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{{short description|Unique circle centered at a given triangle's orthocenter}} {{legend-line|solid #4169E1|Reference triangle {{math|△''ABC''}}}} ...

...ath>p_1(n), p_2(n), \dots, p_n(n)</math>:<ref>{{cite OEIS|A008284|Triangle of partition numbers|mode=cs2}}</ref> Analogously to [[Pascal's triangle]], these numbers may be calculated using the [[recurrence relation]]<ref>{{ ...

{{short description|Array of partial sums of the binomial coefficients}} ...ight=1.5|Derivation of Bernoulli's triangle (blue bold text) from Pascal's triangle (pink italics)]] ...

{{Short description|Splitting a triangle by perpendicular lines}} ...r quadrisections of a triangle. The triangle shown is the unique isosceles triangle for which there are exactly two perpendicular quadrisections.{{r|eberhart}} ...

...ngruence. A triangle is said to be '''5-Con capable''' if there is another triangle which is almost congruent to it. |publisher=National Council of Teachers of Mathematics ...

...1996">{{cite journal|last1=Bailey|first1=D. F.|title=Counting Arrangements of 1's and -1's|journal=Mathematics Magazine|date=1996|volume=69|issue=2|pages ...lished in 1800<ref name="arbogast">{{cite book|last1=Arbogast|first1=L. F. A.|date=1800|title=Du Calcul des Derivations|url=https://archive.org/details/ ...

{{short description|Trigonometric identity relating the sides and angles of a triangle}} ...the [[incenter]], which is the center of the [[Incircle and excircles of a triangle|incircle]].]] ...

...[triangles]]<br/> (20 [[Equilateral triangle|equilateral]]; 60 [[Isosceles triangle|isosceles]]) ...], and 42 [[Vertex (geometry)|vertices]]. It is a [[Dual polyhedron|dual]] of the ''truncated rhombic triacontahedron'' ([[chamfered dodecahedron]]). ...

[[File:Pentagramma-mirificum.gif|thumb|right|275px|Sample configurations of ''pentagramma mirificum'']] ...s <math>(a,</math> <math>\pi/2-B,</math> <math>\pi/2-c,</math> <math>\pi/2-A,</math> <math>b)</math>]] ...

{{Short description|Type of triangle}} ...le:Isosceles skinny triangle.svg|thumb|100px|'''Fig. 1''' Isosceles skinny triangle]] ...

...theory of [[homogeneous coordinates]].<ref>D. Pedoe ''Notes on the History of Geometrical Ideas I: Homogeneous Coordinates''. Math Magazine (1975), 215-2 [[Image:Mass points3.png|thumb|Example of mass point addition]] ...

...olymosi | author-link = József Solymosi | chapter=Note on a generalization of Roth's theorem | title=Discrete and computational geometry | mr=2038505 | i ...dots,N\}^2</math> with size at least <math>\varepsilon N^2</math> contains a corner. ...

* the first proof of the existence of the [[orthocentre]] of a triangle, ...theorem in geometry|distance between the incentre and circumcentre]] of a triangle, ...

{{short description|1=Equation of the form 1/a + 1/b = 1/c}} ...{filepath:optic_equation_integer_solutions.svg}} the SVG file,] hover over a circle to see its solution.]] ...

...right|250px|Equilateral pentagon built with four equal circles disposed in a chain.]] ...]s can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the [[regular pentagon]] is unique, because it is ...

{{short description|Simplex formed from a right-angled path}} ...basis for [[trigonometry]], orthoschemes form the basis of a trigonometry of ''n'' dimensions, as developed by [[Pieter Hendrik Schoute|Schoute]] who ca ...

...[[ellipse]] and an [[equilateral triangle]] is fatter than a very [[obtuse triangle]]. ...in computational geometry can perform much better if their input consists of only fat objects; see the [[#Applications|applications]] section below. ...

...ort description|Complex numbers with unit norm and both real and imaginary parts rational numbers}} [[File:Pythagorean triple and rational point on unit triangle 1.svg|thumb|300px|The [[Pythagorean triple]] (4,3,5) is associated to the r ...

...] (and later independently by [[Leonhard Euler]]), which is a special case of [[Poncelet's closure theorem]], as well as the [[Grace–Danielsson inequalit ...ius <math>R</math> of its [[circumcircle]] and the distance <math>d</math> of their centers are related through [[Euler's theorem in geometry]]: ...

[[Image:Box fractal.svg|thumb|245px|right|Vicsek fractal (5th iteration of cross form)]] ...actal}}</ref> is a [[fractal]] arising from a construction similar to that of the [[Sierpiński carpet]], proposed by [[Tamás Vicsek]]. It has application ...