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The author of this book has discovered an innovative method of determining the True value of Pi ( = 10 = 3.1623 or 3.16227766016838). This new Pi value is derived from the geometric relationships among the circle’s components with the use of the Circle Theorem and Pythagorean Theorem. Figure 1 contains an inscribed circle in the square consisting of gridlines equally spaced into one-fourth of the side of the square or the diameter of the inscribed circle. The resulting precise Pi value is validated with the use of the Polygon Area formula, Binomial Theorem, and Quadratic Equation. This contemporary approach to finding the true Pi value reputes the traditional method of finding the Pi value. For the past four centuries, many mathematicians have attempted to find the precise Pi value. It began with measuring the circumference and the diameter of a circle and dividing the former by the latter. The erroneous Pi calculation began during the era of Archimedes of Syracuse circa 287–212 before the Christian era (BCE). Archimedes one of the greatest mathematicians of the ancient world introduced the approximate value of Pi as 3.14 (between 3-1/7 and 3-10/17 bound). Since then, humans have been trying to add more digits to the two-decimal placed Pi in an attempt to find a precise Pi which is still an approximation value.
Our intention in this collection is to provide, largely through original writings, an ex tended account of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a signifi cant number of the most important mathematicians have contributed to its unfolding directly or otherwise. Pi is one of the few mathematical concepts whose mention evokes a response of recog nition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty-five hundred years. The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research. To pursue this topic as it developed throughout the millennia is to follow a thread through the history of mathematics that winds through geometry, analysis and special functions, numerical analysis, algebra, and number theory. It offers a subject that provides mathe maticians with examples of many current mathematical techniques as weIl as a palpable sense of their historical development. Why a Source Book? Few books serve wider potential audiences than does a source book. To our knowledge, there is at present no easy access to the bulk of the material we have collected.
This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, and new translations of works by Viete and Huygen.
Computers in Science and Mathematics, Revised Edition examines notable contributions to the advancement of computer technology, as well as the many ways in which scientists and mathematicians use computers in their daily work. This newly revised edition places a focus on the development of computer hardware and software, the theory underlying the design of computer systems, and the use of computers to advance science and mathematics. Computers in Science and Mathematics, Revised Edition also provides a history of computers as scientific and mathematical tools, followed by examples of how computers are used to solve an increasingly wide range of scientific and mathematical problems. Chapters include: Before Computers: Mechanizing Arithmetic, Counting, and Sorting Early Computers: Automating Computation Cryptography: Sending Secret Messages Mathematical Proofs: Computers Find Truth Simulation: Creating Worlds Inside a Computer Weather: Mapping the Past, Predicting the Future Computer-Inspired Biology: Making Computers from Living Things Biology-Inspired Computing: Learning from Nature Recent Developments.