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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 ...
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 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 ...
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 ]
This guy gave new meaning to the slogan “Gottahava Wawa.” Police in East Windsor, N.J., arrested a 24-year-old man on Dec. 23, and charged him with misusing the town’s 911 system for ...
Best: Nature’s Own Thick-Sliced White Bread. $2.97 . While the majority of the white bread brands I tried were extremely similar, the top two sit in a major league of their own.
License plate readers in Las Vegas first detected the vehicle at about 7:30 a.m., and McMahill said it traveled up and down Las Vegas Boulevard before pulling into the Trump hotel valet area.
Download as PDF; Printable version; In other projects ... Ptolemy's inequality; ... This page was last edited on 30 March 2013, ...