# Kuttaka: Mathematical Elegance from Ancient India

Take a broad look at the Mathematics developed by the early Indian mathematicians/ astronomers, and dive deep into the Kuttaka method used to solve indeterminate equations with multiple solutions- the most elegant and effective method to do so, even today.

Starts

17 June 2020

Time

8:00 - 9:15pm

On Days

Fee (₹, incl taxes)

Audience

We/Sa/We/Sa

2950

Grown-Ups/ Lifelong Learners!

<p><em>(This   course is intended for Math enthusiasts Grade 9 and above i.e. high school   students and grown-ups of any age)</em></p>
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<p>In high school we learn to solve linear algebraic equations of one   or two or three variables. We also learn to solve quadratic equations in one   variable. We don�t learn solving indeterminate equations, which have multiple   solutions.</p>
<p>A classic example of the above problem in what is known as Chinese   Remainder Theorem, which is posed as follows: Find a number N which leaves a   remainder 3 when divided by 7 and a remainder 1 when divided by 9. The most   comprehensive generalised algorithm to solve such a problem was given by   Aryabhata, in the 6th century CE. The solution method is known as   Kuttaka.</p>
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<p>These problems occur naturally in Astronomy and that is why the   Indian mathematicians/astronomers were looking to solve them. For example, in   a particular case of finding the number of days and the revolutions performed   by the Sun, the following equation</p>
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<p>y&#61; (576x-86638)/ 210389</p>
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<p>has to be solved for x, y as positive integers. It can be shown   that the above astronomy problem and the remainder problem are one and the   same. They end up in similar looking equations. To this day, Aryabhata�s   method of solving them is the most elegant and efficient   available.</p>
<p>We will take a broad look at the Mathematics developed by the   early Indian mathematicians and then study the above problem in depth. We   will solve such problems using modular arithmetic and then move to   Aryabhata�s kuttaka algorithm.</p>
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