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The estimates of his dates of birth and death are in dispute. He is
known to have given public lectures in Alexandria between years 125-140.
Ptolemy is most commonly associated with the development of the mathematics
of astronomy. His most famous work is a thirteen-volume set now referred
to as the Almagest (which roughly translates from the Arabic as 'The
Greatest', a name intended to single out his work from among several
of a similar, but less significant type). This book established theories
for explaining the movements of planets, sun, and moons. In his development
of this complex theory, Ptolemy established many basic math facts, and
invented a type of function that he referred to as the 'chord'. He used
this chord function to establish relationships between angles, and developed
a theory of these relationships that is a precursor to what we now know
as trigonometry. If A is the name of an angle, the sine(A) is equivalent
to 120 times the chord (2A). His work with the chord function allowed
him to formulate counterparts to several of our commonly used trig identities,
such as sines of sums and differences, half angle and double angle formulas.
After establishing general properties of the chord function, he applied
this function to various special angles to generate many such identities,
which he subsequently used to formulate a theory of spherical trigonometry,
as well as a crude counterpart to more contemporary trig tables.
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