By Leo Corry

ISBN-10: 0191007064

ISBN-13: 9780191007064

The area round us is saturated with numbers. they seem to be a basic pillar of our sleek society, and permitted and used with not often a moment proposal. yet how did this situation grow to be? during this ebook, Leo Corry tells the tale at the back of the belief of quantity from the early days of the Pythagoreans, up until eventually the flip of the 20 th century. He provides an summary of ways numbers have been dealt with and conceived in classical Greek arithmetic, within the arithmetic of Islam, in ecu arithmetic of the center a long time and the Renaissance, in the course of the clinical revolution, throughout to the maths of the 18th to the early twentieth century. targeting either foundational debates and useful use numbers, and displaying how the tale of numbers is in detail associated with that of the assumption of equation, this publication offers a worthwhile perception to numbers for undergraduate scholars, academics, engineers, specialist mathematicians, and a person with an curiosity within the background of arithmetic.

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596–ca. 475 BCE) and the Pythagoreans, who were members of a school that was active in the city of Crotona, in 32 | NUMBERS AND MAGNITUDES IN THE GREEK TRADITION what is today the south of Italy. Many legends and myths came to be associated with their name, and it is sometimes difficult to separate such legends from historical truth. Nevertheless, there is no doubt about the seminal importance of their mathematical contributions. The best known of these is the famous theorem about right-angled triangles that bears the name of Pythagoras: the square described upon the hypotenuse of a right-angled triangle is equal to the sum of the squares described upon the other two sides.

But we can easily think of the following alternative ordering: 1, 3, 5, 7, . . 2, 4, 6, 8, . . , 80 is “greater than” 8,000,003). Notice that this is really a different ordering and not just a way of renaming the members of the sequence. How do we see this? , 1), whereas in the alternative order just presented, there are two elements with that property, namely, 1 and 2. Indeed, in the alternative ordering, 2 is greater than any given odd number, but no specific odd number can be said to appear immediately before the number 2.

Our interest in the Pythagoreans, at any rate, lies in a different aspect of their work, namely, the focused attention and intense research they devoted to natural numbers and their properties. The interest of the Pythagoreans in numbers goes way beyond the purely arithmetical. For them, number was the universal principle that underlies the cosmos and allows it to be understood. As part of a unique blend of a rational approach to understanding nature with numerology and other mystical practices, the Pythagoreans saw the natural numbers as a clearly discernible, stable element that hides behind the apparent chaos of day-to-day experience and helps to make sense of it.

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A Brief History of Numbers by Leo Corry

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