Virasena

Āchārya Virasena was an 8th century India

India

India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

n mathematician

Indian mathematics

Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today was first...

 and Jain

Jainism

Jainism is an Indian religion that prescribes a path of non-violence towards all living beings. Its philosophy and practice emphasize the necessity of self-effort to move the soul towards divine consciousness and liberation. Any soul that has conquered its own inner enemies and achieved the state...

 philosopher and scholar. He was a student of the Jain sage Elāchārya. He is also known to be a famous orator and an accomplished poet. His most reputed work is the Jain treatise Dhavala. Late Dr. Hiralal Jain places the completion of this treatise in 816 AD.

Virasena was a noted mathematician. He gave the derivation of the volume

Volume

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

 of a frustum

Frustum

In geometry, a frustum is the portion of a solid that lies between two parallel planes cutting it....

 by a sort of infinite procedure. He worked with the concept of ardhaccheda: the number of times a number could be divided by 2; effectively logarithms to base 2. He also worked with logarithms in base 3 (trakacheda) and base 4 (caturthacheda).

Virasena gave the approximate formula C = 3d + (16d+16)/113 to relate the circumference of a circle, C, to its diameter, d. For large values of d, this gives the approximation π ≈ 355/113 = 3.14159292..., which is more accurate than the approximation π ≈ 3.1416 given by Aryabhata

Aryabhata

Aryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...

 in the Aryabhatiya

Aryabhatiya

Āryabhaṭīya or Āryabhaṭīyaṃ, a Sanskrit astronomical treatise, is the magnum opus and only extant work of the 5th century Indian mathematician, Āryabhaṭa.- Structure and style:...

.