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{{Short description|Special ordering of numbers on a triangle}} A '''magic triangle''' is a magic arrangement of the [[integer]]s from 1 to {{mvar|n}} to triangular figure. ...

...in the set and ''n''&nbsp;−&nbsp;1 triangles are directly similar, then n triangles are directly similar.<ref name=":0" /> ...on, if all but one of the triangles were directly similar, then all of the triangles are directly similar.<ref name=":0" /> ...

{{Short description|Triangular arrangement of numbers based on the Fibonacci numbers}} ...e]]) based on the [[Fibonacci number]]s. Each number is the sum of the two numbers above in either the left diagonal or the right diagonal.<ref>{{Cite journal ...

...eflections. These groups have many uses, including producing the rotations of [[Platonic solid]]s and tessellating the plane. ...finite number of polygons in which any two sharing a side are reflections of each other along that side. ...

{{short description|Array of partial sums of the binomial coefficients}} [[File:Bernoulli triangle derivation.svg|thumb|upright=1.5|Derivation of Bernoulli's triangle (blue bold text) from Pascal's triangle (pink italics) ...

...(geometry)|similar]] to the original one whose sides are translated copies of the medians]] ...an triangle may be [[translation (geometry)|translated]] to form the sides of a second triangle that is [[Similarity (geometry)|similar]] to the first on ...

{{Short description|On triangles in line arrangements}} ...le, four lines form at least two triangles, five lines form at least three triangles, etc. It is named after [[Samuel Roberts (mathematician)|Samuel Roberts]], ...

{{Short description|Theorem about right triangles}} [[File:Hoehensatz2.svg|thumb|upright=1.2|area of grey square = area of grey rectangle: <math> h^2=pq \Leftrightarrow h=\sqrt{pq}</math>]] ...

{{Short description|Triangles without a right angle}} ...nd obtuse triangles are the two different types of '''oblique triangles'''—triangles that are not [[right triangle]]s because they do not have any [[right angle ...

{{Short description|On rearrangement of bases in matroids}} ...t bases ''C_i'', each of which consists of one element from each of the bases ''B_i''. ...

...shed by [[Galileo Galilei]] who was the first to make quantitative studies of [[free fall]]. ...eo's_law_of_odd_numbers.svg|thumb|300px|Derivation of Galileo's law of odd numbers]] ...

{{Short description|Triangular array of integers following a modular formula}} :''Dudley Triangle may also refer to a neighborhood of [[Boston, Massachusetts]].'' ...

..._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>{{citation ...

...the three placements of its largest square. The placement on the long side of the triangle is inscribed; the other two are not.]] ...square's vertices, and the edge between them, must lie on one of the sides of the triangle. For instance, for the [[Calabi triangle]] depicted, the squar ...

...s]], [[statistics]] and elsewhere, '''sums of squares''' occur in a number of contexts: * For partitioning of variance, see [[Partition of sums of squares]] ...

{{short description|Rational right triangles cannot have square area}} ...and <math>c^2</math> form an [[arithmetic progression]] separated by a gap of <math>d^2</math>. It is not possible for all four lengths <math>a</math>, < ...

[[File:Pentagramma-mirificum.gif|thumb|right|275px|Sample configurations of ''pentagramma mirificum'']] ...r right spherical triangles|Napier’s circles]] contain [[circular shift]]s of parts <math>(a,</math> <math>\pi/2-B,</math> <math>\pi/2-c,</math> <math>\p ...

{{short description|Polygonal curve made from right triangles}} ...b|right|400px|The spiral of Theodorus up to the triangle with a hypotenuse of <math>\sqrt{17}</math>]] ...

...ne touching at least one other on the edge.<ref>{{Cite OEIS|A006534|Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not ...2</sup>=94249.<ref>{{Cite OEIS|A028818|Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots}}</ref> ...

{{Short description|Theorem relating the number of edges, vertices and faces of a polyhedron}} ...convex polyhedron|convex polyhedra]]. It states that, for given numbers of triangles, quadrilaterals, pentagons, heptagons, and other polygons other than hexago ...