A History of the Kerala School of Hindu Astronomy (in Perspective) c8.s7.3

c8.s7.3

The *Kuṭṭakāra-gaṇita*, which is a complex type of calculation involving the Rule of three, Indeterminate equations and Continued fractions, has been developed by Kerala mathematicians to a high degree. It enabled them to solve various problems which require the application of higher algebra according to modern working. *Śaṅkaranārāyaṇa* (*c.* 825-900) quotes in his commentary on the *Lahgubhāskarīya* (*op. cit.*, pp. 95-97) a short disquisition on the subject from *Govindakṛti*, a lost work of Govindasvāmin, while the later works like *Yuktibhāṣā* (16th cent.) give full accounts of the processes involved.¹ Nīlakaṇṭha Somayājī (1444-1545) has made significant contributions including logical proofs and demonstrations to geometrical theorems, a formula for the sum of an infinite, geometrically progressing convergent series, and the rationale for the formula for the sum of a geometrical progression. He has also offered geometrical demonstrations for the sum of an arithmetic progression, the sum of triangular numbers and the sums of squares and cubes of natural numbers.²