Madhava's sine table

Madhava's sine table is the table of trigonometric sines constructed by the 14th century Kerala mathematician-astronomer Madhava of Sangamagrama (c. 1340 – c. 1425). The table lists the jya-s or Rsines of the twenty-four angles from 3.75° to 90° in steps of 3.75° (1/24 of a right angle, 90°). Rsine is just the sine multiplied by a selected radius and given as an integer. In this table, as in Aryabhata's earlier table, R is taken as 21600 ÷ 2π ≈ 3437.75.

The table is encoded in the letters of the Sanskrit alphabet using the Katapayadi system, giving entries the appearance of the verses of a poem.

Madhava's original work containing the table has not been found. The table is reproduced in the Aryabhatiyabhashya of Nilakantha Somayaji (1444–1544) and also in the Yuktidipika/Laghuvivrti commentary of Tantrasamgraha by Sankara Variar (circa. 1500–1560).

The verses below are given as in Cultural foundations of mathematics by C.K. Raju. They are also given in the Malayalam Commentary of Karanapaddhati by P.K. Koru but slightly differently.

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