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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 ]
By Ted Hesson. WASHINGTON (Reuters) -U.S. President-elect Donald Trump aims to deport all immigrants in the U.S. illegally over his four-year term but wants a deal to protect so-called "Dreamer ...
526 × 526 (11 kb) Tcharvin {{Information |Description= Non-cyclic quadrilateral with cercle, to illustrate Ptolemy's inequality / Quadrilatère non inscriptible pour illustrer l'inégalité de Ptolémée |Source= en:wikipedia |Date= 8 October 2006 |Author= Dicklyon |Permission= Pub
MINEOLA, N.Y. — A Republican official who oversees Nassau County on New York's Long Island has seemingly refused to lower flags to half-staff in memory of the late Democratic President Jimmy ...
An undocumented immigrant was charged with setting a woman on fire, killing her, as she slept in the New York City subway -- a horrific alleged crime that officials called "beyond comprehension."