- Japanese theorem
The term Japanese theorem refers to either of the following 2 geometrical theorems:
*
Japanese theorem for concyclic polygons
*Japanese theorem for concyclic quadrilaterals
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Japanese theorem
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Japanese theorem for concyclic polygons — In geometry, the Japanese theorem states that no matter how we triangulate a concyclic polygon, the sum of inradii of triangles is constant. Conversely, if the sum of inradii independent from the triangulation, then the polygon is cyclic. The… … Wikipedia
Japanese theorem for concyclic quadrilaterals — The Japanese theorem states that the centers of the incircles of certain triangles inside a concyclic quadrilateral are vertices of a rectangle.Triangulate an arbitrary concyclic quadrilateral by its diagonals, this yields four overlapping… … Wikipedia
Equal incircles theorem — In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of rays are drawn from a given point to a given line such that the inscribed circles of the triangles formed by… … Wikipedia
Carnot's theorem — In Euclidean geometry, Carnot s theorem, named after Lazare Carnot (1753 ndash;1823), is as follows. Let ABC be an arbitrary triangle. Then the sum of the signed distances from the circumcenter D to the sides of triangle ABC is : DF + DG + DH = R … Wikipedia
Okishio's theorem — is a mathematical theorem formulated by Japanese economist Nobuo Okishio. It has had a major impact on debates about Marx s theory of value. Intuitively, it can be understood as saying that if one capitalist raises his profits by introducing a… … Wikipedia
Nyquist–Shannon sampling theorem — Fig.1: Hypothetical spectrum of a bandlimited signal as a function of frequency The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular… … Wikipedia
Modularity theorem — In mathematics the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture and several related names) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity … Wikipedia
Infinite monkey theorem in popular culture — The infinite monkey theorem and its associated imagery is considered a popular and proverbial illustration of the mathematics of probability, widely known to the general public because of its transmission through popular culture rather than… … Wikipedia
Hartogs' extension theorem — In mathematics, precisely in the theory of functions of several complex variables, Hartogs extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that the support of the… … Wikipedia
Ado's theorem — In mathematics, Ado s theorem states that every finite dimensional Lie algebra L over a field K of characteristic zero can be viewed as a Lie algebra of square matrices under the commutator bracket. More precisely, the theorem states that L has a … Wikipedia
