A departure from mathematical standards is then a mortal sin, whereas an error in history is venial. According to one, Hippasus was expelled for political insubordination, having headed a democratic move- ment against the conservative Pythagorean rule.
There is always the temptation in a class in history of mathematics to assume that the fundamental purpose of the course is to teach mathematics. The exact cause of the break is unknown, in part because of the rule of secrecy, but there are three suggested possibilities.
Many of them had been proposed by earlier mathematicians.
Possibly the greatest value of Euclid's writings is that they present the ideas as a comprehensive, well-organized reference.
The principals are supported by mathematical proofs, which geometry students learn even to this day.
: The author of this book profiles 60 famous mathematicians who were born between 17 and provides insight into their remarkable lives and their contributions to the field of math.In the 19th century, other types of geometry were described.Now, Euclid's work is called Euclidean geometry to distinguish it from the other methods. It would be folly, in a book of this scope, to expect that every date, as well as every decimal point, is correct. A third explanation holds that the expulsion was coupled with the disclosure of a mathematical discovery of devastating significance for Pythagorean philo- sophy — the existence of incommensurable magnitudes. I have striven to avoid such an attitude, and the purpose of the book is to present the history of mathematics with fidelity, not only to mathematical structure and exacti- tude, but also to historical perspective and detail. A second tradition attributes the expulsion to disclosures concerning the geometry of the pentagon or the dodecahedron — perhaps a construction of one of the figures.It is one of the oldest algorithms known and was included in Euclid's Elements. Euclid also discusses perfect numbers, infinite prime numbers, and Mersenne primes (the Euclid-Euler theorem).The concepts presented in The Elements weren't all original.A History Mathematics Carl R Boyer WILEY INTERNATIONAL EDITION MATHEMATICAL CENTERS IN THE THALASSIC AGE 1. Crotona Alexandria 25 (Euclid, Heron, Ptolemy, Pappus Menelaus and others) 3. In the field of the history of mathematics perhaps nothing PREFACE ix is more to be desired than that there should appear a latter-day Felix Klein who would complete for our century the type of project Klein essayed for for the nineteenth century, but did not live to finish. Just when and how the discovery was made is not known, but much ink has been spilled in support of one hypothesis or another. In particular, the last chapter attempts merely to point out a few of the salient characteristics of the twentieth century. The line segments are incommensurable, no matter how small a unit of measure is chosen.This text is organized chronologically and provides interesting information about the details of the mathematicians' lives.At the time, and for many centuries, Euclid's work was simply called "geometry" because it was assumed to be the only possible method of describing space and the position of figures.