कुट्टक-चक्रवालन्यासविधि - The Solutions of Linear and Quadratic Indeterminate Equation

A Modern Approach to Ancient Bharatiya Mathematics

₹1600.00

Course Overview

Bharat has a long tradition of mathematics as a core discipline since the Vedic era. Eminent scholars—Baudhayana, Aryabhata, Brahmagupta, Shridhara, Bhaskara, Narayana Pandita, Madhava, Ramanujan, among others—have ensured an unbroken Ganita-Ganga, a continuous flow of mathematical knowledge.

A key contribution is the study of indeterminate equations, where variables outnumber equations. In Bharatiya terminology, first-degree indeterminate equations are called कुट्टक (kuttaka)—from kutta, “to pulverize”—and second-degree equations are called वर्ग प्रकृती, denoting their quadratic nature. While such solutions are traced to around 800 BC, systematic methods were pioneered by Aryabhata (499 AD) and refined by Brahmagupta (629 AD), Mahavira (850 AD), Bhaskara II (1150 AD), Narayana Pandita (1356 AD), and others.

This course studies Bharatiya methods for solving first- and second-degree equations, presenting them in modern notation and algorithms. It highlights the intellectual approach of Bharatiya mathematicians and their advanced solutions for integer equations, centuries ahead of their global counterparts—deepening both understanding and pride in this legacy.

Course Curriculum

1 Subject

Kuttaka

13 Learning Materials

Course Content

Introduction to Linear Indeterminate Equations

Video
00:28:32

Solutions of Linear Indeterminate Equations (Type 1 and Type 2)

Video
00:47:34

Solutions of Linear Indeterminate Equations (Type 3: Amended Valli Method)

Video
00:46:50

Solutions of Linear Indeterminate Equations (Type 3: Amended Division Method)

Video
00:42:12

Two-and Three-Remainder Problems

Video
00:58:04

Four and More Remainder Problems

Video
00:53:45

Simultaneous Indeterminate Equations (Equal and Unequal Divisors)

Video
00:36:22

Second Degree Indeterminate Equations Type 1 (Rational Solutions)

Video
00:17:12

Second Degree Indeterminate Equations Type 1 (Integer Solutions: Bhavana Method)

Video
01:10:00

Second Degree Indeterminate Equations Type 1 (Integer Solutions: Chakravala Method)

Video
00:36:48

Second Degree Indeterminate Equations Type 1 (Integer Solutions: New Algorithm)

Video
00:54:17

Second Degree Indeterminate Equations Type 2 (Rational and Integer Solutions)

Video
00:37:49

Second Degree Indeterminate Equations Type 2 (Integer Solutions: Chakravala Method)

Video
00:33:18

About Dr. Shriram Chauthaiwale

Dr. Shriram Chauthaiwale, M.Sc. (Mathematics), Ph.D., B.A. (Philosophy), B.Ed., is a retired lecturer from Amolakchand College, Yavatmal (Amravati University). He currently serves as Chairperson of the National Curriculum Focus Group – Mathematics at NCERT, New Delhi, and is a member of:

  • Indian Society for History of Mathematics, New Delhi

  • Bhandarkar Oriental Research Institute, Pune

  • Executive Council, Chennai Mathematical Institute

  • Board of Studies, Central Sanskrit University, Delhi

He is the All India Convenor for Vedic Ganit and IKS at Shiksha Samskriti Nyas, and a national member of the Vedic Ganit team, Vidya Bharati. As Chief Faculty for Vedic Mathematics Teacher Training at the Art of Living International Centre, Bengaluru, he has trained educators across India.

Recipient of the 10th Madhav Ganit Puraskar (Kerala), Dr. Chauthaiwale has authored 11 books and published 30+ research papers on the history and pedagogy of mathematics in national and international journals. He has delivered 100+ lectures, webinars, and workshops for students and teachers at leading universities and institutions across India.

His outreach includes popular articles, radio talks, a 10-episode UGC Gyanaranjan TV series on Vedic Mathematics, and a podcast on Ancient Bharatiya Mathematics (October 2024).

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