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The Finsler–Hadwiger theorem is statement in Euclidean plane geometry that describes a third square derived from any two squares that share a vertex. The theorem is named after Paul Finsler and Hugo Hadwiger , who published it in 1937 as part of the same paper in which they published the Hadwiger–Finsler inequality relating the side lengths ...
A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]
Newton's theorem (quadrilateral) Nicomachus's theorem (number theory) Nielsen fixed-point theorem (fixed points) Nielsen–Ninomiya theorem (quantum field theory) Nielsen realization problem (geometric topology) Nielsen–Schreier theorem (free groups) Niven's theorem (number theory) No-broadcasting theorem (quantum information theory)
Euler's rotation theorem; Euler spiral – a curve whose curvature varies linearly with its arc length; Euler squares, usually called Graeco-Latin squares; Euler's theorem in geometry, relating the circumcircle and incircle of a triangle; Euler's quadrilateral theorem, an extension of the parallelogram law to convex quadrilaterals
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four straight sides of equal length and four equal angles (90-degree angles, π /2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides.
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 ...
The proof of the theorem can be presented in various ways. [10] Here the proof is first given in the language of coordinates and Christoffel symbols, and then in the coordinate-free language of covariant derivatives. Regardless of the presentation, the idea is to use the metric-compatibility and torsion-freeness conditions to obtain a direct ...
The converse also holds: If the sum of the distances from a point in the interior of a quadrilateral to the sides is independent of the location of the point, then the quadrilateral is a parallelogram. [3] The result generalizes to any 2n-gon with opposite sides parallel. Since the sum of distances between any pair of opposite parallel sides is ...