Ptolemy's Theorem

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy.

If the quadrilateral is given with its four vertices A, B, C, and D in order, then the theorem states that:

where the vertical lines denote the lengths of the line segments between the named vertices.

This relation may be verbally expressed as follows:

If a quadrilateral is inscribable in a circle then the product of the measures of its diagonals is equal to the sum of the products of the measures of the pairs of opposite sides.

Moreover, the converse of Ptolemy's theorem is also true:

In a quadrilateral, if the sum of the products of its two pairs of opposite sides is equal to the product of its diagonals, then the quadrilateral can be inscribed in a circle.

Read more about Ptolemy's TheoremCorollaries, Ptolemy's Inequality

Other articles related to "ptolemy":

Siege Of Alexandria (47 BC) - Events
... He demanded the money Ptolemy's father Ptolemy XII Auletes had been lent by Rome and agreed to settle the dispute between Ptolemy and his sister and co-regent Cleopatra VII ... Meanwhile, Arsinoe, the younger sister of Ptolemy, escaped from Caesar and joined Achillas ... Under a pretext of wanting peace, they negotiated with Caesar to exchange Arsinoƫ for Ptolemy XIII, who was subsequently released only to continue the war ...
Luentinum - Ptolemy
... The name Luentinum appears only in Ptolemy's Geographia ... It appears to be related to the Brythonic word for 'washing', as suggested by George Boon of the National Museum of Wales ...
Named After Ptolemy
... There are several characters or items named after Ptolemy, including The crater Ptolemaeus on the Moon The crater Ptolemaeus on Mars The asteroid 4001 Ptolemaeus A character in the ... The Ptolemy Stone used in the mathematics courses at both St ... and TV presenter Sir Patrick Moore has a cat named Ptolemy ...
... Ptolemy I sent ambassadors to visit the shrine of Pythian Apollo at Delphi ... Years passed and Ptolemy continued his appeals to Scydrothemis, upgrading his gifts all the time ... explained to them the orders of the deity, his own vision and that of Ptolemy, and their ever growing afflictions ...
List Of Women Warriors In Folklore - Near East - Ancient Egypt
... a Hellenistic co-ruler of Egypt with her father (Ptolemy XII Auletes) and later with her brothers/husbands Ptolemy XIII and Ptolemy XIV ...

Famous quotes containing the word theorem:

    To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.
    Albert Camus (1913–1960)