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In mathematics, a corollary is a theorem connected by a short proof to an existing theorem. The use of the term corollary , rather than proposition or theorem , is intrinsically subjective. More formally, proposition B is a corollary of proposition A , if B can be readily deduced from A or is self-evident from its proof.
Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.
A corollary of the Mason–Stothers theorem is the analog of Fermat's Last Theorem for function fields: if a(t) n + b(t) n = c(t) n for a, b, c relatively prime polynomials over a field of characteristic not dividing n and n > 2 then either at least one of a, b, or c is 0 or they are all constant.
Diagram of Stewart's theorem. Let a, b, c be the lengths of the sides of a triangle. Let d be the length of a cevian to the side of length a.If the cevian divides the side of length a into two segments of length m and n, with m adjacent to c and n adjacent to b, then Stewart's theorem states that + = (+).
Cl – conjugacy class. cl – topological closure. CLT – central limit theorem. cod, codom – codomain. cok, coker – cokernel. colsp – column space of a matrix. conv – convex hull of a set. Cor – corollary. corr – correlation. cos – cosine function. cosec – cosecant function. (Also written as csc.) cosech – hyperbolic ...
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
A porism is a mathematical proposition or corollary. It has been used to refer to a direct consequence of a proof, analogous to how a corollary refers to a direct consequence of a theorem. In modern usage, it is a relationship that holds for an infinite range of values but only if a certain condition is assumed, such as Steiner's porism. [1]
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified Corollary 1: The property of being God-like is consistent Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing Theorem 3: Necessarily, the property of being God-like is exemplified