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Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .
Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]
Theorems about quadrilaterals and circles (6 P) Pages in category "Theorems about quadrilaterals" The following 11 pages are in this category, out of 11 total.
Van Aubel's theorem (quadrilaterals) Van der Waerden's theorem (combinatorics) Van Schooten's theorem (Euclidean geometry) Van Vleck's theorem (mathematical analysis) Vantieghems theorem (number theory) Varignon's theorem (Euclidean geometry) Vieta's formulas ; Vietoris–Begle mapping theorem (algebraic topology) Vinogradov's theorem (number ...
Siegel–Weil formula; Siegel's theorem on integral points; Six exponentials theorem; Skolem–Mahler–Lech theorem; Sophie Germain's theorem; Størmer's theorem; Subspace theorem; Sum of two squares theorem; Szemerédi's theorem
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]
In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set , though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets .
This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.