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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 .
This is a direct consequence of the inscribed angle theorem and the exterior angle theorem. There are no cyclic quadrilaterals with rational area and with unequal rational sides in either arithmetic or geometric progression. [26] If a cyclic quadrilateral has side lengths that form an arithmetic progression the quadrilateral is also ex-bicentric.
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.
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). [ 1 ]
Japanese theorem for concyclic quadrilaterals (Euclidean geometry) John ellipsoid ; Jordan curve theorem ; Jordan–Hölder theorem (group theory) Jordan–Schönflies theorem (geometric topology) Jordan–Schur theorem (group theory) Jordan's theorem (multiply transitive groups) (group theory) Joubert's theorem ; Jung'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]
Pages in category "Theorems about quadrilaterals and circles" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. B.
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