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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 graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek astronomer and mathematician Ptolemy. The Ptolemaic graphs are exactly the graphs that are both chordal and distance-hereditary ; they include the block graphs [ 1 ] and are a subclass of the ...
More generally, if the quadrilateral is a rectangle with sides a and b and diagonal d then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d 2, the right hand side of Ptolemy's relation is the sum a 2 + b 2.
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 ]
The following other wikis use this file: Usage on ar.wikipedia.org متفاوتة بطليموس; Usage on ca.wikipedia.org Teorema de Ptolemeu
In early March, U.S. Integrity said there was notable line movement ahead of Temple’s game against UAB. The line moved five points in the Blazers’ direction and they closed as 7.5-point favorites.
A passenger on a plane sniffed out another traveler's foul-smelling food in a viral video he recently posted on social media.. Zavier Torrence, 25, told Fox News Digital he was on the second leg ...
Ptolemy's work the Almagest had wide and long-lasting acceptance and influence for over a millennium. He gave a geometrical lunar theory that improved on that of Hipparchus by providing for a second inequality of the Moon's motion, using a device that made the apparent apogee oscillate a little – prosneusis of the epicycle.