A NOVEL METHOD TO FIND THE EQUATION OF CIRCLES

Abstract

The concept of the circle has been known to human beings since before the beginning of recorded history. With the advent of the wheel, the study of the circle in detail played an important role in the field of science and technology. According to the author, there are three types of circles, 1) Countup circle, 2) Countdown circle, and 3) Point circle instead of two types of circles as defined by René Descartes in real plane coordinate geometry and Euler in the complex plane. The author has been successful to solve the equations of three types of circles in the real plane by using three fundamental recent (2021 – 2022) inventions, 1) Theory of Dynamics of Numbers, 2) Rectangular Bhattacharyya’s Co-ordinate System, 3) The novel Concept of Quadratic Equation where the author becomes successful to solve the quadratic equation of x2 + 1 = 0 in real number instead of an imaginary number. In the present paper, the author solved successfully the problem where radius if g2 + f2 < c, c the constant term of the general form of the equation of a circle x2 + y2 + 2gx + 2fy + c = 0 by using Bhattacharyya’s Coordinate system without any help from the complex plane where Euler solved it by using a complex plane. According to Bhattacharyya’s Co-ordinate System, the equation of the countdown circle is as follows : where, the coordinates of the moving point P are (x, y) with Centre C (a, b) and radius = – r The concept of a countdown circle is very much interesting and it exists really in nature. We may consider that the rotational motion of the Earth around the Sun is a countdown rotational motion.