Hipparchus's 3600'-Based Chord Table and Its Place in the History of Ancient Greek and Indian Trigonometry

Indian Journal of History of Science 40 (2):169-203 (2005)

Abstract
With mathematical reconstructions and philosophical arguments I show that Toomer's 1973 paper never contained any conclusive evidence for his claims that Hipparchus had a 3438'-based chord table, and that the Indians used that table to compute their sine tables. Recalculating Toomer's reconstructions with a 3600' radius -- i.e. the radius of the chord table in Ptolemy's Almagest, expressed in 'minutes' instead of 'degrees' -- generates Hipparchan-like ratios similar to those produced by a 3438' radius. It is therefore possible that the radius of Hipparchus's chord table was 3600', and that the Indians independently constructed their 3438'-based sine table.
Keywords ancient Greek mathematics  ancient Indian mathematics  trigonometry  Ptolemy  Hipparchus  Aryabhata
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