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Ancient Greek and Hellenistic mathematicians made use of the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector passes through the center of the circle and bisects the angle. One half of the bisected chord is the sine of one half the bisected angle, that is, [13]
Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
He also discovered the binomial theorem for integer exponents, which "was a major factor in the development of numerical analysis based on the decimal system". 975 – Mesopotamia, al-Battani extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions.
In a lost work, he discovered and enumerated the 13 Archimedean solids, which were later rediscovered by Johannes Kepler around 1620 A.D. Apollonius of Perga (c. 240 – c. 190 BC) is known for his work on conic sections and his study of geometry in 3-dimensional space. He is considered one of the greatest ancient Greek mathematicians.
The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, [1] a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function.
The Ancient Tradition of Geometric Problems studies the three classical problems of circle-squaring, cube-doubling, and angle trisection throughout the history of Greek mathematics, [1] [2] also considering several other problems studied by the Greeks in which a geometric object with certain properties is to be constructed, in many cases through transformations to other construction problems. [2]
Pythagoras of Samos [a] (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) [b], often known mononymously as Pythagoras, was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism.
Continuing the geometrical legacy of ancient China, there were many later figures to come, including the famed astronomer and mathematician Shen Kuo (1031–1095 CE), Yang Hui (1238–1298) who discovered Pascal's Triangle, Xu Guangqi (1562–1633), and many others.