Japanese theorem for cyclic quadrilaterals information

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

the circumcircle. 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 Sangaku, the custom of presenting mathematical...

for cyclic polygons Japanese theorem for cyclic quadrilaterals Kosnita's theorem Lester's theorem Milne-Thomson circle theorem Miquel's theorem Monge's...

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

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...

two digits are a multiple of 4 (for example, 1092 is a multiple of 4 because 92 = 4 × 23). Lagrange's four-square theorem states that every positive integer...

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...

are differentiated from the formative ancient Japanese or Greek elements, due to their emphasis on cyclic transformations and change. The five phases are:...

equations Narayana has also made contributions to the topic of cyclic quadrilaterals. The Navya Nyaya 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]×[]...