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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 ...
Such variations in duration are usually determined by one's reasons for abstaining from food in the first place. For instance, fasting is a common practice in many religions including Judaism ...
"Here’s to a great day filled with all the laughter and love that you deserve. I love you infinity x infinity!!! ️ ️ ️," he added. gisele bundchen/Instagram
The commentary is a reworking of Theon's own lecture notes, and is useful chiefly for including information from lost works by writers such as Pappus. [1] It is also useful for Theon's account of the Greek method of operating with the sexagesimal system as it was applied to calculations. [2] Great Commentary on Ptolemy's Handy Tables. This work ...
Follow Fox News Digital’s sports coverage on X and subscribe to the Fox News Sports Huddle newsletter. Original article source: FBI warns South American crime groups targeting star athletes in ...
Draymond Green may be a four-time NBA champion and one of the Golden State Warriors’ most vocal leaders, but off the court, his biggest role is being a father to his four kids: Olive, Draymond ...