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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 + = (+).
Stewart's theorem. The length of a cevian can be determined by Stewart's theorem: in the diagram, the cevian length d is given by the formula
Steinitz theorem (graph theory) Stewart's theorem (plane geometry) Stinespring factorization theorem (operator theory) Stirling's theorem (mathematical analysis) Stokes's theorem (vector calculus, differential topology) Stolper–Samuelson theorem ; Stolz–Cesàro theorem
Proof of Apollonius's theorem. The theorem can be proved as a special case of Stewart's theorem, or can be proved using vectors (see parallelogram law). The following is an independent proof using the law of cosines. [1] Let the triangle have sides ,, with a median drawn to side .
This proof does not actually require that the game always be over in a finite number of moves, only that it be over in a finite number of moves whenever II wins. That condition, topologically, is that the set A is closed. This fact—that all closed games are determined—is called the Gale–Stewart theorem. Note that by symmetry, all open ...
Pappus's area theorem; Pappus's hexagon theorem; Pascal's theorem; Pasch's axiom; Pasch's theorem; Philo line; Pick's theorem; Plane figure; Pole and polar; Polygon; Polygon with holes; Poncelet point; Poncelet–Steiner theorem; Power of a point; Problem of Apollonius; Projective plane; Pseudotriangle; Ptolemy's theorem; Pythagorean theorem
In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases ...
The following other wikis use this file: Usage on ar.wikipedia.org شيفي; Usage on id.wikipedia.org Teorema Stewart; Cevian; Usage on ja.wikipedia.org