were followed by prose commentaries. Fifth and sixth centuries Surya Siddhanta Though its authorship is unknown, the Surya Siddhanta (c. 400) contains the roots of modern trigonometry. Because it contains many words of foreign origin, some authors consider that it was written under the influence of Mesopotamia and Greece. This ancient text uses the following as trigonometric functions for the first time: Sine (Jya). Cosine (Kojya). Inverse sine (Otkram jya). It also contains the earliest uses of: Tangent. Secant. Later Indian mathematicians such as Aryabhata made references to this text, while later Arabic and Latin translations were very influential in Europe and the Middle East. Chhedi calendar This Chhedi calendar (594) contains an early use of the modern place-value Hindu–Arabic numeral system now used universally. Aryabhata I Aryabhata (476–550) wrote the Aryabhatiya. He described the important fundamental principles of mathematics in 332 shlokas. The treatise contained: Quadratic equations Trigonometry The value of π, correct to 4 decimal places. Aryabhata also wrote the Arya Siddhanta, which is now lost. Aryabhata's contributions include: Trigonometry: (See also : Aryabhata's sine table) Introduced the trigonometric functions. Defined the sine (jya) as the modern relationship between half an angle and half a chord. Defined the cosine (kojya). Defined the versine (utkrama-jya). Defined the inverse sine (otkram jya). Gave methods of calculating their approximate numerical values. Contains the earliest tables of sine, cosine and versine values, in 3.75° intervals from 0° to 90°, to 4 decimal places of accuracy. Contains the trigonometric formula sin(n + 1)x − sin nx = sin nx − sin(n − 1)x − (1/225)sin nx. Spherical trigonometry. Arithmetic: Continued fractions. Algebra: Solutions of simultaneous quadratic equations. Whole number solutions of linear equations by a method equivalent to the modern method. General solution of the indeterminate linear equation . Mathematical astronomy: Accurate calculations for astronomical constants, such as the: Solar eclipse. Lunar eclipse. The formula for the sum of the cubes, which was an important step in the development of integral calculus. Varahamihira Varahamihira (505–587) produced the Pancha Siddhanta (The Five Astronomical Canons). He made important contributions to trigonometry, including sine and cosine tables to 4 decimal places of accuracy and the following formulas relating sine and cosine functions: Seventh and eighth centuries In the 7th century, two separate fields, arithmetic (which included measurement) and algebra, began to emerge in Indian mathematics. The two fields would later be called (literally "mathematics of algorithms")