Aristarchus's 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.

External links

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