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Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.
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 ...
English: Animated visual proof of Ptolemy's theorem, based on W. Derrick, J. Herstein (2012) Proof Without Words: Ptolemy's Theorem, The College Mathematics Journal, v 43, n 5, p 386 Date 22 May 2022
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 ]
Great Commentary on Ptolemy's Handy Tables. This work partially survives. It originally consisted of 5 books, of which books 1–3 and the beginning of book 4 are extant. It describes how to use Ptolemy's tables and gives details on the reasoning behind the calculations. [1] Little Commentary on Ptolemy's Handy Tables. This work survives complete.
Advanced Placement (AP) Psychology (also known as AP Psych) and its corresponding exam are part of the College Board's Advanced Placement Program. This course is tailored for students interested in the field of psychology and as an opportunity to earn Advanced Placement credit or exemption from a college -level psychology course.
An edition in Latin of the Almagestum in 1515. The Almagest (/ ˈ æ l m ə dʒ ɛ s t / AL-mə-jest) is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy (c. AD 100 – c. 170) in Koine Greek. [1]
According to Ptolemy's theorem, The product of the diagonals is equal to the sum of the products of the opposite sides. In this case, c*c = a*a + b*b (By Ptolemy's theorem) Thus a 2 + b 2 = c 2. Hence proved. Midhul 14:58, 10 August 2009 (UTC) Yes, the Pythagorean theorem follows from Ptolemy's theorem, because the latter is a generalization of ...