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Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection. In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit ...
Pompeiu's theorem is a result of plane geometry, discovered by the Romanian mathematician Dimitrie Pompeiu. The theorem is simple, but not classical. It states the following: Given an equilateral triangle ABC in the plane, and a point P in the plane of the triangle ABC, the lengths PA, PB, and PC form the sides of a (maybe, degenerate) triangle.
Sturm passed the request on to other mathematicians and Steiner was among the first to provide a solution. The theorem became a rather popular topic in elementary geometry ever since with a somewhat regular publication of articles on it. [1] [2] [3]
Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis) Fundamental theorem of arbitrage-free pricing (financial mathematics) Fundamental theorem of arithmetic (number theory) Fundamental theorem of calculus ; Fundamental theorem on homomorphisms (abstract algebra)
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 + = (+).
A failed attempt to comb a hairy 3-ball (2-sphere), leaving a tuft at each pole A hairy doughnut (2-torus), on the other hand, is quite easily combable. A continuous tangent vector field on a 2-sphere with only one pole, in this case a dipole field with index 2.
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The British flag theorem can be generalized into a statement about (convex) isosceles trapezoids.More precisely for a trapezoid with parallel sides and and interior point the following equation holds: