or higher-dimensional ball)


círculo de Apolônio

pt-noun

círculo de Apolônio m (plural círculos de Apolônio)

(geometry) Apollonian circle (two sets of circles such that every circle in the first set intersects every circle in the second)


Brocard triangle

en-noun

Brocard triangle (plural Brocard triangles)

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

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


Brocard point

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


siksin

tlb

(physics, chemistry, geometry, neologism)


sagita

Learned borrowing from Latin sagitta (“arrow”). Doublet of sageta, an inherited form.


balisungsong

balingsúngsóng (canonical)
balisungsung (alternative)


degre

degres (plural)
degree (alternative)
degrece (alternative)
de-gre (alternative)
degrie (alternative)

English: degree

Scots: degree

Borrowed from Old French degré, degréz (hence the variant degrece); equivalent to de- + gre.

(geometry) An angular measurement amounting to 1/360 of a circle.


कोण

hi-noun

कोण • (koṇ) m

koṇ (romanization)
कोण (direct singular)
कोण (direct plural)
कोण (oblique singular)
कोणों (oblique plural)
कोण (singular vocative)
कोणो (plural vocative)


nonsqueezing

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

Relying on Gromov's nonsqueezing theorem for finite dimensional Hamiltonian systems, the argument is to approximate the solutions to the original infinite dimensional Hamiltonian system by a frequency truncated finite dimensional system, and then the nonsqueezing property is transferred to the infinite dimensional system.

2015, Sunghyun Hong, Soonsik Kwon, “Nonsqueezing property of the coupled KdV type system without Miura transform”, in arXiv:

(geometry) Being or relating to the theorem in symplectic geometry stating that one cannot embed a sphere into a cylinder via a symplectic map unless the radius of the sphere is less than or equal to the radius of the cylinder.


parallelohedron

en-noun

parallelohedron (plural parallelohedrons or parallelohedra)

parallelohedrons (plural)
parallelohedra (plural)

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

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


Hilbert curve

First described by the German mathematician David Hilbert in 1891.

(geometry) A continuous fractal space-filling curve.


geometrisk

geometrisk (positive)
geometriske (plural positive)
geometriske (positive)


geometrisk

head

geometrisk (neuter singular geometrisk, definite singular and plural geometriske)

geometrisk (neuter singular)
geometriske (definite plural singular)


ἄξων

grc-noun

ἄξων • (áxōn) m (genitive ἄξονος); third declension

áxōn (romanization)
ἄξονος (genitive)
ὁ ἄξων (nominative singular)
ἄξονε (dual nominative)
οἱ ἄξονες (nominative plural)
τοῦ ἄξονος (genitive singular)
ἀξόνοιν (dual genitive)
ἀξόνων (genitive plural)
τῷ ἄξονῐ (dative singular)
ἀξόνοιν (dative dual)
τοῖς ἄξοσῐ (dative plural)
ἄξοσῐν (dative plural)
toîs áxosĭ (dative plural)
toîs áxosĭn (dative plural)
τὸν ἄξονᾰ (accusative singular)
ἄξονε (accusative dual)
τοὺς ἄξονᾰς (accusative plural)
ἄξον (singular vocative)
ἄξονε (dual vocative)
ἄξονες (plural vocative)
αὔξων (alternative)

From Proto-Hellenic *aksōn, from Proto-Indo-European *h₂eḱs-. Cognate with Mycenaean Greek 𐀀𐀒𐀰𐀚 (a-ko-so-ne), Sanskrit अक्ष (akṣa, “axle, axis, balance beam”) and Latin axis.

cog

(geometry) an axis of a solid
of a conic section

(geometry) an axis of a solid
of a cylinder


firkant

head

firkant c (singular definite firkanten, plural indefinite firkanter)

firkanten (definite singular)
firkanter (indefinite plural)
firkant (indefinite nominative singular)
firkanten (definite nominative singular)
firkanter (indefinite nominative plural)
firkanterne (definite nominative plural)
firkants (genitive indefinite singular)
firkantens (definite genitive singular)
firkanters (genitive indefinite plural)
firkanternes (definite genitive plural)

(geometry) A quadrangle. (quadrilateral polygon)


firkant

firkant m (definite singular firkanten, indefinite plural firkanter, definite plural firkantene)

firkanten (definite singular)
firkanter (indefinite plural)
firkantene (definite plural)

(geometry) a quadrilateral (four-sided polygon)


firkant

firkant m (definite singular firkanten, indefinite plural firkantar, definite plural firkantane)

firkanten (definite singular)
firkantar (indefinite plural)
firkantane (definite plural)


hyperball

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

We find packing densities using congruent hyperballs and determine the smallest density upper bound of non-congruent hyperball packings generated by the above tilings..

2015, Jenő Szirmai, “Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings”, in arXiv:

(geometry) The set of all points that make up a hypersphere.


مارپیچ

fa-noun

مارپیچ • (mârpič) (plural مارپیچها (mârpič-hâ))

desctree

→ Ottoman Turkish: مارپیچ (marpıç), մարփըչ (marpıç), մարփուչ (marpuç), մարփուճ (marpuc) — Armeno-Turkish
Turkish: marpuç
→ Albanian: markuç
→ Armenian: մարփուճ (marpʻuč), մարփունջ (marpʻunǰ)
→ Bulgarian: марку́ч (markúč)
→ Romanian: marpici

[mɑːɾ.pʰeːt͡ʃ]

[mɑːɾ.pʰeːt͡ʃ]

[mɑːɾ.pʰeːt͡ʃ]

[mɔːɾ.pʰeːt͡ʃ]

[mɒːɹ.pʰiːt͡ʃ]


پیچه

→ Turkish: peçe


bituon

From Proto-Philippine *bituqən, from Proto-Malayo-Polynesian *bituqen, from Proto-Austronesian *bituqen. Compare Tagalog bituin, Tausug bituun.


hyperbolic geometry

en-noun

hyperbolic geometry (countable and uncountable, plural hyperbolic geometries)

The terminology was introduced in 1871 by Felix Klein, who classified some non-Euclidean geometries as hyperbolisch (“hyperbolic”), elliptisch (“elliptical”), and parabolisch (“parabolic”).

parallel postulate
parallel postulate#English

(geometry) A type of geometry that rejects the parallel postulate. Given a straight line L and a point p not on L, more than one straight line can be drawn through p without intersecting L.

(geometry) A non-Euclidean geometry, that features the hyperbola as geodesic, and has constant negative curvature


底邊

/ti²¹⁴⁻²¹ pi̯ɛn⁵⁵/

/tɐi̯³⁵ piːn⁵⁵/

/te⁴¹⁻⁴⁴ pĩ⁴⁴/

/tue⁵³⁻⁴⁴ pĩ⁴⁴/

/ti²¹⁴⁻²¹ pi̯ɛn⁵⁵/

/tɐi̯³⁵ piːn⁵⁵/

/te⁴¹⁻⁴⁴ pĩ⁴⁴/

/tue⁵³⁻⁴⁴ pĩ⁴⁴/


射線

/ʂɤ⁵¹⁻⁵³ ɕi̯ɛn⁵¹/

/sɛː²² siːn³³/

/sia¹¹ sũã²¹³/

/ʂɤ⁵¹⁻⁵³ ɕi̯ɛn⁵¹/

/sɛː²² siːn³³/

/sia¹¹ sũã²¹³/

(geometry) ray; half-line (Classifier: 條／条)


oktogon

oktogon m (definite singular oktogonen, indefinite plural oktogoner, definite plural oktogonene)

oktogonen (definite singular)
oktogoner (indefinite plural)
oktogonene (definite plural)


oktogon

oktogon m (definite singular oktogonen, indefinite plural oktogonar, definite plural oktogonane)

oktogonen (definite singular)
oktogonar (indefinite plural)
oktogonane (definite plural)


åttekant

åttekant m (definite singular åttekanten, indefinite plural åttekanter, definite plural åttekantene)

åttekanten (definite singular)
åttekanter (indefinite plural)
åttekantene (definite plural)


åttekant

åttekant m (definite singular åttekanten, indefinite plural åttekantar, definite plural åttekantane)

åttekanten (definite singular)
åttekantar (indefinite plural)
åttekantane (definite plural)


trọng tâm

[t͡ɕawŋ͡m˧˨ʔ təm˧˧]

[ʈawŋ͡m˨˩ʔ təm˧˧]

[ʈɔŋ˨˩ʔ təm˧˧]

[ʈawŋ͡m˨˩˨ təm˧˧]

Trọng tâm của bài học hôm nay là trọng tâm tam giác.

Today's lesson focuses on the centroid of triangles.


trực tâm

[t͡ɕɨk̚˧˨ʔ təm˧˧]

[ʈɨk̚˨˩ʔ təm˧˧]

[ʈɨk̚˨˩˨ təm˧˧]

Sino-Vietnamese word from 直心, composed of 直 (“straight; ortho-”) and 心 (“center”), perhaps a direct calque of a European word for "orthocenter". Unintuitively, this term has nothing to do with the point of intersection of the three đường trung trực (“segment-bisecting lines”) of the three sides of a triangle, the circumcenter, which does not have a common name in Vietnamese.


垂心

/ʈ͡ʂʰu̯eɪ̯³⁵ ɕin⁵⁵/

/sɵy̯²¹ sɐm⁵⁵/

/ʈ͡ʂʰu̯eɪ̯³⁵ ɕin⁵⁵/

/sɵy̯²¹ sɐm⁵⁵/


수심

Sino-Korean word from 垂心, from 垂 (“to dangle; to hang”) + 心 (“heart”)


cirkelafsnit

head

cirkelafsnit n (singular definite cirkelafsnittet, plural indefinite cirkelafsnit)

cirkelafsnittet (definite singular)
cirkelafsnit (indefinite plural)
cirkelafsnit (indefinite nominative singular)
cirkelafsnittet (definite nominative singular)
cirkelafsnit (indefinite nominative plural)
cirkelafsnittene (definite nominative plural)
cirkelafsnits (genitive indefinite singular)
cirkelafsnittets (definite genitive singular)
cirkelafsnits (genitive indefinite plural)
cirkelafsnittenes (definite genitive plural)


cirkeludsnit

cirkeludsnit n (singular definite cirkeludsnittet, plural indefinite cirkeludsnit)

cirkeludsnittet (definite singular)
cirkeludsnit (indefinite plural)
cirkeludsnit (indefinite nominative singular)
cirkeludsnittet (definite nominative singular)
cirkeludsnit (indefinite nominative plural)
cirkeludsnittene (definite nominative plural)
cirkeludsnits (genitive indefinite singular)
cirkeludsnittets (definite genitive singular)
cirkeludsnits (genitive indefinite plural)
cirkeludsnittenes (definite genitive plural)

(geometry) circular sector (area between two radii and circumference)


korde

korde c (singular definite korden, plural indefinite korder)

korden (definite singular)
korder (indefinite plural)
korde (indefinite nominative singular)
korden (definite nominative singular)
korder (indefinite nominative plural)
korderne (definite nominative plural)
kordes (genitive indefinite singular)
kordens (definite genitive singular)
korders (genitive indefinite plural)
kordernes (definite genitive plural)

(geometry) chord; straight line connecting points in a circle's circumference, sometimes excluding the diameter


jordakse

jordakse m (definite singular jordaksen)

(geometry) the Earth's axis, the axis of the Earth.


paral·lelepípede

ca-noun

paral·lelepípede m (plural paral·lelepípedes)


coreset

This coreset based learning approach can be applied for both real-time learning of small, varied data and fast learning of big data..

2015, Abhimanyu Dubey, Nikhil Naik, Dan Raviv, Rahul Sukthankar, Ramesh Raskar, “Coreset-Based Adaptive Tracking”, in arXiv:

(computational geometry) A small set of points that approximates the shape of a larger point set, in the sense that applying some geometric measure to the two sets (such as their minimum bounding box volume) results in approximately equal numbers.


tesseractic

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

(geometry) Relating to a tesseract; relating to four-dimensional space or to a 4-polytope


trisector

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

(geometry) A line or curve that trisects something.


spinode

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


정사각형

jeongsagakhyeong (romanization)
正四角形 (hanja)

[ˈt͡ɕɘ(ː)ŋsʰa̠ɡa̠cçʌ̹ŋ]


Houk

From Old Frisian hōk, from Proto-West Germanic *hōk, from Proto-Germanic *hōkaz. Cognates include West Frisian hoek and Dutch hoek.


橢圓

CJKV/code

Sino-Xenic (橢圓):
* → Japanese: 楕(だ)円(えん) (daen)
* → Korean: 타원(楕圓) (tawon)

/tʰu̯ɔ²¹⁴⁻²¹ ɥɛn³⁵/

/tʰu̯ɔ²¹⁴⁻²¹ ɥɑɻ³⁵/

/tʰɔː¹³ jyːn²¹/

/tʰuo³³⁻²¹ uoŋ⁵³/

/tʰo⁴¹⁻⁵⁵⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ¹³/

/tʰo⁵²⁻³⁵ ĩ⁵⁵/

/tʰu̯ɔ²¹⁴⁻²¹ ɥɛn³⁵/

/tʰu̯ɔ²¹⁴⁻²¹ ɥɑɻ³⁵/

/tʰɔː¹³ jyːn²¹/

/tʰuo³³⁻²¹ uoŋ⁵³/

/tʰo⁴¹⁻⁵⁵⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ¹³/

/tʰo⁵²⁻³⁵ ĩ⁵⁵/


starlikeness

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

(geometry) The property of being starlike.


rhombitrihexagonal

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

(geometry) Relating to a semiregular tiling of the Euclidean plane with one triangle, two squares, and one hexagon on each vertex.


isotoxal

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

(geometry, of a polytope or tiling) That has symmetries which act transitively on its edges.

edge-symmetric

having symmetries that act transitively on its edges


linea retta

From linea (“line”) + retta (“straight”).


плоштина

mk-noun

плоштина • (ploština) f

ploština (romanization)
плоштина (indefinite singular)
плоштини (indefinite plural)
плоштината (definite singular unspecified)
плоштините (definite plural unspecified)
плоштинава (definite proximal singular)
плоштиниве (definite plural proximal)
плоштинана (definite distal singular)
плоштинине (definite distal plural)
плоштино (singular vocative)
плоштини (plural vocative)


Inkreis

de-noun

Inkreis m (strong, genitive Inkreises, plural Inkreise)

Inkreises (genitive)
Inkreise (plural)
Inkreis (nominative singular)
Inkreise (definite nominative plural)
Inkreises (genitive singular)
Inkreise (definite genitive plural)
Inkreis (dative singular)
Inkreise (dative singular)
Inkreisen (dative definite plural)
Inkreis (accusative singular)
Inkreise (accusative definite plural)

[ˈɪnˌkʁaɪ̯s]


Inkreisradius

Inkreisradius m (strong, genitive Inkreisradius, plural Inkreisradien)

Inkreisradius (genitive)
Inkreisradien (plural)
Inkreisradius (nominative singular)
Inkreisradien (definite nominative plural)
Inkreisradius (genitive singular)
Inkreisradien (definite genitive plural)
Inkreisradius (dative singular)
Inkreisradien (dative definite plural)
Inkreisradius (accusative singular)
Inkreisradien (accusative definite plural)

[ˈɪnˌkʁaɪ̯sˌʁaːdi̯ʊs]

From Inkreis (“incircle”) + Radius (“radius”).


остар

mk-adj

остар • (ostar) (comparative поостар, superlative најостар, diminutive остричок, abstract noun острина)

ostar (romanization)
поостар (comparative)
најостар (superlative)
остричок (diminutive)
острина (abstract-noun)
остар (indefinite masculine)
остра (feminine indefinite)
остро (indefinite neuter)
остри (indefinite plural)
остриот (definite masculine unspecified)
острата (definite feminine unspecified)
острото (definite neuter unspecified)
острите (definite plural unspecified)
остриов (definite masculine proximal)
острава (definite feminine proximal)
острово (definite neuter proximal)
остриве (definite plural proximal)
острион (definite distal masculine)
острана (definite distal feminine)
остроно (definite distal neuter)
острине (definite distal plural)
поостар (indefinite masculine)
поостра (feminine indefinite)
поостро (indefinite neuter)
поостри (indefinite plural)
поостриот (definite masculine unspecified)
поострата (definite feminine unspecified)
поострото (definite neuter unspecified)
поострите (definite plural unspecified)
поостриов (definite masculine proximal)
поострава (definite feminine proximal)
поострово (definite neuter proximal)
поостриве (definite plural proximal)
поострион (definite distal masculine)
поострана (definite distal feminine)
поостроно (definite distal neuter)
поострине (definite distal plural)
најостар (indefinite masculine)
најостра (feminine indefinite)
најостро (indefinite neuter)
најостри (indefinite plural)
најостриот (definite masculine unspecified)
најострата (definite feminine unspecified)
најострото (definite neuter unspecified)
најострите (definite plural unspecified)
најостриов (definite masculine proximal)
најострава (definite feminine proximal)
најострово (definite neuter proximal)
најостриве (definite plural proximal)
најострион (definite distal masculine)
најострана (definite distal feminine)
најостроно (definite distal neuter)
најострине (definite distal plural)


geometria não-euclidiana

pt-noun

geometria não-euclidiana f (plural geometrias não-euclidianas)

non-Euclidean geometry
non-Euclidean geometry

(geometry) non-Euclidean geometry (any system of geometry not based on the set of axioms of Euclidean geometry)


scalebound

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

From scale + bound, coined by the mathematician Benoit Mandelbrot in a 1981 paper.

(geometry) Of an object: for which characteristic elements of scale, such as length and width, are few in number and each with a clearly distinct size.


heptaedro

[ˌɛ.ptɐˈɛ.ðɾu]

(geometry) heptahedron (polyhedron with seven faces)


nauhcampa nacaceh machiyotl

nāuhcāmpa nacaceh machiyōtl (canonical)
nauhcampanacacemachiotl (alternative)

From nāuhcāmpa (“in four directions”) + nacaceh (“cornered object”) + machiyōtl (“model, figure”).

compound

Figura de quatro angulos. nauhcampanacacemachiotl. y aſ / ſi delos de mas`

1555, Alonso de Molina, Aqui comienca vn vocabulario en la lengua castellana y mexicana, f. 123v:

A shape with four angles. nauhcampanacacemachiotl. and likewise for the rest of them.

(geometry) (it is) a plane figure or object with four straight angles; a square or rectangle.


idirlíne

head

idirlíne f (genitive singular idirlíne, nominative plural idirlínte)

idirlíne (genitive singular)
idirlínte (nominative plural)
idirlíne (indefinite nominative singular)
idirlínte (indefinite nominative plural)
a idirlíne (indefinite singular vocative)
a idirlínte (indefinite plural vocative)
idirlíne (genitive indefinite singular)
idirlínte (genitive indefinite plural)
idirlíne (dative indefinite singular)
idirlínte (dative indefinite plural)
an idirlíne (definite nominative singular)
na hidirlínte (definite nominative plural)
na hidirlíne (definite genitive singular)
na n-idirlínte (definite genitive plural)
leis an idirlíne (dative definite singular)
don idirlíne (dative definite singular)
leis na hidirlínte (dative definite plural)
idirlíne
n-idirlíne
hidirlíne


idirlínigh

idirlínigh (present analytic idirlíníonn, future analytic idirlíneoidh, verbal noun idirlíniú, past participle idirlínithe)

idirlíníonn (analytic present)
idirlíneoidh (analytic future)
idirlíniú (noun-from-verb)
idirlínithe (participle past)
idirlíniú (noun-from-verb)
idirlínithe (participle past)
idirlíním (first-person indicative present singular)
idirlíníonn tú (indicative present second-person singular)
idirlínír (indicative present second-person singular)
idirlíníonn sé (indicative present singular third-person)
sí (indicative present singular third-person)
idirlínímid (first-person indicative plural present)
idirlíníonn muid (first-person indicative plural present)
idirlíníonn sibh (indicative plural present second-person)
idirlíníonn siad (indicative plural present third-person)
idirlíníd (indicative plural present third-person)
a idirlíníonn (indicative present relative)
a idirlíníos (indicative present relative)
a n-idirlíníonn (indicative present relative)
idirlínítear (autonomous indicative present)
d'idirlínigh mé (first-person indicative past singular)
d'idirlíníos (first-person indicative past singular)
idirlínigh mé‡ (first-person indicative past singular)
idirlíníos‡ (first-person indicative past singular)
d'idirlínigh tú (indicative past second-person singular)
d'idirlínís (indicative past second-person singular)
idirlínigh tú‡ (indicative past second-person singular)
idirlínís‡ (indicative past second-person singular)
d'idirlínigh sé (indicative past singular third-person)
sí (indicative past singular third-person)
idirlínigh sé (indicative past singular third-person)
sí‡ (indicative past singular third-person)
d'idirlíníomar (first-person indicative past plural)
d'idirlínigh muid (first-person indicative past plural)
idirlíníomar‡ (first-person indicative past plural)
idirlínigh muid‡ (first-person indicative past plural)
d'idirlínigh sibh (indicative past plural second-person)
d'idirlíníobhair (indicative past plural second-person)
idirlínigh sibh‡ (indicative past plural second-person)
idirlíníobhair‡ (indicative past plural second-person)
d'idirlínigh siad (indicative past plural third-person)
d'idirlíníodar (indicative past plural third-person)
idirlínigh siad‡ (indicative past plural third-person)
idirlíníodar‡ (indicative past plural third-person)
a d'idirlínigh (indicative past relative)
ar idirlínigh (indicative past relative)
idirlíníodh (autonomous indicative past)
hidirlíníodh (autonomous indicative past)
d'idirlínínn (first-person habitual indicative past singular)
idirlínínn‡ (first-person habitual indicative past singular)
n-idirlínínn‡‡ (first-person habitual indicative past singular)
d'idirlíníteá (habitual indicative past second-person singular)
idirlíníteá‡ (habitual indicative past second-person singular)
n-idirlíníteá‡‡ (habitual indicative past second-person singular)
d'idirlíníodh sé (habitual indicative past singular third-person)
sí (habitual indicative past singular third-person)
idirlíníodh sé (habitual indicative past singular third-person)
sí‡ (habitual indicative past singular third-person)
n-idirlíníodh sé (habitual indicative past singular third-person)
sí‡‡ (habitual indicative past singular third-person)
d'idirlínímis (first-person habitual indicative past plural)
d'idirlíníodh muid (first-person habitual indicative past plural)
idirlínímis‡ (first-person habitual indicative past plural)
idirlíníodh muid‡ (first-person habitual indicative past plural)
n-idirlínímis‡‡ (first-person habitual indicative past plural)
n-idirlíníodh muid‡‡ (first-person habitual indicative past plural)
d'idirlíníodh sibh (habitual indicative past plural second-person)
idirlíníodh sibh‡ (habitual indicative past plural second-person)
n-idirlíníodh sibh‡‡ (habitual indicative past plural second-person)
d'idirlínídís (habitual indicative past plural third-person)
d'idirlíníodh siad (habitual indicative past plural third-person)
idirlínídís (habitual indicative past plural third-person)
idirlíníodh siad‡ (habitual indicative past plural third-person)
n-idirlínídís‡‡ (habitual indicative past plural third-person)
n-idirlíníodh siad‡‡ (habitual indicative past plural third-person)
a d'idirlíníodh (habitual indicative past relative)
a n-idirlíníodh (habitual indicative past relative)
d'idirlínítí (autonomous habitual indicative past)
idirlínítí‡ (autonomous habitual indicative past)
n-idirlínítí‡‡ (autonomous habitual indicative past)
idirlíneoidh mé (first-person future indicative singular)
idirlíneod (first-person future indicative singular)
idirlíneochaidh mé (first-person future indicative singular)
idirlíneoidh tú (future indicative second-person singular)
idirlíneoir (future indicative second-person singular)
idirlíneochaidh tú (future indicative second-person singular)
idirlíneoidh sé (future indicative singular third-person)
sí (future indicative singular third-person)
idirlíneochaidh sé (future indicative singular third-person)
idirlíneoimid (first-person future indicative plural)
idirlíneoidh muid (first-person future indicative plural)
idirlíneochaimid (first-person future indicative plural)
idirlíneochaidh muid (first-person future indicative plural)
idirlíneoidh sibh (future indicative plural second-person)
idirlíneochaidh sibh (future indicative plural second-person)
idirlíneoidh siad (future indicative plural third-person)
idirlíneoid (future indicative plural third-person)
idirlíneochaidh siad (future indicative plural third-person)
a idirlíneoidh (future indicative relative)
a idirlíneos (future indicative relative)
a idirlíneochaidh (future indicative relative)
a idirlíneochas (future indicative relative)
a n-idirlíneoidh (future indicative relative)
a n-idirlíneochaidh (future indicative relative)
idirlíneofar (autonomous future indicative)
idirlíneochar (autonomous future indicative)
d'idirlíneoinn (conditional first-person singular)
d'idirlíneochainn (conditional first-person singular)
idirlíneoinn‡ (conditional first-person singular)
idirlíneochainn^†‡ (conditional first-person singular)
n-idirlíneoinn‡‡ (conditional first-person singular)
n-idirlíneochainn^†‡‡ (conditional first-person singular)
d'idirlíneofá (conditional second-person singular)
d'idirlíneochthá (conditional second-person singular)
idirlíneofá‡ (conditional second-person singular)
idirlíneochthá^†‡ (conditional second-person singular)
n-idirlíneofá‡‡ (conditional second-person singular)
n-idirlíneochthá^†‡‡ (conditional second-person singular)
d'idirlíneodh sé (conditional singular third-person)
sí (conditional singular third-person)
d'idirlíneochadh sé (conditional singular third-person)
idirlíneodh sé (conditional singular third-person)
sí‡ (conditional singular third-person)
idirlíneochadh sé (conditional singular third-person)
sí^†‡ (conditional singular third-person)
n-idirlíneodh sé (conditional singular third-person)
sí‡‡ (conditional singular third-person)
n-idirlíneochadh sé (conditional singular third-person)
sí^†‡‡ (conditional singular third-person)
d'idirlíneoimis (conditional first-person plural)
d'idirlíneodh muid (conditional first-person plural)
d'idirlíneochaimis (conditional first-person plural)
d'idirlíneochadh muid (conditional first-person plural)
idirlíneoimis‡ (conditional first-person plural)
idirlíneodh muid‡ (conditional first-person plural)
idirlíneochaimis^†‡ (conditional first-person plural)
idirlíneochadh muid^†‡ (conditional first-person plural)
n-idirlíneoimis‡‡ (conditional first-person plural)
n-idirlíneodh muid‡‡ (conditional first-person plural)
n-idirlíneochaimis^†‡‡ (conditional first-person plural)
n-idirlíneochadh muid^†‡‡ (conditional first-person plural)
d'idirlíneodh sibh (conditional plural second-person)
d'idirlíneochadh sibh (conditional plural second-person)
idirlíneodh sibh‡ (conditional plural second-person)
idirlíneochadh sibh^†‡ (conditional plural second-person)
n-idirlíneodh sibh‡‡ (conditional plural second-person)
n-idirlíneochadh sibh^†‡‡ (conditional plural second-person)
d'idirlíneoidís (conditional plural third-person)
d'idirlíneodh siad (conditional plural third-person)
d'idirlíneochadh siad (conditional plural third-person)
idirlíneoidís‡ (conditional plural third-person)
idirlíneodh siad‡ (conditional plural third-person)
idirlíneochadh siad^†‡ (conditional plural third-person)
n-idirlíneoidís‡‡ (conditional plural third-person)
n-idirlíneodh siad‡‡ (conditional plural third-person)
n-idirlíneochadh siad^†‡‡ (conditional plural third-person)
a d'idirlíneodh (conditional relative)
a d'idirlíneochadh (conditional relative)
a n-idirlíneodh (conditional relative)
a n-idirlíneochadh (conditional relative)
d'idirlíneofaí (autonomous conditional)
d'idirlíneochthaí (autonomous conditional)
idirlíneofaí‡ (autonomous conditional)
idirlíneochthaí^†‡ (autonomous conditional)
n-idirlíneofaí‡‡ (autonomous conditional)
n-idirlíneochthaí^†‡‡ (autonomous conditional)
go n-idirlíní mé (first-person present singular subjunctive)
go n-idirlíníod (first-person present singular subjunctive)
go n-idirlíní tú (present second-person singular subjunctive)
go n-idirlínír (present second-person singular subjunctive)
go n-idirlíní sé (present singular subjunctive third-person)
sí (present singular subjunctive third-person)
go n-idirlínímid (first-person plural present subjunctive)
go n-idirlíní muid (first-person plural present subjunctive)
go n-idirlíní sibh (plural present second-person subjunctive)
go n-idirlíní siad (plural present subjunctive third-person)
go n-idirlíníd (plural present subjunctive third-person)
go n-idirlínítear (autonomous present subjunctive)
dá n-idirlínínn (first-person past singular subjunctive)
dá n-idirlíníteá (past second-person singular subjunctive)
dá n-idirlíníodh sé (past singular subjunctive third-person)
sí (past singular subjunctive third-person)
dá n-idirlínímis (first-person past plural subjunctive)
dá n-idirlíníodh muid (first-person past plural subjunctive)
dá n-idirlíníodh sibh (past plural second-person subjunctive)
dá n-idirlínídís (past plural subjunctive third-person)
dá n-idirlíníodh siad (past plural subjunctive third-person)
dá n-idirlínítí (autonomous past subjunctive)
idirlíním (first-person imperative singular)
idirlínigh (imperative second-person singular)
idirlíníodh sé (imperative singular third-person)
sí (imperative singular third-person)
idirlínímis (first-person imperative plural)
idirlínígí (imperative plural second-person)
idirlínídh (imperative plural second-person)
idirlínídís (imperative plural third-person)
idirlínítear (autonomous imperative)
idirlínigh
n-idirlínigh
hidirlínigh

From idirlíne (“interline; intercept”, noun) + -igh (verbal suffix).

affix

(algebraic geometry, transitive) to intercept


vuông

head

𣃱, 𣄇, 𣄖, 𩖫, 𪯵, 𪯾

vi-adj

𣃱, 𣄇, 𣄖, 𩖫, 𪯵, 𪯾

𣃱 (CJK)
𣄇 (CJK)
𣄖 (CJK)
𩖫 (CJK)
𪯵 (CJK)
𪯾 (CJK)

LL-Q9199 (vie)-Jessica Nguyen (Pamputt)-vuông.wav

Non-Sino-Vietnamese reading of Chinese 方 (“square”, SV: phương).

der

SV: <i class="Latn mention" lang="vi">phương</i>

vi-etym-sino

góc vuông

tam giác vuông

Đường thẳng d vuông góc với đường thẳng t.


sextantal

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


ピタゴラスの定理

ja-noun

^ピタゴラス の ていり

ピタゴラスの定理 (canonical)
Pitagorasu no teiri (romanization)

ピタゴラス (Pitagorasu, “Pythagoras”) + の (no, “'s”) + 定理 (teiri, “theorem”)

com

(geometry, functional analysis) the Pythagorean theorem


आस

→ Gujarati: આંસ (ā̃sa)

Etymology tree
Proto-Indo-European *h₂eǵ-?
Proto-Indo-European *-os?
Proto-Indo-European *h₂eḱs-
Proto-Indo-European *-os
Proto-Indo-Iranian *Háćšas
Sanskrit अक्ष॑ (ákṣa)
Prakrit 𑀅𑀓𑁆𑀔 (akkha)
Old Marathi 𑘁𑘽𑘏 (āṃkha)
Marathi आस (ās)
Inherited from Old Marathi *𑘁𑘽𑘭 (*āṃsa) (see 𑘁𑘽𑘏 (āṃkha)), from Prakrit *𑀅𑀘𑁆𑀙 (*accha) (see 𑀅𑀓𑁆𑀔 (akkha)), from Sanskrit अक्ष॑ (ákṣa). Doublet of अक्ष (akṣa).


geodetisk

head

geodetisk (neuter singular geodetisk, definite singular and plural geodetiske)

geodetisk (neuter singular)
geodetiske (definite plural singular)


uillinn istigh

uillinn istigh f (genitive singular uillinne istigh, nominative plural uilleannacha istigh)

uillinne istigh (genitive singular)
uilleannacha istigh (nominative plural)
uillinn istigh (indefinite nominative singular)
uilleannacha istigh (indefinite nominative plural)
a uillinn istigh (indefinite singular vocative)
a uilleannacha istigh (indefinite plural vocative)
uillinne istigh (genitive indefinite singular)
uilleannacha istigh (genitive indefinite plural)
uillinn istigh (dative indefinite singular)
uilleannacha istigh (dative indefinite plural)
an uillinn istigh (definite nominative singular)
na huilleannacha istigh (definite nominative plural)
na huillinne istigh (definite genitive singular)
na n-uilleannacha istigh (definite genitive plural)
leis an uillinn istigh (dative definite singular)
don uillinn istigh (dative definite singular)
leis na huilleannacha istigh (dative definite plural)
uillinn istigh
n-uillinn istigh
huillinn istigh


องศา

/ʔoŋ˧.saː˩˩˦/

From Sanskrit अंश (aṃśa, “fraction; part; portion; etc”). Cognate with Khmer អង្សា (ʼɑɑʼɑngsaa).

der

(geometry, geology, astronomy) degree: unit of angle, equal to ¹⁄₃₆₀ of a circle.


apeirogonal

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

(geometry) Having the form of an apeirogon.


จัตุรัส

th-noun

จัตุรัส • (jàt-dtù-ràt)


מחומש

he-noun

מְחֻמָּשִׁים

מחומש / מְחֻמָּשׁ • (m'khumásh) m (plural indefinite מחומשים / מְחֻמָּשִׁים)

מְחֻמָּשׁ (canonical)
m'khumásh (romanization)
מחומשים (indefinite plural)
מְחֻמָּשִׁים (indefinite plural)


tetradimensional

gl-adj

tetradimensional m or f (plural tetradimensionais)

(algebraic geometry, physics) four-dimensional


tetradimensional

es-adj

tetradimensional m or f (masculine and feminine plural tetradimensionales)

tetradimensionales (feminine masculine plural)


cuadridimensional

gl-adj

cuadridimensional m or f (plural cuadridimensionais)


cuadridimensional

es-adj

cuadridimensional m or f (masculine and feminine plural cuadridimensionales)

cuadridimensionales (feminine masculine plural)


góc bẹt

[ɣawk͡p̚˧˦ ʔɓɛt̚˧˨ʔ]

[ɣawk͡p̚˦˧˥ ʔɓɛt̚˨˩ʔ]

[ɣawk͡p̚˦˥ ʔɓɛk̚˨˩˨]


góc phụ nhau

[ɣawk͡p̚˧˦ fu˧˨ʔ ɲaw˧˧]

[ɣawk͡p̚˦˧˥ fʊw˨˩ʔ ɲaw˧˧]

[ɣawk͡p̚˦˥ fʊw˨˩˨ ɲa(ː)w˧˧]


góc kề nhau

[ɣawk͡p̚˧˦ ke˨˩ ɲaw˧˧]

[ɣawk͡p̚˦˧˥ kej˦˩ ɲaw˧˧]


góc bù nhau

[ɣawk͡p̚˧˦ ʔɓu˨˩ ɲaw˧˧]

[ɣawk͡p̚˦˧˥ ʔɓʊw˦˩ ɲaw˧˧]

[ɣawk͡p̚˦˥ ʔɓʊw˨˩ ɲa(ː)w˧˧]


góc đối đỉnh

head

góc đối đỉnh

vi-noun

góc đối đỉnh

[ɣawk͡p̚˧˦ ʔɗoj˧˦ ʔɗïŋ˧˩]

[ɣawk͡p̚˦˧˥ ʔɗoj˨˩˦ ʔɗɨn˧˨]

[ɣawk͡p̚˦˥ ʔɗoj˦˥ ʔɗɨn˨˩˦]

(geometry) vertical angles; opposite angles


đường tròn nội tiếp

[ʔɗɨəŋ˨˩ t͡ɕɔn˨˩ noj˧˨ʔ tiəp̚˧˦]

[ʔɗɨəŋ˦˩ ʈɔŋ˦˩ noj˨˩ʔ tiəp̚˦˧˥]

[ʔɗɨəŋ˨˩ ʈɔŋ˨˩ noj˨˩˨ tip̚˦˥]

Compare Chinese 內接圓 /内接圆 (nội tiếp viên), Japanese 内接円 (naisetsuen), Korean 내접원 (naejeobwon).


đường tròn bàng tiếp

[ʔɗɨəŋ˨˩ t͡ɕɔn˨˩ ʔɓaːŋ˨˩ tiəp̚˧˦]

[ʔɗɨəŋ˦˩ ʈɔŋ˦˩ ʔɓaːŋ˦˩ tiəp̚˦˧˥]

[ʔɗɨəŋ˨˩ ʈɔŋ˨˩ ʔɓaːŋ˨˩ tip̚˦˥]

Compare Japanese 傍接円 (bōsetsuen, bàng tiếp viên), Korean 방접원 (bangjeobwon).


đường tròn ngoại tiếp

[ʔɗɨəŋ˨˩ t͡ɕɔn˨˩ ŋwaːj˧˨ʔ tiəp̚˧˦]

[ʔɗɨəŋ˦˩ ʈɔŋ˦˩ ŋwaːj˨˩ʔ tiəp̚˦˧˥]

[ʔɗɨəŋ˨˩ ʈɔŋ˨˩ ŋwaːj˨˩˨ tip̚˦˥]

Compare Chinese 外接圓 /外接圆 (ngoại tiếp viên), Japanese 外接円 (gaisetsuen), Korean 외접원 (oejeobwon).


circumscribed circle

en-noun

circumscribed circle (plural circumscribed circles)


外接圓

/waɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/ŋɔːi̯²² t͡siːp̚³ jyːn²¹/

/waɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/ŋɔːi̯²² t͡siːp̚³ jyːn²¹/


외접원

[ˈø̞(ː)d͡ʑʌ̹bwʌ̹n]

Sino-Korean word from 外接圓, from 外 (“outside”) + 接 (“to connect”) + 圓 (“circle”)


外接円

ja-noun

外(がい)接(せつ)円(えん) • (gaisetsuen) ^(←ぐわいせつゑん (gwaisetwen)?)

外接円 (canonical)
gaisetsuen (romanization)
gwaisetwen (romanization)
ぐわいせつゑん (hiragana historical)

[ɡa̠ise̞t͡sɨẽ̞ɴ]


内接円

内(ない)接(せつ)円(えん) • (naisetsuen) ^(←ないせつゑん (naisetwen)?)

内接円 (canonical)
naisetsuen (romanization)
naisetwen (romanization)
ないせつゑん (hiragana historical)

ja:三角形の内接円と傍接円 ja:内接円


傍接円

傍(ぼう)接(せつ)円(えん) • (bōsetsuen) ^(←ばうせつゑん (bausetwen)?)

傍接円 (canonical)
bōsetsuen (romanization)
bausetwen (romanization)
ばうせつゑん (hiragana historical)

[bo̞ːse̞t͡sɨẽ̞ɴ]

ja:三角形の内接円と傍接円


inscribed circle

en-noun

inscribed circle (plural inscribed circles)


傍心

ja-noun

傍(ぼう)心(しん) • (bōshin) ^(←ばうしん (bausin)?)

傍心 (canonical)
bōshin (romanization)
bausin (romanization)
ばうしん (hiragana historical)


內接圓

/neɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/nɔːi̯²² t͡siːp̚³ jyːn²¹/

/neɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/nɔːi̯²² t͡siːp̚³ jyːn²¹/

(geometry) Alternative name for 內切圓／内切圆 (nèiqiēyuán, “incircle”).


내접원

[ˈnɛ(ː)d͡ʑʌ̹bwʌ̹n]

Sino-Korean word from 內接圓, from 內 (“inside”) + 接 (“to connect”) + 圓 (“circle”)


방접원

[pa̠ŋd͡ʑʌ̹bwʌ̹n]

Sino-Korean word from 傍接圓, from 傍 (“side”) + 接 (“to connect”) + 圓 (“circle”)


방심

Sino-Korean word from 傍心, from 傍 (“side”) + 心 (“center”)


외심

[ˈø̞(ː)ɕʰim]

Sino-Korean word from 外心, from 外 (“outside”) + 心 (“center”)


point of tangency

en-noun

point of tangency (plural points of tangency)

(geometry) The point where a tangent line and its curve meet

切點 /切点

the point where a tangent line and its curve meet


접선

[t͡ɕʌ̹ps͈ʌ̹n]

Sino-Korean word from 接線, from 接 (“to connect”) + 線 (“line”)


Frobenioid

Blend of Frobenius + monoid, since certain Frobenius morphisms between Frobenioids are analogues of the usual Frobenius morphism.

(arithmetic geometry) A category with some extra structure that generalizes the theory of line bundles on models of finite extensions of global fields.


Coxeter group

Named for British-born Canadian mathematician H. S. M. Coxeter (1907–2003).

We may ask in general which Coxeter groups arise as subgroups of a given Coxeter group. This question is of course far too general. However, there are Coxeter groups which arise canonically as subgroups of a given Coxeter group.

1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. de Clerck, editors, Finite Geometries and Combinatorics, page 277:

The above definitions, of Cayley graph, reflection, wall, half-space, folding, Bruhat order, etc., work for any Coxeter group.

2007, Michael B. Smythe, Julian Webster, “12: Discrete Spatial Models”, in Marco Aiello, Ian Pratt-Hartmann, Johan van Benthem, editors, Handbook of Spatial Logics, page 795:

The problem of classifying all reflective lattices of given rank is also of interest in its own right from the perspectives of Coxeter groups and arithmetic subgroups of O(n,1).

2012, Daniel Allcock, “The Reflective Lorentzian Lattices of Rank 3”, in Memoirs of the American Mathematical Society, number 1033, page vii:

(mathematics, geometry, group theory) Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.

Coxeter group
Harold Scott MacDonald Coxeter


vertex figure

1970, Harold Scott Macdonald Coxeter, Twisted Honeycombs, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics: Number 4, American Mathematical Society, page 14,
Thus the vertex figure of a polygon is the line-segment whose end-points are the vertex figures of the two edges at one vertex, the vertex figure of a polyhedron or tessellation {p, q} is the polygon {q} whose edges are the vertex figures of the q faces at one vertex, and the analogous "vertex figure" of the honeycomb of cubes (§1) is the polyhedron whose faces are the vertex figures of the eight cubic cells that come together at one vertex.

Now try to see which of these vertex figures cannot be continued to give a semiregular tiling of the whole plane.

1987, A. Gardiner, Mathematical Puzzling, Dover, published 1999, page 137:

At each vertex of a tessellation, the vertex figure is the polygon formed by joining in order the mid-points of all edges incident with the vertex. A tessellation of a surface for which all the participating polygons and vertex figures are regular and equal is termed a regular tessellation.

2004, Michael F. Worboys, Matt Duckham, GIS: A Computing Perspective, 2nd edition, page 188:

(geometry) The figure exposed when a corner of a polyhedron or polytope is sliced off.


ἰσοσκελής

ἰσοσκελής • (isoskelḗs) m or f (neuter ἰσοσκελές); third declension

isoskelḗs (romanization)
ἰσοσκελές (neuter)
ἰσοσκελής (feminine masculine nominative singular)
ἰσοσκελές (neuter nominative singular)
ἰσοσκελεῖ (dual feminine masculine nominative)
ἰσοσκελεῖ (dual neuter nominative)
ἰσοσκελεῖς (feminine masculine nominative plural)
ἰσοσκελῆ (neuter nominative plural)
ἰσοσκελοῦς (feminine genitive masculine singular)
ἰσοσκελοῦς (genitive neuter singular)
ἰσοσκελοῖν (dual feminine genitive masculine)
ἰσοσκελοῖν (dual genitive neuter)
ἰσοσκελῶν (feminine genitive masculine plural)
ἰσοσκελῶν (genitive neuter plural)
ἰσοσκελεῖ (dative feminine masculine singular)
ἰσοσκελεῖ (dative neuter singular)
ἰσοσκελοῖν (dative dual feminine masculine)
ἰσοσκελοῖν (dative dual neuter)
ἰσοσκελέσῐ (dative feminine masculine plural)
ἰσοσκελέσῐν (dative feminine masculine plural)
isoskelésĭ (dative feminine masculine plural)
isoskelésĭn (dative feminine masculine plural)
ἰσοσκελέσῐ (dative neuter plural)
ἰσοσκελέσῐν (dative neuter plural)
isoskelésĭ (dative neuter plural)
isoskelésĭn (dative neuter plural)
ἰσοσκελῆ (accusative feminine masculine singular)
ἰσοσκελές (accusative neuter singular)
ἰσοσκελεῖ (accusative dual feminine masculine)
ἰσοσκελεῖ (accusative dual neuter)
ἰσοσκελεῖς (accusative feminine masculine plural)
ἰσοσκελῆ (accusative neuter plural)
ἰσοσκελές (feminine masculine singular vocative)
ἰσοσκελές (neuter singular vocative)
ἰσοσκελεῖ (dual feminine masculine vocative)
ἰσοσκελεῖ (dual neuter vocative)
ἰσοσκελεῖς (feminine masculine plural vocative)
ἰσοσκελῆ (neuter plural vocative)
ἰσοσκελῶς (adverbial feminine masculine neuter)
ἰσοσκελέστερος (comparative feminine masculine neuter)
ἰσοσκελέστᾰτος (feminine masculine neuter superlative)

Latin: īsoscelēs

English: isosceles

Italian: isoscele

Sicilian: isòscili

ἴσος (ísos, “equal”) + σκέλος (skélos, “leg”) + -ής (-ḗs, adjective suffix)

affix

(geometry, of triangles) Having two sides equal, isosceles


σκαληνός

σκᾰληνός • (skălēnós) m (feminine σκᾰληνή, neuter σκᾰληνόν); first/second declension

σκᾰληνός (canonical)
skălēnós (romanization)
σκᾰληνή (feminine)
σκᾰληνόν (neuter)
σκᾰληνός (masculine nominative singular)
σκᾰληνή (feminine nominative singular)
σκᾰληνόν (neuter nominative singular)
σκᾰληνώ (dual masculine nominative)
σκᾰληνᾱ́ (dual feminine nominative)
σκᾰληνώ (dual neuter nominative)
σκᾰληνοί (masculine nominative plural)
σκᾰληναί (feminine nominative plural)
σκᾰληνᾰ́ (neuter nominative plural)
σκᾰληνοῦ (genitive masculine singular)
σκᾰληνῆς (feminine genitive singular)
σκᾰληνοῦ (genitive neuter singular)
σκᾰληνοῖν (dual genitive masculine)
σκᾰληναῖν (dual feminine genitive)
σκᾰληνοῖν (dual genitive neuter)
σκᾰληνῶν (genitive masculine plural)
σκᾰληνῶν (feminine genitive plural)
σκᾰληνῶν (genitive neuter plural)
σκᾰληνῷ (dative masculine singular)
σκᾰληνῇ (dative feminine singular)
σκᾰληνῷ (dative neuter singular)
σκᾰληνοῖν (dative dual masculine)
σκᾰληναῖν (dative dual feminine)
σκᾰληνοῖν (dative dual neuter)
σκᾰληνοῖς (dative masculine plural)
σκᾰληναῖς (dative feminine plural)
σκᾰληνοῖς (dative neuter plural)
σκᾰληνόν (accusative masculine singular)
σκᾰληνήν (accusative feminine singular)
σκᾰληνόν (accusative neuter singular)
σκᾰληνώ (accusative dual masculine)
σκᾰληνᾱ́ (accusative dual feminine)
σκᾰληνώ (accusative dual neuter)
σκᾰληνούς (accusative masculine plural)
σκᾰληνᾱ́ς (accusative feminine plural)
σκᾰληνᾰ́ (accusative neuter plural)
σκᾰληνέ (masculine singular vocative)
σκᾰληνή (feminine singular vocative)
σκᾰληνόν (neuter singular vocative)
σκᾰληνώ (dual masculine vocative)
σκᾰληνᾱ́ (dual feminine vocative)
σκᾰληνώ (dual neuter vocative)
σκᾰληνοί (masculine plural vocative)
σκᾰληναί (feminine plural vocative)
σκᾰληνᾰ́ (neuter plural vocative)
σκᾰληνῶς (adverbial feminine masculine neuter)
σκᾰληνότερος (comparative feminine masculine neuter)
σκᾰληνότᾰτος (feminine masculine neuter superlative)

→ Greek: σκαληνός (skalinós)

→ Latin: scalēnus

→ English: scalene, scalenus

Perhaps from Proto-Indo-European *(s)kel- (“to curve, bend”) or from *(s)kelH- (“to cut, carve, split”).

der

(geometry, of triangles) Having unequal sides, scalene.


σκαληνός

head

σκαληνός • (skalinós) m (feminine σκαληνή, neuter σκαληνό)

skalinós (romanization)
σκαληνή (feminine)
σκαληνό (neuter)
σκαληνός (masculine nominative singular)
σκαληνή (feminine nominative singular)
σκαληνό (neuter nominative singular)
σκαληνοί (masculine nominative plural)
σκαληνές (feminine nominative plural)
σκαληνά (neuter nominative plural)
σκαληνού (genitive masculine singular)
σκαληνής (feminine genitive singular)
σκαληνού (genitive neuter singular)
σκαληνών (genitive masculine plural)
σκαληνών (feminine genitive plural)
σκαληνών (genitive neuter plural)
σκαληνό (accusative masculine singular)
σκαληνή (accusative feminine singular)
σκαληνό (accusative neuter singular)
σκαληνούς (accusative masculine plural)
σκαληνές (accusative feminine plural)
σκαληνά (accusative neuter plural)
σκαληνέ (masculine singular vocative)
σκαληνή (feminine singular vocative)
σκαληνό (neuter singular vocative)
σκαληνοί (masculine plural vocative)
σκαληνές (feminine plural vocative)
σκαληνά (neuter plural vocative)

el-decl-adj-table

σκαληνός (skalinós)

σκαληνή (skaliní)

σκαληνό (skalinó)

σκαληνοί (skalinoí)

σκαληνές (skalinés)

σκαληνά (skaliná)

σκαληνού (skalinoú)

σκαληνής (skalinís)

σκαληνού (skalinoú)

σκαληνών (skalinón)

σκαληνών (skalinón)

σκαληνών (skalinón)

σκαληνό (skalinó)

σκαληνή (skaliní)

σκαληνό (skalinó)

σκαληνούς (skalinoús)

σκαληνές (skalinés)

σκαληνά (skaliná)

σκαληνέ (skaliné)

σκαληνή (skaliní)

σκαληνό (skalinó)

σκαληνοί (skalinoí)

σκαληνές (skalinés)

σκαληνά (skaliná)

(geometry) scalene, having unequal sides


trirettangolo

it-adj

trirettangolo (feminine trirettangola, masculine plural trirettangoli, feminine plural trirettangole)

trirettangola (feminine)
trirettangoli (masculine plural)
trirettangole (feminine plural)

From tri- (“three”) + rettangolo (“rectangle”).


oloid

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

Furthermore, we derive the expectations of the mean width, the surface area and the volume of the intersections of a fixed oloid and a moving ball, as well as of a fixed and a moving oloid.

2016, Uwe Bäsel, “The mean width of the oloid and integral geometric applications of it”, in arXiv:

(geometry) A three-dimensional curved geometric object, the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle.


storsirkel

storsirkel m (definite singular storsirkelen, indefinite plural storsirkler, definite plural storsirklene)

storsirkelen (definite singular)
storsirkler (indefinite plural)
storsirklene (definite plural)


storsirkel

storsirkel m (definite singular storsirkelen, indefinite plural storsirklar, definite plural storsirklane)

storsirkelen (definite singular)
storsirklar (indefinite plural)
storsirklane (definite plural)


triangolo ottuso

it-noun

triangolo ottuso m (plural triangoli ottusi)

triangoli ottusi (plural)
triangolo ottusangolo (alternative)

From triangolo (“triangle”) + ottuso (“obtuse”).


triangolo acuto

triangolo acuto m (plural triangoli acuti)

triangoli acuti (plural)
triangolo acutangolo (alternative)

From triangolo (“triangle”) + acuto (“acute”).


triangolo ottusangolo

triangolo ottusangolo m (plural triangoli ottusangoli)

From triangolo (“triangle”) + ottusangolo (“obtuse-angled”).

triangolo ottuso
triangolo ottuso#Italian

(geometry) Alternative form of triangolo ottuso


obtuza

Borrowed from English obtuse, French obtus, Italian ottuso, Spanish obtuso, from Latin obtūsus, past participle of obtundere.


triangolo acutangolo

triangolo acutangolo m (plural triangoli acutangoli)

From triangolo (“triangle”) + acutangolo (“acute-angled”).

(geometry) Alternative form of triangolo acuto


spirallikeness

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

(geometry) The property of being spirallike.


forskyde

head

forskyde (imperative forskyd, infinitive at forskyde, present tense forskyder, past tense forskød, perfect tense har forskudt)

forskyd (imperative)
at forskyde (infinitive)
forskyder (present)
forskød (past)
har forskudt (perfect)


rhombic dodecahedron

en-noun

rhombic dodecahedron (plural rhombic dodecahedra or rhombic dodecahedrons)

rhombic dodecahedra (plural)
rhombic dodecahedrons (plural)
rhombicdodecahedron (alternative)

Doing this we would find that the network which is dual to the space filling array of rhombic dodecahedra is the space filling array of tetrahedra and octahedra in which 12 edges meet at the vertices which fall at the centers of the original rhombic dodecahedra.

1990, [1978], Peter Pearce, Structure in Nature Is a Strategy for Design, page 5:

Crystallographers are familiar with the rhombic dodecahedron as a domain of reference with which to account for the growth and structure of natural crystals.

2007, Scott Eastham, American Dreamer: Bucky Fuller and the Sacred Geometry of Nature, page 160:

Rhombic Dodecahedrons appear as well in the unit cells of diamonds, four vertices absent with the chemical bonds on the remaining edges. The Rhombic Dodecahedron can be used to tessellate 3D space in a manner similar to the Cube.

2013, L. Dennis, Brender McNair, N. J. Woolf, L. H. Kauffman, “6: The Mereon 120/80 — Form Informing Function”, in Lynnclaire Dennis, Jytte Brender McNair, Louis H. Kauffman, editors, The Mereon Matrix: Unity, Perspective and Paradox, page 135:

(geometry) A convex polyhedron that has 12 congruent rhombic faces, 24 edges and 14 vertices of two types (eight 3-edge and six 4-edge) and is a Catalan solid.


Schläfli symbol

Schläfli symbol (plural Schläfli symbols)

From Schläfli (“a surname”) + symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895).

1995, Unnamed translator, E. B. Vinberg, Polynomial Group, article in M. Hazewinkel (editor), Encyclopaedia of Mathematics, Volume 4: Monge–Ampère Equation — Rings and Algebras, 2013, International Edition, page 481,
The three-dimensional regular polytopes (Platonic solids) have the following Schläfli symbols: the tetrahedron — {3, 3}, the cube — {4, 3}, the octahedron — {3, 4} — the dodecahedron — {5, 3}, and the icosahedron — {3, 5}.

For the regular tiling of squares the Schläfli symbol is {4,4}, indicating that there are four squares surrounding each vertex. And for the regular tiling of hexagons the Schläfli symbol is {6,3}, indicating that there are three hexagons surrounding each vertex.

2007, Michael E. Mortenson, chapter L, in Geometric Transformations for 3D Modeling, page 248:

The 24-cell has has 24 octahedral cells, 24 vertices, 96 triangular faces and 96 edges. Its Schläfli symbol is {3, 4, 3} from which we see that the vertex figure is a cube.

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

(geometry) A notation that recursively encodes certain properties of a specified regular polytope or tessellation.

Schläflin symboli

notation encoding certain properties of a regular polytope or tessellation


Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence.

1984, London Mathematical Society lecture note series, numbers 88-90, page 101:

The situation for 4-polytopes is fundamentally different from that for 3-dimensional polytopes. One reason is that there is no similar reduction of 4-polytope theory to a combinatorial (graph) problem.

2004, Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler, “16: Basic properties of convex polytopes”, in Joseph O'Rourke, Jacob E. Goodman, editors, Handbook of Discrete and Computational Geometry, 2nd edition, page 369:

For d = 4, Hamiltonian cycles in the regular 4-polytopes are known to exist. However, it seems that so far no decision about the existence or non-existence of 1-Hamiltonian surfaces in the 2-skeleton of any of the three sporadic regular 4-polytopes can be made, compare [120].

2011, Felix Effenberger, Hamiltonian Submanifolds of Regular Polytopes, page 40:


tetrakis hexahedron

tetrakis hexahedron (plural tetrakis hexahedra or tetrakis hexahedrons)

tetrakis hexahedra (plural)
tetrakis hexahedrons (plural)
tetrakishexahedron (alternative)
tetrakis-hexahedron (alternative)

Of the fourteen crystals examined, five were from the Karnul district (four tetrakis-hexahedra and one octahedron with tetrakis-hexahedron), one from Sambalpur (tetrakis-hexahedron with octahedron, four from Panna (much distorted tetrakis-hexahedra), the remaining four said to have come from Simla.

1904, Max Bauer, translated by L. J. Spencer, Precious Stones, volume 1, published 1968, page 154:

In the Isometric Tribe can be found the families of the Tetrakis Hexahedrons and Octahedrons, with their various descendants.

1909, Marshman Edward Wadsworth, Crystallography: An Elementary Manual for the Laboratory, page 189:

The goniometrical angle over the longer edges, that is, the angle between the normals to each pair of faces intersecting in a longer edge, in the cases of the two tetrakis hexahedra most frequently met with, has the following values:

1922, Alfred Edwin Howard Tutton, Crystallography and Practical Crystal Measurement, volume 1, page 153:

Not one exhibits plane faces or straight edges, being mostly distorted triakis-octahedra or tetrakis-hexahedra with finely striated curved faces.

1946, Mineralogical Society of America, Mineralogical Abstracts, volume 9, page 109:

Because of this another polyhedron – the tetrakis hexahedron – that has 14 vertices and 24 faces might be also a good model. The tetrakis hexahedron is slightly less regular than an icosahedron.

2010, Sumudu P. Leelananda, Yaping Feng, Pawel Gniewek, Andrzej Kloczkowski, Robert L. Jernigan, “6: Statistical Contact Potentials in Protein Coarse-Grained Modeling: From Pair to Multi-body Potentials”, in Andrzej Kolinski, editor, Multiscale Approaches to Protein Modeling, page 150:

(geometry) A Catalan solid that has 24 congruent triangular faces and 36 edges and can be imagined as a cube with a square pyramid on each face.

tetrakis-heksaedri

polyhedron with 24 triangular faces and 36 edges


Schlegel diagram

Schlegel diagram (plural Schlegel diagrams)

From Schlegel (“a surname”) + diagram, after German mathematician Victor Schlegel, who introduced the diagram in 1886.

The location of the point x₀ can always be chosen so that the edges in the Schlegel diagram can be drawn as non-intersecting straight lines.

1999, R. B. King, “1: Topology in Chemistry”, in D Bonchev, D.H Rouvray, editors, Chemical Topology: Introduction and Fundamentals, page 21:

Schlegel diagrams are a useful way to explore how these polyhedra can be linked (Hoppe and Köhler 1988).

2002, Ian David Brown, chapter L, in The Chemical Bond in Inorganic Chemistry: The Bond Valence, page 150:

These structures may all be represented on a planar surface by their Schlegel diagrams. A polyhedron Schlegel diagram is its networks of edges and vertices drawn in a special way: if you hold the polyhedron so close to your face that one of faces frames the entire polyhedron and you see all the other edges meeting inside that frame, then you have a Schlegel diagram.

2013, Arthur L. Loeb, “5: Polyhedra: Surfaces or Solids?”, in Marjorie Senechal, editor, Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination, page 69:

(geometry) A projection of a polytope from n-dimensional space to n-1 dimensions through a point beyond one of its faces; especially such a projection (itself represented in 2 dimensions) of a 3- or 4-dimensional polytope.


餘角

/y³⁵ t͡ɕi̯ɑʊ̯²¹⁴⁻²¹⁽⁴⁾/

/y³⁵ t͡ɕi̯aʊ̯ɻʷ²¹⁴⁻²¹⁽⁴⁾/

/jyː²¹ kɔːk̚³/

/y³⁵ t͡ɕi̯ɑʊ̯²¹⁴⁻²¹⁽⁴⁾/

/y³⁵ t͡ɕi̯aʊ̯ɻʷ²¹⁴⁻²¹⁽⁴⁾/

/jyː²¹ kɔːk̚³/


projektiopinta

projektiopinta (nominative singular)
projektiopinnat (nominative plural)
projektiopinta (accusative nominative singular)
projektiopinnat (accusative nominative plural)
projektiopinnan (accusative genitive singular)
projektiopinnat (accusative genitive plural)
projektiopinnan (genitive singular)
projektiopintojen (genitive plural)
projektiopintain (genitive plural rare)
projektiopintaa (partitive singular)
projektiopintoja (partitive plural)
projektiopinnassa (inessive singular)
projektiopinnoissa (inessive plural)
projektiopinnasta (elative singular)
projektiopinnoista (elative plural)
projektiopintaan (illative singular)
projektiopintoihin (illative plural)
projektiopinnalla (adessive singular)
projektiopinnoilla (adessive plural)
projektiopinnalta (ablative singular)
projektiopinnoilta (ablative plural)
projektiopinnalle (allative singular)
projektiopinnoille (allative plural)
projektiopintana (essive singular)
projektiopintoina (essive plural)
projektiopinnaksi (singular translative)
projektiopinnoiksi (plural translative)
projektiopinnatta (abessive singular)
projektiopinnoitta (abessive plural)
projektiopinnoin (instructive plural)
See the possessive forms below. (comitative)
projektiopintani (nominative singular)
projektiopintani (nominative plural)
projektiopintani (accusative nominative singular)
projektiopintani (accusative nominative plural)
projektiopintani (accusative genitive singular)
projektiopintani (accusative genitive plural)
projektiopintani (genitive singular)
projektiopintojeni (genitive plural)
projektiopintaini (genitive plural rare)
projektiopintaani (partitive singular)
projektiopintojani (partitive plural)
projektiopinnassani (inessive singular)
projektiopinnoissani (inessive plural)
projektiopinnastani (elative singular)
projektiopinnoistani (elative plural)
projektiopintaani (illative singular)
projektiopintoihini (illative plural)
projektiopinnallani (adessive singular)
projektiopinnoillani (adessive plural)
projektiopinnaltani (ablative singular)
projektiopinnoiltani (ablative plural)
projektiopinnalleni (allative singular)
projektiopinnoilleni (allative plural)
projektiopintanani (essive singular)
projektiopintoinani (essive plural)
projektiopinnakseni (singular translative)
projektiopinnoikseni (plural translative)
projektiopinnattani (abessive singular)
projektiopinnoittani (abessive plural)
projektiopintoineni (comitative plural)
projektiopintasi (nominative singular)
projektiopintasi (nominative plural)
projektiopintasi (accusative nominative singular)
projektiopintasi (accusative nominative plural)
projektiopintasi (accusative genitive singular)
projektiopintasi (accusative genitive plural)
projektiopintasi (genitive singular)
projektiopintojesi (genitive plural)
projektiopintaisi (genitive plural rare)
projektiopintaasi (partitive singular)
projektiopintojasi (partitive plural)
projektiopinnassasi (inessive singular)
projektiopinnoissasi (inessive plural)
projektiopinnastasi (elative singular)
projektiopinnoistasi (elative plural)
projektiopintaasi (illative singular)
projektiopintoihisi (illative plural)
projektiopinnallasi (adessive singular)
projektiopinnoillasi (adessive plural)
projektiopinnaltasi (ablative singular)
projektiopinnoiltasi (ablative plural)
projektiopinnallesi (allative singular)
projektiopinnoillesi (allative plural)
projektiopintanasi (essive singular)
projektiopintoinasi (essive plural)
projektiopinnaksesi (singular translative)
projektiopinnoiksesi (plural translative)
projektiopinnattasi (abessive singular)
projektiopinnoittasi (abessive plural)
projektiopintoinesi (comitative plural)
projektiopintamme (nominative singular)
projektiopintamme (nominative plural)
projektiopintamme (accusative nominative singular)
projektiopintamme (accusative nominative plural)
projektiopintamme (accusative genitive singular)
projektiopintamme (accusative genitive plural)
projektiopintamme (genitive singular)
projektiopintojemme (genitive plural)
projektiopintaimme (genitive plural rare)
projektiopintaamme (partitive singular)
projektiopintojamme (partitive plural)
projektiopinnassamme (inessive singular)
projektiopinnoissamme (inessive plural)
projektiopinnastamme (elative singular)
projektiopinnoistamme (elative plural)
projektiopintaamme (illative singular)
projektiopintoihimme (illative plural)
projektiopinnallamme (adessive singular)
projektiopinnoillamme (adessive plural)
projektiopinnaltamme (ablative singular)
projektiopinnoiltamme (ablative plural)
projektiopinnallemme (allative singular)
projektiopinnoillemme (allative plural)
projektiopintanamme (essive singular)
projektiopintoinamme (essive plural)
projektiopinnaksemme (singular translative)
projektiopinnoiksemme (plural translative)
projektiopinnattamme (abessive singular)
projektiopinnoittamme (abessive plural)
projektiopintoinemme (comitative plural)
projektiopintanne (nominative singular)
projektiopintanne (nominative plural)
projektiopintanne (accusative nominative singular)
projektiopintanne (accusative nominative plural)
projektiopintanne (accusative genitive singular)
projektiopintanne (accusative genitive plural)
projektiopintanne (genitive singular)
projektiopintojenne (genitive plural)
projektiopintainne (genitive plural rare)
projektiopintaanne (partitive singular)
projektiopintojanne (partitive plural)
projektiopinnassanne (inessive singular)
projektiopinnoissanne (inessive plural)
projektiopinnastanne (elative singular)
projektiopinnoistanne (elative plural)
projektiopintaanne (illative singular)
projektiopintoihinne (illative plural)
projektiopinnallanne (adessive singular)
projektiopinnoillanne (adessive plural)
projektiopinnaltanne (ablative singular)
projektiopinnoiltanne (ablative plural)
projektiopinnallenne (allative singular)
projektiopinnoillenne (allative plural)
projektiopintananne (essive singular)
projektiopintoinanne (essive plural)
projektiopinnaksenne (singular translative)
projektiopinnoiksenne (plural translative)
projektiopinnattanne (abessive singular)
projektiopinnoittanne (abessive plural)
projektiopintoinenne (comitative plural)
projektiopintansa (nominative singular)
projektiopintansa (nominative plural)
projektiopintansa (accusative nominative singular)
projektiopintansa (accusative nominative plural)
projektiopintansa (accusative genitive singular)
projektiopintansa (accusative genitive plural)
projektiopintansa (genitive singular)
projektiopintojensa (genitive plural)
projektiopintainsa (genitive plural rare)
projektiopintaansa (partitive singular)
projektiopintojaan (partitive plural)
projektiopintojansa (partitive plural)
projektiopinnassaan (inessive singular)
projektiopinnassansa (inessive singular)
projektiopinnoissaan (inessive plural)
projektiopinnoissansa (inessive plural)
projektiopinnastaan (elative singular)
projektiopinnastansa (elative singular)
projektiopinnoistaan (elative plural)
projektiopinnoistansa (elative plural)
projektiopintaansa (illative singular)
projektiopintoihinsa (illative plural)
projektiopinnallaan (adessive singular)
projektiopinnallansa (adessive singular)
projektiopinnoillaan (adessive plural)
projektiopinnoillansa (adessive plural)
projektiopinnaltaan (ablative singular)
projektiopinnaltansa (ablative singular)
projektiopinnoiltaan (ablative plural)
projektiopinnoiltansa (ablative plural)
projektiopinnalleen (allative singular)
projektiopinnallensa (allative singular)
projektiopinnoilleen (allative plural)
projektiopinnoillensa (allative plural)
projektiopintanaan (essive singular)
projektiopintanansa (essive singular)
projektiopintoinaan (essive plural)
projektiopintoinansa (essive plural)
projektiopinnakseen (singular translative)
projektiopinnaksensa (singular translative)
projektiopinnoikseen (plural translative)
projektiopinnoiksensa (plural translative)
projektiopinnattaan (abessive singular)
projektiopinnattansa (abessive singular)
projektiopinnoittaan (abessive plural)
projektiopinnoittansa (abessive plural)
projektiopintoineen (comitative plural)
projektiopintoinensa (comitative plural)

projektio (“projection”) + pinta (“surface”)

compound

(geometry) viewing surface (in orthographic projection, the surface onto which an object is projected)


projektiotaso

projektiotaso (nominative singular)
projektiotasot (nominative plural)
projektiotaso (accusative nominative singular)
projektiotasot (accusative nominative plural)
projektiotason (accusative genitive singular)
projektiotasot (accusative genitive plural)
projektiotason (genitive singular)
projektiotasojen (genitive plural)
projektiotasoa (partitive singular)
projektiotasoja (partitive plural)
projektiotasossa (inessive singular)
projektiotasoissa (inessive plural)
projektiotasosta (elative singular)
projektiotasoista (elative plural)
projektiotasoon (illative singular)
projektiotasoihin (illative plural)
projektiotasolla (adessive singular)
projektiotasoilla (adessive plural)
projektiotasolta (ablative singular)
projektiotasoilta (ablative plural)
projektiotasolle (allative singular)
projektiotasoille (allative plural)
projektiotasona (essive singular)
projektiotasoina (essive plural)
projektiotasoksi (singular translative)
projektiotasoiksi (plural translative)
projektiotasotta (abessive singular)
projektiotasoitta (abessive plural)
projektiotasoin (instructive plural)
See the possessive forms below. (comitative)
projektiotasoni (nominative singular)
projektiotasoni (nominative plural)
projektiotasoni (accusative nominative singular)
projektiotasoni (accusative nominative plural)
projektiotasoni (accusative genitive singular)
projektiotasoni (accusative genitive plural)
projektiotasoni (genitive singular)
projektiotasojeni (genitive plural)
projektiotasoani (partitive singular)
projektiotasojani (partitive plural)
projektiotasossani (inessive singular)
projektiotasoissani (inessive plural)
projektiotasostani (elative singular)
projektiotasoistani (elative plural)
projektiotasooni (illative singular)
projektiotasoihini (illative plural)
projektiotasollani (adessive singular)
projektiotasoillani (adessive plural)
projektiotasoltani (ablative singular)
projektiotasoiltani (ablative plural)
projektiotasolleni (allative singular)
projektiotasoilleni (allative plural)
projektiotasonani (essive singular)
projektiotasoinani (essive plural)
projektiotasokseni (singular translative)
projektiotasoikseni (plural translative)
projektiotasottani (abessive singular)
projektiotasoittani (abessive plural)
projektiotasoineni (comitative plural)
projektiotasosi (nominative singular)
projektiotasosi (nominative plural)
projektiotasosi (accusative nominative singular)
projektiotasosi (accusative nominative plural)
projektiotasosi (accusative genitive singular)
projektiotasosi (accusative genitive plural)
projektiotasosi (genitive singular)
projektiotasojesi (genitive plural)
projektiotasoasi (partitive singular)
projektiotasojasi (partitive plural)
projektiotasossasi (inessive singular)
projektiotasoissasi (inessive plural)
projektiotasostasi (elative singular)
projektiotasoistasi (elative plural)
projektiotasoosi (illative singular)
projektiotasoihisi (illative plural)
projektiotasollasi (adessive singular)
projektiotasoillasi (adessive plural)
projektiotasoltasi (ablative singular)
projektiotasoiltasi (ablative plural)
projektiotasollesi (allative singular)
projektiotasoillesi (allative plural)
projektiotasonasi (essive singular)
projektiotasoinasi (essive plural)
projektiotasoksesi (singular translative)
projektiotasoiksesi (plural translative)
projektiotasottasi (abessive singular)
projektiotasoittasi (abessive plural)
projektiotasoinesi (comitative plural)
projektiotasomme (nominative singular)
projektiotasomme (nominative plural)
projektiotasomme (accusative nominative singular)
projektiotasomme (accusative nominative plural)
projektiotasomme (accusative genitive singular)
projektiotasomme (accusative genitive plural)
projektiotasomme (genitive singular)
projektiotasojemme (genitive plural)
projektiotasoamme (partitive singular)
projektiotasojamme (partitive plural)
projektiotasossamme (inessive singular)
projektiotasoissamme (inessive plural)
projektiotasostamme (elative singular)
projektiotasoistamme (elative plural)
projektiotasoomme (illative singular)
projektiotasoihimme (illative plural)
projektiotasollamme (adessive singular)
projektiotasoillamme (adessive plural)
projektiotasoltamme (ablative singular)
projektiotasoiltamme (ablative plural)
projektiotasollemme (allative singular)
projektiotasoillemme (allative plural)
projektiotasonamme (essive singular)
projektiotasoinamme (essive plural)
projektiotasoksemme (singular translative)
projektiotasoiksemme (plural translative)
projektiotasottamme (abessive singular)
projektiotasoittamme (abessive plural)
projektiotasoinemme (comitative plural)
projektiotasonne (nominative singular)
projektiotasonne (nominative plural)
projektiotasonne (accusative nominative singular)
projektiotasonne (accusative nominative plural)
projektiotasonne (accusative genitive singular)
projektiotasonne (accusative genitive plural)
projektiotasonne (genitive singular)
projektiotasojenne (genitive plural)
projektiotasoanne (partitive singular)
projektiotasojanne (partitive plural)
projektiotasossanne (inessive singular)
projektiotasoissanne (inessive plural)
projektiotasostanne (elative singular)
projektiotasoistanne (elative plural)
projektiotasoonne (illative singular)
projektiotasoihinne (illative plural)
projektiotasollanne (adessive singular)
projektiotasoillanne (adessive plural)
projektiotasoltanne (ablative singular)
projektiotasoiltanne (ablative plural)
projektiotasollenne (allative singular)
projektiotasoillenne (allative plural)
projektiotasonanne (essive singular)
projektiotasoinanne (essive plural)
projektiotasoksenne (singular translative)
projektiotasoiksenne (plural translative)
projektiotasottanne (abessive singular)
projektiotasoittanne (abessive plural)
projektiotasoinenne (comitative plural)
projektiotasonsa (nominative singular)
projektiotasonsa (nominative plural)
projektiotasonsa (accusative nominative singular)
projektiotasonsa (accusative nominative plural)
projektiotasonsa (accusative genitive singular)
projektiotasonsa (accusative genitive plural)
projektiotasonsa (genitive singular)
projektiotasojensa (genitive plural)
projektiotasoaan (partitive singular)
projektiotasoansa (partitive singular)
projektiotasojaan (partitive plural)
projektiotasojansa (partitive plural)
projektiotasossaan (inessive singular)
projektiotasossansa (inessive singular)
projektiotasoissaan (inessive plural)
projektiotasoissansa (inessive plural)
projektiotasostaan (elative singular)
projektiotasostansa (elative singular)
projektiotasoistaan (elative plural)
projektiotasoistansa (elative plural)
projektiotasoonsa (illative singular)
projektiotasoihinsa (illative plural)
projektiotasollaan (adessive singular)
projektiotasollansa (adessive singular)
projektiotasoillaan (adessive plural)
projektiotasoillansa (adessive plural)
projektiotasoltaan (ablative singular)
projektiotasoltansa (ablative singular)
projektiotasoiltaan (ablative plural)
projektiotasoiltansa (ablative plural)
projektiotasolleen (allative singular)
projektiotasollensa (allative singular)
projektiotasoilleen (allative plural)
projektiotasoillensa (allative plural)
projektiotasonaan (essive singular)
projektiotasonansa (essive singular)
projektiotasoinaan (essive plural)
projektiotasoinansa (essive plural)
projektiotasokseen (singular translative)
projektiotasoksensa (singular translative)
projektiotasoikseen (plural translative)
projektiotasoiksensa (plural translative)
projektiotasottaan (abessive singular)
projektiotasottansa (abessive singular)
projektiotasoittaan (abessive plural)
projektiotasoittansa (abessive plural)
projektiotasoineen (comitative plural)
projektiotasoinensa (comitative plural)

projektio (“projection”) + taso (“plane”)


projektiokuva

projektiokuva (nominative singular)
projektiokuvat (nominative plural)
projektiokuva (accusative nominative singular)
projektiokuvat (accusative nominative plural)
projektiokuvan (accusative genitive singular)
projektiokuvat (accusative genitive plural)
projektiokuvan (genitive singular)
projektiokuvien (genitive plural)
projektiokuvain (genitive plural rare)
projektiokuvaa (partitive singular)
projektiokuvia (partitive plural)
projektiokuvassa (inessive singular)
projektiokuvissa (inessive plural)
projektiokuvasta (elative singular)
projektiokuvista (elative plural)
projektiokuvaan (illative singular)
projektiokuviin (illative plural)
projektiokuvalla (adessive singular)
projektiokuvilla (adessive plural)
projektiokuvalta (ablative singular)
projektiokuvilta (ablative plural)
projektiokuvalle (allative singular)
projektiokuville (allative plural)
projektiokuvana (essive singular)
projektiokuvina (essive plural)
projektiokuvaksi (singular translative)
projektiokuviksi (plural translative)
projektiokuvatta (abessive singular)
projektiokuvitta (abessive plural)
projektiokuvin (instructive plural)
See the possessive forms below. (comitative)
projektiokuvani (nominative singular)
projektiokuvani (nominative plural)
projektiokuvani (accusative nominative singular)
projektiokuvani (accusative nominative plural)
projektiokuvani (accusative genitive singular)
projektiokuvani (accusative genitive plural)
projektiokuvani (genitive singular)
projektiokuvieni (genitive plural)
projektiokuvaini (genitive plural rare)
projektiokuvaani (partitive singular)
projektiokuviani (partitive plural)
projektiokuvassani (inessive singular)
projektiokuvissani (inessive plural)
projektiokuvastani (elative singular)
projektiokuvistani (elative plural)
projektiokuvaani (illative singular)
projektiokuviini (illative plural)
projektiokuvallani (adessive singular)
projektiokuvillani (adessive plural)
projektiokuvaltani (ablative singular)
projektiokuviltani (ablative plural)
projektiokuvalleni (allative singular)
projektiokuvilleni (allative plural)
projektiokuvanani (essive singular)
projektiokuvinani (essive plural)
projektiokuvakseni (singular translative)
projektiokuvikseni (plural translative)
projektiokuvattani (abessive singular)
projektiokuvittani (abessive plural)
projektiokuvineni (comitative plural)
projektiokuvasi (nominative singular)
projektiokuvasi (nominative plural)
projektiokuvasi (accusative nominative singular)
projektiokuvasi (accusative nominative plural)
projektiokuvasi (accusative genitive singular)
projektiokuvasi (accusative genitive plural)
projektiokuvasi (genitive singular)
projektiokuviesi (genitive plural)
projektiokuvaisi (genitive plural rare)
projektiokuvaasi (partitive singular)
projektiokuviasi (partitive plural)
projektiokuvassasi (inessive singular)
projektiokuvissasi (inessive plural)
projektiokuvastasi (elative singular)
projektiokuvistasi (elative plural)
projektiokuvaasi (illative singular)
projektiokuviisi (illative plural)
projektiokuvallasi (adessive singular)
projektiokuvillasi (adessive plural)
projektiokuvaltasi (ablative singular)
projektiokuviltasi (ablative plural)
projektiokuvallesi (allative singular)
projektiokuvillesi (allative plural)
projektiokuvanasi (essive singular)
projektiokuvinasi (essive plural)
projektiokuvaksesi (singular translative)
projektiokuviksesi (plural translative)
projektiokuvattasi (abessive singular)
projektiokuvittasi (abessive plural)
projektiokuvinesi (comitative plural)
projektiokuvamme (nominative singular)
projektiokuvamme (nominative plural)
projektiokuvamme (accusative nominative singular)
projektiokuvamme (accusative nominative plural)
projektiokuvamme (accusative genitive singular)
projektiokuvamme (accusative genitive plural)
projektiokuvamme (genitive singular)
projektiokuviemme (genitive plural)
projektiokuvaimme (genitive plural rare)
projektiokuvaamme (partitive singular)
projektiokuviamme (partitive plural)
projektiokuvassamme (inessive singular)
projektiokuvissamme (inessive plural)
projektiokuvastamme (elative singular)
projektiokuvistamme (elative plural)
projektiokuvaamme (illative singular)
projektiokuviimme (illative plural)
projektiokuvallamme (adessive singular)
projektiokuvillamme (adessive plural)
projektiokuvaltamme (ablative singular)
projektiokuviltamme (ablative plural)
projektiokuvallemme (allative singular)
projektiokuvillemme (allative plural)
projektiokuvanamme (essive singular)
projektiokuvinamme (essive plural)
projektiokuvaksemme (singular translative)
projektiokuviksemme (plural translative)
projektiokuvattamme (abessive singular)
projektiokuvittamme (abessive plural)
projektiokuvinemme (comitative plural)
projektiokuvanne (nominative singular)
projektiokuvanne (nominative plural)
projektiokuvanne (accusative nominative singular)
projektiokuvanne (accusative nominative plural)
projektiokuvanne (accusative genitive singular)
projektiokuvanne (accusative genitive plural)
projektiokuvanne (genitive singular)
projektiokuvienne (genitive plural)
projektiokuvainne (genitive plural rare)
projektiokuvaanne (partitive singular)
projektiokuvianne (partitive plural)
projektiokuvassanne (inessive singular)
projektiokuvissanne (inessive plural)
projektiokuvastanne (elative singular)
projektiokuvistanne (elative plural)
projektiokuvaanne (illative singular)
projektiokuviinne (illative plural)
projektiokuvallanne (adessive singular)
projektiokuvillanne (adessive plural)
projektiokuvaltanne (ablative singular)
projektiokuviltanne (ablative plural)
projektiokuvallenne (allative singular)
projektiokuvillenne (allative plural)
projektiokuvananne (essive singular)
projektiokuvinanne (essive plural)
projektiokuvaksenne (singular translative)
projektiokuviksenne (plural translative)
projektiokuvattanne (abessive singular)
projektiokuvittanne (abessive plural)
projektiokuvinenne (comitative plural)
projektiokuvansa (nominative singular)
projektiokuvansa (nominative plural)
projektiokuvansa (accusative nominative singular)
projektiokuvansa (accusative nominative plural)
projektiokuvansa (accusative genitive singular)
projektiokuvansa (accusative genitive plural)
projektiokuvansa (genitive singular)
projektiokuviensa (genitive plural)
projektiokuvainsa (genitive plural rare)
projektiokuvaansa (partitive singular)
projektiokuviaan (partitive plural)
projektiokuviansa (partitive plural)
projektiokuvassaan (inessive singular)
projektiokuvassansa (inessive singular)
projektiokuvissaan (inessive plural)
projektiokuvissansa (inessive plural)
projektiokuvastaan (elative singular)
projektiokuvastansa (elative singular)
projektiokuvistaan (elative plural)
projektiokuvistansa (elative plural)
projektiokuvaansa (illative singular)
projektiokuviinsa (illative plural)
projektiokuvallaan (adessive singular)
projektiokuvallansa (adessive singular)
projektiokuvillaan (adessive plural)
projektiokuvillansa (adessive plural)
projektiokuvaltaan (ablative singular)
projektiokuvaltansa (ablative singular)
projektiokuviltaan (ablative plural)
projektiokuviltansa (ablative plural)
projektiokuvalleen (allative singular)
projektiokuvallensa (allative singular)
projektiokuvilleen (allative plural)
projektiokuvillensa (allative plural)
projektiokuvanaan (essive singular)
projektiokuvanansa (essive singular)
projektiokuvinaan (essive plural)
projektiokuvinansa (essive plural)
projektiokuvakseen (singular translative)
projektiokuvaksensa (singular translative)
projektiokuvikseen (plural translative)
projektiokuviksensa (plural translative)
projektiokuvattaan (abessive singular)
projektiokuvattansa (abessive singular)
projektiokuvittaan (abessive plural)
projektiokuvittansa (abessive plural)
projektiokuvineen (comitative plural)
projektiokuvinensa (comitative plural)

projektio (“projection”) + kuva (“image”)

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


zuzen

zuzen (absolutive indefinite)
zuzena (absolutive indefinite singular)
zuzenak (absolutive indefinite plural)
zuzenek (ergative indefinite)
zuzenak (ergative indefinite singular)
zuzenek (ergative indefinite plural)
zuzeni (dative indefinite)
zuzenari (dative indefinite singular)
zuzenei (dative indefinite plural)
zuzenen (genitive indefinite)
zuzenaren (genitive indefinite singular)
zuzenen (genitive indefinite plural)
zuzenekin (comitative indefinite)
zuzenarekin (comitative indefinite singular)
zuzenekin (comitative indefinite plural)
zuzenengatik (causative indefinite)
zuzenarengatik (causative indefinite singular)
zuzenengatik (causative indefinite plural)
zuzenentzat (benefactive indefinite)
zuzenarentzat (benefactive indefinite singular)
zuzenentzat (benefactive indefinite plural)
zuzenez (indefinite instrumental)
zuzenaz (indefinite instrumental singular)
zuzenez (indefinite instrumental plural)
zuzenetan (indefinite inessive)
zuzenean (indefinite inessive singular)
zuzenetan (indefinite inessive plural)
zuzenetako (indefinite locative)
zuzeneko (indefinite locative singular)
zuzenetako (indefinite locative plural)
zuzenetara (allative indefinite)
zuzenera (allative indefinite singular)
zuzenetara (allative indefinite plural)
zuzenetaraino (indefinite terminative)
zuzeneraino (indefinite singular terminative)
zuzenetaraino (indefinite plural terminative)
zuzenetarantz (directive indefinite)
zuzenerantz (directive indefinite singular)
zuzenetarantz (directive indefinite plural)
zuzenetarako (destinative indefinite)
zuzenerako (destinative indefinite singular)
zuzenetarako (destinative indefinite plural)
zuzenetatik (ablative indefinite)
zuzenetik (ablative indefinite singular)
zuzenetatik (ablative indefinite plural)
zuzenik (indefinite partitive)
zuzentzat (indefinite prolative)


angular defect

Prop. XVI. If the angular defects of two triangles are equal, the areas of the triangles are equal.

1864, Transactions of the Royal Society of Edinburgh, volume 23, page 444:

We have seen that under any reasonable definition of area, the angular defect of a triangle is proportional to its area.

1995, Arlan Ramsay, Robert D. Richtmyer, Introduction to Hyperbolic Geometry, page 120:

In hyperbolic geometry, similar triangles do not exist and the area of a triangle is directly proportional to its angular defect[…].

1998, Kappa Mu Epsilon, The Pentagon: A Mathematics Magazine for Students, page 7:

(geometry, non-Euclidean geometry) The amount by which the sum of the interior angles of a triangle is less than 180° (π radians); the amount by which the sum of the internal angles of a polygon is less than what would be expected on the Euclidean plane.

angular deficiency

amount by which the total of the interior angles of a polygon is less than on the Euclidean plane

The angular defect clearly has something to do with curvature, because the larger it is, the more pointed the surface is at the vertex.

2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, page 604:

2014, C. R. Calladine, The Static-geometric Analogy in the Equations of Thin Shell Structures, W. Olszak, Thin Shell Theory: New Trends and Applications, page 294,
Figure 4(c) shows a flattened view of a small part of the undeformed polygonalized S-surface, consisting of the triangles surrounding a particular vertex. When the S-surface is strained there will be a consequent change of angular defect, which we wish to calculate.

2015, Jan Guichelaar (translator and editor), Alex Van Den Brandhof, Arnout Jaspers (editors), Half a Century of Pythagoras Magazine, page 164,
Theorem. For a spherical polyhedron the total angular defect equals 720°.

(geometry) The amount by which the total of the angles around a vertex of a polyhedron is less than 360° (2π radians).


កាំ

From Proto-Austroasiatic *kam (“arrow”).


symmetry group

[The] situation is more delicate in the case of higher dimensional symmetry groups; it is not in general possible to reduce the order of an equation invariant under an r-parameter symmetry group by r using only quadratures.

1993, Peter J. Olver, Applications of Lie Groups to Differential Equations, published 2000, page 76:

It is often assumed that the design unit inside each fundamental region (particularly for monotranslational symmetry groups p111 and p1a1 and ditranslational symmetry groups p1 and pg) is asymmetric.

2000, C. E. Horne, Geometric Symmetry in Patterns and Tilings, page 79:

The structure of the symmetry group of a molecule affects several spectroscopic aspects and vice versa. Thus, it is clearly important to know the possible symmetries of fullerenes and similar structures.
In this chapter, we study symmetry groups of fulleroids.

2010, Stanislav Jendrol, František Kardoš, “28: Symmetry of Fulleroids”, in Klaus D. Sattler, editor, Handbook of Nanophysics: Clusters and Fullerenes, pages 28–1:

(geometry, algebra, group theory) A group whose elements are all the transformations under which a given object remains invariant and whose group operation is function composition.

full symmetry group

emphasises the inclusion of orientation-reversing transformations


vinkelhalveringslinie

head

vinkelhalveringslinie c (singular definite vinkelhalveringslinien, plural indefinite vinkelhalveringslinier)

vinkelhalveringslinien (definite singular)
vinkelhalveringslinier (indefinite plural)
vinkelhalveringslinie (indefinite nominative singular)
vinkelhalveringslinien (definite nominative singular)
vinkelhalveringslinier (indefinite nominative plural)
vinkelhalveringslinierne (definite nominative plural)
vinkelhalveringslinies (genitive indefinite singular)
vinkelhalveringsliniens (definite genitive singular)
vinkelhalveringsliniers (genitive indefinite plural)
vinkelhalveringsliniernes (definite genitive plural)
vinkelhalveringslinje (alternative)

vinkel (“angle”) + halvering (“halfing”) + linie (“line”)


vinkelhalveringslinje

head

vinkelhalveringslinje c (singular definite vinkelhalveringslinjen, plural indefinite vinkelhalveringslinjer)

vinkelhalveringslinjen (definite singular)
vinkelhalveringslinjer (indefinite plural)
vinkelhalveringslinje (indefinite nominative singular)
vinkelhalveringslinjen (definite nominative singular)
vinkelhalveringslinjer (indefinite nominative plural)
vinkelhalveringslinjerne (definite nominative plural)
vinkelhalveringslinjes (genitive indefinite singular)
vinkelhalveringslinjens (definite genitive singular)
vinkelhalveringslinjers (genitive indefinite plural)
vinkelhalveringslinjernes (definite genitive plural)

(geometry) Alternative spelling of vinkelhalveringslinie


midtnormal

midtnormal c (singular definite midtnormalen, plural indefinite midtnormaler)

midtnormalen (definite singular)
midtnormaler (indefinite plural)
midtnormal (indefinite nominative singular)
midtnormalen (definite nominative singular)
midtnormaler (indefinite nominative plural)
midtnormalerne (definite nominative plural)
midtnormals (genitive indefinite singular)
midtnormalens (definite genitive singular)
midtnormalers (genitive indefinite plural)
midtnormalernes (definite genitive plural)

(geometry) A line perpendicular to a segment which it intersects at that segment's midpoint; the perpendicular bisector of a segment.


εξάγωνο

exágono (romanization)
εξάγωνα (plural)
εξάγωνο (nominative singular)
εξάγωνα (nominative plural)
εξαγώνου (genitive singular)
εξάγωνου (genitive singular)
εξαγώνων (genitive plural)
εξάγωνο (accusative singular)
εξάγωνα (accusative plural)
εξάγωνο (singular vocative)
εξάγωνα (plural vocative)


cross-polytope

cross-polytopes (plural)
cross polytope (alternative)

The case p = 1, which is actually important to us, is illustrated in Figure 1.14; we are looking at the intersection of a cross-polytope with the probability simplex.

2006, Ingemar Bengtsson, Karol Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, page 25:

2008, Robert Erdahl, Andrei Ordine, Konstantin Rybnikov, Perfect Delaunay Polytopes and Perfect Quadratic Functions on Lattices, Matthias Beck, et al. (editors), Contemporary Mathematics 452: Integer Points in Polyhedra — Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics, AMS-IMS-SIAM Joint Summer Conference, June 11-15, 2006, page 104,
The convex hulls of such crosses often appear as cells in Delaunay tilings – cross polytopes are examples, as are the more spectacular symmetric perfect Delaunay polytopes.

The cross polytope βₙ is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (±1,0,0,...,0), and has therefore 2n vertices. It is named so because its vertices are located equidistant from the origin, along the Cartesian axes in n-space. The cross polytope in n dimensions is bounded by 2ⁿ (n - 1)-simplices, has 2n vertices and 2ⁿ(n - 1) edges.

2009, Herbert W. Hamber, Quantum Gravitation: The Feynman Path Integral Approach, Springer, page 263:

If one works with the l₁ norm, a ball (the set of all points whose distance lies within a certain radius around a point of interest) has the shape of a cross-polytope. A one-dimensional cross-polytope is a line segment, a two-dimensional cross-polytope is a square, for three dimensions, an octahedron, and so forth.

2010, Rainer Typke, Agatha Walczak-Typke, “Indexing Techniques for Non-metric Music Dissimilarity Measures”, in Zbigniew W. Raś, Alicja A. Wieczorkowska, editors, Advances in Music Information Retrieval, Springer, page 10:

While centrally symmetric d-polytopes with 2d vertices are affinely equivalent to the d-dimensional cross-polytope, a complete classification of the centrally symmetric d-polytopes with 2d + 2 vertices is out of reach.

2003, Branko Grünbaum, Convex Polytopes, 2nd edition, Springer, page 121b:

(geometry) A polytope that is the convex hull of points, two on each Cartesian axis of a Euclidean space, that are equidistant from the origin; an orthoplex.


Coxeter diagram

en-noun

Coxeter diagram (plural Coxeter diagrams)

It suffices to make use of the tables above and observe that the Coxeter diagram of a direct sum of C-matrices is the disconnected union of the Coxeter diagrams of the summands.
For the description of C⁻-matrices satisfying condition (2) we shall use Coxeter diagrams with the additional stipulation that in case aᵢⱼ < −1 the vertices vᵢ and vⱼ are joined by a dotted line with index −aᵢⱼ. By the Coxeter diagram of a Coxeter polyhedron and a lattice generated by reflections we mean the Coxeter diagram of the corresponding C⁻-matrix.

1991, Gregori A. Margulis, Discrete Subgroups of Semisimple Lie Groups, page 358:

An automorphism of a Coxeter diagram M leads in a natural way to a Coxeter subgroup of the Coxeter group of type M. We introduce admissible partitions of Coxeter diagrams in order to generalize this situation.

1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. Buekenhout, J. Doyen, F. de Clerck, J. A. Thas, J. W. P. Hirschfeld, editors, Finite Geometries and Combinatorics, 2nd International Conference, page 277:

The Coxeter diagrams of type E₇ and E₈ have no nontrivial automorphisms, so σ₀ is trivial in those cases.[…]The Coxeter diagram of type F₄ has a unique nontrivial automorphism, but σ₀ is trivial in this case. One can see this by using the Dynkin diagram instead of the Coxeter diagram and noting that it does not have any nontrivial automorphisms.

2008, Peter Abramenko, Kenneth S. Brown, Buildings: Theory and Applications, page 259:

Coxeter-Dynkin diagram
Coxeter-Dynkin diagram

(geometry, algebra) A Coxeter-Dynkin diagram.