Aristarchus' inequality
Encyclopedia
In trigonometry
, Aristarchus' inequality, named after the ancient astronomer Aristarchus of Samos
, states that if α and β are acute angles (i.e. between 0 and a right angle) and β < α then
The first of these inequalities was used by Ptolemy
in constructing his table of chords
.
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
, Aristarchus' inequality, named after the ancient astronomer Aristarchus of Samos
Aristarchus of Samos
Aristarchus, or more correctly Aristarchos , was a Greek astronomer and mathematician, born on the island of Samos, in Greece. He presented the first known heliocentric model of the solar system, placing the Sun, not the Earth, at the center of the known universe...
, states that if α and β are acute angles (i.e. between 0 and a right angle) and β < α then
The first of these inequalities was used by Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
in constructing his table of chords
Ptolemy's table of chords
The table of chords, created by the astronomer and geometer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function...
.