Aristarchus' inequality

Aristarchus' 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

{\frac {\sin \alpha }{\sin \beta }}<{\frac {\alpha }{\beta }}<{\frac {\tan \alpha }{\tan \beta }}.

Ptolemy used the first of these inequalities while constructing his table of chords.^[1]

Notes and references

↑ Toomer, G. J. (1998), Ptolemy's Almagest, Princeton University Press, p. 54, ISBN 0-691-00260-6

External links

Hellenistic Astronomers and the Origins of Trigonometry, by Professor Gerald M. Leibowitz

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