In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle...

circumradius respectively. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given...

sum of the inradii. The quadrilateral case follows from a simple extension of the Japanese theorem for cyclic quadrilaterals, which shows that a rectangle...

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

any quadrilateral with perpendicular diagonals form a rectangle. A parallelogram with equal diagonals is a rectangle. The Japanese theorem for cyclic quadrilaterals...

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

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

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

proofs for eyeball theorem, one of them shows that this theorem is a consequence of the Japanese theorem for cyclic quadrilaterals. Japanese theorem for cyclic...

Iwasawa for primes satisfying the Kummer–Vandiver conjecture and proved for all primes by Mazur and Wiles. Japanese theorem for cyclic quadrilaterals In geometry...

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

Girard's theorem, but demonstrating the angle invariants in the triangle △ A ∗ B ∗ C {\displaystyle \triangle A^{*}B^{*}C} by constructing a cyclic quadrilateral...

tetrahedron. The smallest non-cyclic group has four elements; it is the Klein four-group. An alternating groups are not simple for values n {\displaystyle n}...

In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic...

B P X {\displaystyle ABPX} and X P C D {\displaystyle XPCD} are cyclic quadrilaterals. Thus, ∠ X A B = 180 ∘ − ∠ B P X = ∠ X P D = ∠ X C D {\displaystyle...

this article. Polygons with higher numbers of sides (4-sided spherical quadrilaterals, 5-sided spherical pentagons, etc.) are defined in similar manner. Analogously...

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...

equal. Since an isosceles trapezoid is cyclic, an isosceles tangential trapezoid is a bicentric quadrilateral. That is, it has both an incircle and a...

Alexandrov's first comparison theorem for Hadamard spaces implies that the function g(t) = d(y,γ(t))2 − t2 is convex. Hence for 0< s < t g ( s ) ≤ ( 1 − s...

equations Narayana has also made contributions to the topic of cyclic quadrilaterals. The Navya-Nyāya school began around eastern India and Bengal, and...

hidden. A Coxeter group can be used for a simpler notation, as (p q r) for cyclic graphs, and (p q 2) = [p,q] for (right triangles), and (p 2 2) = [p]×[]...