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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.
Download as PDF; Printable version; ... Ono's inequality; Pedoe's inequality; Ptolemy's inequality ... Text is available under the Creative Commons Attribution ...
The officers quickly got the shooter handcuffed, Boyd said. But he didn’t stay quiet. “He loses his mind in the handcuffs and tries to get up and starts cussing and being aggressive,” Boyd said.
Howard spent four years at Kansas State, not winning the full-time starting job until last season, before choosing the Buckeyes over the NFL draft. “This has been a little different for us ...
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 ]
Slaven Vlasic/Getty. Bill Bellichick and Jordon Hudson attend The American Museum of Natural History's 2024 Museum Gala at American Museum of Natural History on Dec. 5, 2024 in New York City.