In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant.: p. 193  Conversely...

This theorem may be extended to prove the Japanese theorem for cyclic polygons, according to which the sum of inradii of a triangulated cyclic polygon does...

term Japanese theorem refers to either of the following two geometrical theorems: Japanese theorem for cyclic polygons Japanese theorem for cyclic quadrilaterals...

Shuke (1797–1865) Omura Isshu (1824–1871) Japanese theorem for cyclic polygons Japanese theorem for cyclic quadrilaterals Hungarian mathematics Sangaku...

In geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral (four-sided polygon) whose vertices all lie on a single circle, making...

in 1880. Japanese theorem for cyclic polygons — In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum...

Hyperbolic function Japanese theorem for cyclic polygons Japanese theorem for cyclic quadrilaterals Tangent lines to circles Equal Incircles Theorem at cut-the-knot...

applicable to any closed curve Japanese theorem for cyclic polygons – Theorem in Euclidean geometry Japanese theorem for cyclic quadrilaterals – Centers of...

segments in plane geometry. Such polygons may have any number of sides greater than 1. Two-sided spherical polygons—lunes, also called digons or bi-angles—are...

rectangle. The Japanese theorem for cyclic quadrilaterals states that the incentres of the four triangles determined by the vertices of a cyclic quadrilateral...

regular polygons that are constructible (this characterization was previously given by Gauss but without the proof that the list of constructible polygons was...

as the golden rectangle and the silver rectangle. Methods for folding most regular polygons up to and including the regular 19-gon have been developed...

theorem, any group of prime order is a cyclic group, and by Burnside's theorem any group whose order is divisible by only two primes is solvable. For...

abelian subgroups of Γ are virtually cyclic, so that it does not contain a subgroup isomorphic to Z×Z. Myers theorem. If a complete Riemannian manifold...

three-dimensional analogs of two-dimensional orthogonal polygons, also known as rectilinear polygons. Orthogonal polyhedra are used in computational geometry...

branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions...

Sommer-Simpson, Jasha (2 November 2013). "Automorphism groups for semidirect products of cyclic groups" (PDF). p. 13. Archived (PDF) from the original on...

et transformation des polygones sphériques, d'après M. Steiner" [Lexell's theorem, and transformation of spherical polygons, after Mr. Steiner], Nouvelles...

triangle from an equilateral triangle. Some irregular polygons also generate Reuleaux polygons. In a closely related construction, called by Martin Gardner...

Books. MR 0207802. Maskit, Bernard (1971), "On Poincaré's theorem for fundamental polygons", Advances in Mathematics, 7 (3): 219–230, doi:10.1016/s0001-8708(71)80003-8...

this set. The only other finite simple groups are the infinite families of cyclic groups and alternating groups. An exception is the Tits group T {\displaystyle...

cyclic shifting of rows or of columns or both. This allows us to position a given number in any one of the n2 cells of an n order square. Thus, for a...

Satake, Ichirô (1957). "The Gauss-Bonnet theorem for V-manifolds". Journal of the Mathematical Society of Japan. 9 (4): 464–492. doi:10.2969/jmsj/00940464...

itself Systems theory – Interdisciplinary study of systems Strange loop – Cyclic structure that goes through several levels in a hierarchical system Turbulence –...

and vertices which can be unfolded to form a possibly infinite set of polygons which tile either the sphere, the plane or the hyperbolic plane. When it...

two geodesic polygons with 2k−1 + 1 sides along a common side). Hence if M ≤ 2k + 2, the same estimate holds for a polygon with M sides. For yi = Δ(i) let...

Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for Scientific American magazine. During the next 5+1⁄2 years, until June 1986...

widely depending on many factors. In ecology it is theoretically (i.e. cyclic succession, patch dynamics, Megaherbivorenhypothese) taken that a grazing...