## Table of Contents

## Introduction to Chakravala approach

Algorithms are used in mathematics to solve complex problems and reveal the secrets of numbers. They act as a guide that illuminates the way of solving indeterminate quadratic equations. The Chakravala approach, which unites traditional Indian mathematical knowledge with cutting-edge problem-solving methodologies, stands out among the myriad mathematical techniques as a rare gem. This approach, which has its roots in number theory, continues to enthrall mathematicians and exemplifies how brilliant mathematics is always relevant.

One of the famous mathematicians of the seventh century CE, Brahmagupta, invented this technique for getting integer solutions. Later, mathematician named Jayadeva developed this approach for a wider range of equations, and Bhskara II further improved it in his Bijaganita treatise.

## Contribution from Bhaskara II:

In particular, the eminent mathematician Bhaskaracharya II, who lived in the 12th century, is where the Chakravala method got prominence. The “Bijaganita,” a work by Bhaskaracharya, contained a wealth of mathematical information, including the Chakravala technique. The word “Chakravala” means “cyclic” or “repeating process,” which accurately captures the cyclical nature of this technique.

## Chakravala Method:

The Chakravala method is fundamentally an algorithm for resolving quadratic Diophantine equations. Finding integer answers to equations of the form ax + by = cz is required for these problems. The method uses an organized approach to simplify a given problem while keeping the ability to use the solutions of the simplified equation to get answers to the original equation.

The algorithm consists of a series of operations that alter the equation’s coefficients in order to get closer to a solution. Although the procedure may appear complicated, it demonstrates a clever blend of modular algebra, quadratic operations, and cyclic patterns that testifies to the profound number theory knowledge of ancient Indian mathematicians.

The Chakravala method dates back to the ages, although it still has value in contemporary mathematics. The elegance and efficiency of the method demonstrate how mathematical concepts are ageless. The Chakravala approach also acts as a link between traditional problem-solving methods and historical mathematical background.

## Ancient Indian Wisdom:

The Chakravala technique has been the subject of ongoing research and study by academics and mathematicians because of its importance to mathematics as well as the window it offers into the superior thinking abilities of early Indian mathematicians. The cyclical structure and clever modifications of the algorithm continue to motivate new generations of mathematicians to solve problems in novel and imaginative ways.

The Chakravala method of algorithms serves as a reminder that innovation is not limited by geography or time. Human intelligence is characterized by the capacity to come up with elegant and effective solutions, and the Chakravala technique is evidence of the creativity of mathematicians who attempted to understand the secrets of numbers.

It inspires us to value past experiences and use them to push ourselves in a proactive manner today. We continue to build upon the foundations provided by the ancient mathematicians, broadening the boundaries of human knowledge, just as they did.