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The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, [1] a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function.
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.
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]
Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
A theorem that was central to Ptolemy's calculation of chords was what is still known today as Ptolemy's theorem, that the sum of the products of the opposite sides of a cyclic quadrilateral is equal to the product of the diagonals. A special case of Ptolemy's theorem appeared as proposition 93 in Euclid's Data.
In the 2nd century AD, the Greco-Egyptian astronomer Ptolemy (from Alexandria, Egypt) constructed detailed trigonometric tables (Ptolemy's table of chords) in Book 1, chapter 11 of his Almagest. [11] Ptolemy used chord length to define his trigonometric functions, a minor difference from the sine convention we use today. [12] (The value we call ...
The first of these theorems is the spherical analogue of a plane theorem, and the second theorem is its dual, that is, the result of interchanging great circles and their poles. [32] Kiper et al. [ 33 ] proved a converse of the theorem: If the summations of the opposite sides are equal in a spherical quadrilateral, then there exists an ...
Chord (geometry) Circle (also see List of circle topics) Unit circle; Hypotenuse; Opposites post; π (pi) Ptolemy's theorem; Pythagorean theorem; Regiomontanus' angle maximization problem; Thales' theorem; Trigonometric function; Trigonometry of a tetrahedron; Triangle (also see List of triangle topics)