Trigonometry & Geometry Article

Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right.[21] Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof. His book, Elements, is widely considered the most successful and influential textbook of all time.[22] The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse.[23] He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.[24] Other notable achievements of Greek mathematics are conic sections (Apollonius of Perga, 3rd century BC),[25] trigonometry (Hipparchus of Nicaea, 2nd century BC),[26] and the beginnings of algebra (Diophantus, 3rd century AD).[27]
The numerals used in the Bakhshali manuscript, dated between the 2nd century BC and the 2nd century AD.

The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics.[28] Other notable developments of Indian mathematics include the modern definition and approximation of sine and cosine,[28] and an early form of infinite series.