Development of the Accuracy of Pi in Different Cultures over Time (original) (raw)
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What is π (on the history, development and use of π, beginning more than 2000 years BC)
conference paper, 2023
What is π, we all grow up understanding the circle number π, which helps to calculate the circumference and other parameters of the circle. Nevertheless, how and when was this constant or coefficient, discovered? Were there developments? Which steps were necessary for these? This short essay tries to shed light on the darkness of the past. In this elaboration, the main focus should be on the emergence or gradual discovery of this circular constant, from where it arose with high probability, is our present-day π really the ancient used constant or coefficient itself? Why did π or the underlying ratio gain scientific importance? When and how was π calculated more precisely in ancient times?
Indian Methods of finding the approximate value of π and the development of calculus
Many Indian mathematicians calculate the approximate value of π. The value of π stated by Āryabhata – I was accepted by all the mathematicians which is (π = 22/7). Indian mathematicians used different methods to find the values of π. Madhava of Sangamgram of Kerala calculated the value of π in terms of infinite series. This method of finding the value of π is the beginning of idea of calculus in India. These methods are found in the text Yuktibhasha of Jyesthadeva (1500-1610 ad.),Tantrasangraha of Nilakantha (1443-1560 ad.),Kriyakramakari of Sankara Variyar (1500-1560 ad.). We have discussed here three methods of finding the value of π and also calculus involved in it. These three methods cover the idea of infinitesimal calculus. These methods are as follows.
2018
There is little known about the methods used by the ancient Babylonians and Egyptians to arrive at their recorded estimates of the value of Pi. A surprisingly accurate estimate of Pi was recently revealed coded within a verse in the book of 1 Kings, the value of which suggests how it might have been measured. The coded value is 111/106, which is a continued fraction representation of Pi/3. This suggests that the value may have been measured using an iterative measurement of remainders when comparing the two lengths C (circumference of the circle) and 6R (6 times the radius). This article describes a method that could have been used 3000 years ago to make such a measurement, the expected measurement errors, and a computer simulation that assesses the chances of such a method succeeding in obtaining the coded value of 111/106. The result indicate that with the technology available at the time the proposed measurement method would have been possible and would have had about a 75% chanc...
Geometrical Method of Determination of the Value of Pi (π)
OM PUBLICATION, 2019
The value of an irrational number pi (π) is determined from the ancient times up to the modern super computer era. It is found to be irrational number. We give here geometrical method of determination of Pi (π) and we determind it as 3.141592653. This perticualer value is named as “Goba" and the relation between Circumference of Circle and its radius is fixed as Circumference of Circle = 2 x Goba x r.
Value of Pi Were Babylonians the most accurate
International Journal of Advancements in Research & Technology – (ISSN 2278-7763), 2013
Area of an inscribed circle in a square is equal to square of 1/4th of sums of square roots of the squares on the opposite diagonals and the square root of the area of Secondary Square formed by overlapping of squares on the opposite diagonals
National Institute of Vedic Sciences Seminar Proceedings, 2015
William Jones is said to be the first person to use Pi, for representing the ratio of the circumference of a circle to its diameter. This gained popularity when Leonard Euler adopted the symbol. In 1761 Lambert proved that Pi is irrational and C. L. F. Lindemann, a German mathematician, established that Pi is a transcendental number which cannot be expressed as a root of an algebraic equation with rational co-efficients. In the first quarter of the nineteenth century, Benjamin Heyne and Charles Whish, officers serving under the East India Company, came across traditional practitioners of Indian astronomy who seemed to be conversant with several infinite series for the ratio of the circumference of a circle (Pi, a Greek alphabet). Such series were generally believed to have been discovered first in Europe by Gregory, Newton and Leibniz in the second half of the 17th Century. But in India, during the Vedic period, the Śulbasūtras record an approximation for Pi. Āryabhaṭa I, of the 5th Century, was the first gave an approximate value (āsanna) for Pi. After a long gap this approximation was taken up by a well known Kerala mathematician Mādhava from Sangamagrama in his work Veṇvāroha. After Mādhava, Nīlakaṇṭa Somayāji's Tantrasaṇgraha, Jyeṣṭadeva's Yuktibhāṣa, Putumana Somayāji's Karṇapaddhati, Śaṅkaravarman's Sadratnamālā, have given various approximations for Pi. Indian Architecture (Vāstuvidyā) is as old as atleast the Indus Valley Civilization. Tantrasamuccaya of Nārāyaṇan Namboothirippad, Śilparatna of Śrīkumāra, Vāstuvidyā, Manuṣyālayacandrikā of Thirumangalath Neelakanthan etc., are some of the well known architectural texts of Kerala. These texts also give approximations for Pi while discussing the construction of various prāsādas.
The research, the theory of À is not connected with economics activities, but it is a pure science & pure mathematics, which does not gain anything much to the society and does not motivate the economic activities like applied research. This research does not have much important to society in general, but can be useful to astronomy, astrophysics, space calculations, nuclear science, pure geometry and exact measurement of curved area, surfaces & volume with curved surface in physics only. The research, the theory of À uses the major tool as algebra, geometry, trigonometry, arithmetic, statistics & calculus with the help of even simple calculator, pc. , Main framed computer & super computer in the form of mathematical formulas and Computer programming. Present value of Àt -3.141592653589793238462643383279502884197169399375105820974944592307816406286209 is not correct at all. It is not the area of circle but it is area of regular polygon having infinite sides. Hence we create vertical line at equi-distance method and with the help of computer program UP09R that is based on our method, we calculate value of À that is 3.1416 which we have suggested is the area of circle and is rational & exact most probable number.