Ad
related to: proof of ptolemy's theorem of geometry pdfstudy.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
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 ]
For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: ¯ ¯ + ¯ ¯ = ¯ ¯. In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to become collinear, so the triangle equality for these three points (from which Ptolemy's inequality may ...
In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey. Formulation of the theorem [ edit ]
Proof of law of cosines using Ptolemy's theorem. Referring to the diagram, triangle ABC with sides AB = c, BC = a and AC = b is drawn inside its circumcircle as shown. Triangle ABD is constructed congruent to triangle ABC with AD = BC and BD = AC. Perpendiculars from D and C meet base AB at E and F respectively.
The first of these theorems is the spherical analogue of a plane theorem, and the second theorem is its dual, that is, the result of interchanging great circles and their poles. [32] Kiper et al. [ 33 ] proved a converse of the theorem: If the summations of the opposite sides are equal in a spherical quadrilateral, then there exists an ...
The proofs include: Six proofs of the infinitude of the primes, including Euclid's and Furstenberg's; Proof of Bertrand's postulate; Fermat's theorem on sums of two squares; Two proofs of the Law of quadratic reciprocity; Proof of Wedderburn's little theorem asserting that every finite division ring is a field; Four proofs of the Basel problem
Menelaus's theorem, case 1: line DEF passes inside triangle ABC. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A ...
Van Schooten's theorem, named after the Dutch mathematician Frans van Schooten, describes a property of equilateral triangles.It states: For an equilateral triangle with a point on its circumcircle the length of longest of the three line segments ,, connecting with the vertices of the triangle equals the sum of the lengths of the other two.