A timeline of algebra and geometry

## 1st millennium

• ca. 340 – Pappus of Alexandria states his hexagon theorem and his centroid theorem
• 500 – Aryabhata writes the “Aryabhata-Siddhanta”, which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of sine and cosine, and also contains the earliest tables of sine and cosine values (in 3.75-degree intervals from 0 to 90 degrees)
• 7th century – Bhaskara I gives a rational approximation of the sine function
• 8th century – Virasena gives explicit rules for the Fibonacci sequence, gives the derivation of the volume of a frustum using an infinite procedure, and also deals with the logarithm to base 2 and knows its laws
• 8th century – Shridhara gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations
• 820 – Al-Mahani conceived the idea of reducing geometrical problems such as doubling the cube to problems in algebra.
• ca. 900 – Abu Kamil of Egypt had begun to understand what we would write in symbols as ${\displaystyle x^{n}\cdot x^{m}=x^{m+n))$
• 975 – Al-Batani – Extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions. Derived the formula: ${\displaystyle \sin \alpha =\tan \alpha /{\sqrt {1+\tan ^{2}\alpha ))}$ and ${\displaystyle \cos \alpha =1/{\sqrt {1+\tan ^{2}\alpha ))}$.

## 17th century

• 17th century – Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series
• 1619 – Johannes Kepler discovers two of the Kepler-Poinsot polyhedra.