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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.
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 .
A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6] 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]
Printable version; In other projects ... Koebe 1/4 theorem ... Varignon's theorem (Euclidean geometry) Vieta's formulas
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
Polarization identity – Formula relating the norm and the inner product in a inner product space; Ptolemy – Roman astronomer and geographer (c. 100–170) Ptolemy's table of chords – 2nd century AD trigonometric table; Ptolemy's theorem – Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
Bretschneider's formula allows for the calculation of the area of a general quadrilateral if the lengths of all sides are known. Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from Gotha, Germany. Bretschneider worked in geometry, number theory, and history of geometry.
Moreover, the converse of Ptolemy's theorem is also true: In a quadrilateral, if the sum of the products of the lengths of its two pairs of opposite sides is equal to the product of the lengths of its diagonals, then the quadrilateral can be inscribed in a circle i.e. it is a cyclic quadrilateral.
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