e and pi

This book is intended for anyone who wants to learn, or refresh their understanding of, some of the basic elements of mathematics and how they relate to each other. It differs from conventional texts primarily in terms of the sequence in which its material is presented, and in the connecting threads between topics. Where possible, it seeks to present mathematics in the order in which humankind discovered it, giving passing references to the discoverers of particular branches as it does so, and showing how one discovery led to the next. As a result, at whatever point a student leaves the course, he or she ought to have acquired a body of knowledge which has a definite beginning and progresses intelligibly towards a definite end. In particular, we celebrate in this book the Swiss mathematician Leonhard Euler (pronounced "oiler") (1707-1783), surely the greatest mathematician of the eighteenth century and unquestionably one of the greatest of all time. As Laplace said of him, 'He is the master of us all.' Euler's celebrated unification of trigonometry, complex numbers, and exponentials, described in his Introductio in Analysin Infinitorum (1744, published 1748), takes us to the climax of this book. In it he brings together the three most fundamental constants around which this book is based: e : central to logarithms, exponentials and the calculus, i : central to complex numbers, and pi : central to trigonometry (and much else). From this follows what is probably the most beautiful and astonishing equation in all mathematics: e^i*pi + 1 = 0 or, re-expressed, e^i*pi = -1 This book attempts to chart the path which leads to that climax. In addition it touches on the philosophy of mathematics, commenting from time to time on the famous debate as to maths is discovered or invented.

This paper has been prepared to demonstrate a Pythagorean relationship between three transcendental and irrational numbers ߮, ݁, and π , creating a triangle with internal angles of 30 o , 60 o and 90 o within an accuracy of 1% in 2 dimensions. and to within 0.02% by incorporating the imaginary number i, √-1, in the 3 dimensional relationship.

The Story of Number pi, 2018

Physics Today

Erkenntnis, 2008

We explore aspects of an experimental approach to mathematical proof, most notably number crunching, or the verification of subsequent particular cases of universal propositions. Since the rise of the computer age, this technique has indeed conquered practice, although it implies the abandonment of the ideal of absolute certainty. It seems that also in mathematical research, the qualitative criterion of effectiveness, i.e. to reach one's goals, gets increasingly balanced against the quantitative one of efficiency, i.e. to minimize one's means/ends ratio. Our story will lead to the consideration of some limit cases, opening up the possibility of proofs of infinite length being surveyed in a finite time. By means of example, this should show that mathematical practice in vital aspects depends upon what the actual world is like.

The Metaphysical Significance of Pi, 2008

22nd July, 2008. This treatise uses the mathematical Pi constant to develop a blueprint for understanding the metaphysical nature of the universe and the human condition. It derives certain fundamental esoteric principles that are based on Pi, and that help explain the nature of consciousness and universal cycles. These Pi-based principles explain both the linear and non-linear characteristics of subjective experience and 'objective' manifestation. Using the symbolism of the basic structure of the Pi constant, it is shown that there exists a singularity (or Monad) located beyond space and time, but around which consciousness (focused within space and time) revolves and evolves.

The research, the theory of π 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 π 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 πt -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 π that is 3.1416 which we have suggested is the area of circle and is rational & exact most probable number.

International Journal of Mathematics Trends and Technology, 2018

The value of an irrational number pi (π) is determined from the ancient times up to the modern super computer era. In this research paper, I divide the circumference of circle in to 6 equal arc radius of length λ (Lambda). 6 λ (lambda) = 2 r s , This gives Goba = 3 λ (lambda) ÷ straight radius, with the aid of equation measurement of λ (lambda) and arc radius give the Goba constant. The researcher has given this name, "GOBA" it's as symbolic, this Goba, this letter. Its equations given, its value is computed as 3.141592653 The self -proving theorem of Goba and its explanation on the basis of a formula, is based on the extinction and creation of the world. The world becomes extinct in an invisible degree and the evolution or creation of the world or the radius of a circle and circumference of circle is achieved by exploding that invisible degree or bisecting that degree. In geometry, symbol for measurement accepted by world scientists (world official) is degree and the very degree is the root, scale, source and base of the research. Degree: closed chop (compass), tip of the compass means point, means 1 point, means 1° degree, means dot • = degree means unit of measurement. The degrees of a circle without support means without circumference are 36°, this is the base of this whole research is 36° measure of circle. This is a fundamental research.

2011

The value of an irrational number pi (π) is determined from the ancient times up to the modern super computer era. In this research paper, I divide the circumference of circle in to 6 equal arc radius of length λ (Lambda). 6 λ (lambda) = 2 Goba r, This gives Goba = 3 λ (lambda) ÷ straight radius, with the aid of equation measurement of λ (lambda) and arc radius give the Goba constant. The researcher has given this name, " GOBA " it's as symbolic, this Goba, this letter. Its equations given, its value is computed as 3.141592653 The self-proving theorem of Goba and its explanation on the basis of a formula, is based on the extinction and creation of the world. The world becomes extinct in an invisible degree and the evolution or creation of the world or the radius of a circle and circumference of circle is achieved by exploding that invisible degree or bisecting that degree. In geometry, symbol for measurement accepted by world scientists (world official) is degree and the very degree is the root, scale, source and base of the research. Degree: closed chop (compass), tip of the compass means point, means 1 point, means 1° degree, means dot • = degree means unit of measurement. The degrees of a circle without support means without circumference are 36°, this is the base of this whole research is 36° measure of circle. This is a fundamental research.