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The area of the square can be calculated with the help of side (a) of it. The formula is a2. Similarly, the area of the triangle can be calculated with the help of altitude (a) and base (b) of the triangle. The formula is ½ ab.
The area of the square can be calculated with the help of side (a) of it. The formula is a2. Similarly, the area of the triangle can be calculated with the help of altitude (a) and base (b) of the triangle. The formula is ½ ab.
The area and the length of the circumference of the circle can be calculated with the following formulae: where r = radius
The official value 3.14159265358… though has been in vogue for the last 2000 years, nobody could succeed to devise a formula with radius alone. The main reason is that 3.14159265358… is not value. Radius, invariably gives the true value in the simplest formula.
Further, in the above formulae the involvement of is questioned by almost all who are carried away by the CLF Lindemann’s proof of 1882 saying that 3.14159265358… is a transcendental number. He is right if he says 3.14159265358… is a transcendental number. Unfortunately, it is not the of the circle.
Secondly, if anybody asks, is square or circle is first on the lines of “egg and chick” which is first ? This author believes that circle is first. How ? One can draw circle easily with fingers only and without the help of the instrument compass. But, drawing a square is not difficult but impossible. 2. All the celestial bodies: stars, planets etc. are spherical in shape. Eyeball is spherical and iris and pupil in the eyeball are circular in shape.
Though the irrational number was discovered first in the square by Hippasus (5th Century BC) of Metapontum (and for his great discovery he was drowned by the fellow Pythagoreans), square root two’s ( ) existence was not noticed in the circle, then is a hidden truth in the circle.
A square can be created with circle as its four equidistant chords.And also, a square can be created as a circumscribed one about a circle, as its four equidistant tangents. Similarly, can be obtained with just circles arranged in different patterns. Thus, is originally a part of the circle although it was discovered from the square first. The above formulae are thus the proof to associate that with circle is a natural phenomenon of Geometry and not, and circle, are the two incompatible entities, definitely.
It is sad to hear about Hippasus, that “If true, the story indicates the dangers inherent in free thinking, even in the relatively austere discipline of mathematics” (William Dunham, Journey through Genius, Page 10). Truth cannot be suppressed permanently. It is proved now that is an algebraic number with the March 1998 discovery of =
3.14644660941… Mathematicians have been trying squaring a circle. Prof. Petr Beckmann (1971) in his book, The History of Pi (Page 173) says “But undaunted by either the Academy’s resolution or Lindemann’s proof, the circle squares marched on; and they are still marching, spiteful of the cruel world that will not recognize their grand intellectual achievements”.
The search for truth thus puts the scholar sometimes in a helpless situation. This happened to Hippasus and Bruno, killing them both, the former for introducing and the latter in supporting the Heliocentric theory. It appears that, the “intolerance” still persists now in the academic world.
This author is being laughed at, at his very face by some local Professors and some became very furious too. Some outside Professors have gone to the extent of abusing this author personally through their emails using filthy words. Is it not much more grievous than killing, Sir ? I request every mathematician to spend a few minutes and decide for or against the algebraic nature of, which is a fundamental concept in Mathematics.
(Hundred different geometrical methods are available in support of the above formulae. Contact the author at [email protected]. Two simple methods will be sent by e-mail on request)
By:RSJ Reddy
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