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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 ]
Ptolemy's Handy Tables. A collection of astronomical tables originally compiled by Ptolemy. [11] It has often been claimed in modern times that Theon edited this text. [12] However, none of the surviving manuscripts mention Theon, [13] and the evidence suggests that the surviving tables must be very similar to the tables Ptolemy provided.
Aristarchus's inequality (after the Greek astronomer and mathematician Aristarchus of Samos; c. 310 – c. 230 BCE) is a law of trigonometry which states that if α and β are acute angles (i.e. between 0 and a right angle) and β < α then
Ptolemy, a general and one of the somatophylakes (bodyguard companions) of Alexander the Great, was appointed satrap of Egypt after Alexander's death in 323 BC. In 305 BC he declared himself Pharaoh Ptolemy I, later known as Sōter "Saviour". The Egyptians soon accepted the Ptolemies as the successors to the pharaohs of independent Egypt.
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]