Knowra Madhava of Sangamagrama Madhava of Sangamagrama Madhava of Sangamagrama was a 14th-century Indian mathematician and astronomer who founded the Kerala school of mathematics and derived infinite series for trigonometric functions.
Infinite series : A sum of infinitely many terms defined by a sequence of partial sums. Madhava used convergent infinite series to represent trigonometric quantities.
Madhava–Leibniz series : The alternating series for arctangent whose value at one is pi divided by four. This rapidly recognized form is associated with Madhava’s calculation of pi.
Kerala : A state on India’s southwestern coast, historically home to the Kerala school of mathematics. Sangamagrama, Madhava’s associated place, is identified with a location in this region.
Calculus : The branch of mathematics concerned with limits, derivatives, integrals, and infinite processes. Madhava’s series anticipated techniques later central to calculus, without establishing the same European framework.
Trigonometric functions : Functions that relate angles to ratios or coordinates, including sine, cosine, and tangent. His best-known series express sine, cosine, and arctangent.
Madhava sine series : An infinite power series expressing the sine of an angle through alternating odd powers. It is one of the trigonometric expansions attributed to Madhava.
Sangamagrama : The historical place-name associated with Madhava, commonly identified with Irinjalakuda in Kerala. It forms the place-name in Madhava’s conventional title.
History of calculus : The historical development of differential and integral calculus across mathematical cultures. Madhava’s work complicates accounts focused only on seventeenth-century Europe.
Power series : An infinite series whose terms are coefficients multiplied by successive powers of a variable. His trigonometric expansions take this form.
Madhava cosine series : An infinite power series expressing the cosine of an angle through alternating even powers. It complements Madhava’s sine expansion in his trigonometric work.
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