The History of Mathematics: An Introduction

The History of Mathematics: An Introduction

Language: English

Pages: 816

ISBN: 0073383155

Format: PDF / Kindle (mobi) / ePub

The History of Mathematics: An Introduction, Seventh Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools. Elegantly written in David Burton’s imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics’ greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Seventh Edition a valuable resource that teachers and students will want as part of a permanent library.

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1962, establishes conclusively that the Egyptians of 300 B.C. not only knew that the (3, 4, 5) triangle was right-angled, but also that the (5, 12, 13) and (20, 21, 29) triangles had this property. Dating from the early Ptolemeic dynasties, this papyrus contains 40 problems of a mathematical nature, of which 9 deal exclusively with the Pythagorean theorem. One, for instance, translates as, “A ladder of 10 cubits has its foot 6 cubits from a wall; to what height will it reach?” Two problems are

“Untie every day one of the knots; if I do not return before the last day to which the knots will hold out, then leave your station and return to your several homes.” 7 8 Burton: The History of Mathematics: An Introduction, Sixth Edition 1. Early Number Systems and Symbols Text © The McGraw−Hill Companies, 2007 5 Primitive Counting Three views of a Paleolithic wolfbone used for tallying. (The Illustrated London News Picture Library.) Burton: The History of Mathematics: An

number.” (By “number” was meant a positive integer.) All this culminated in the notion that without the help of mathematics, a rational understanding of the ruling principles at work in the universe would be impossible. Aristotle wrote in the Metaphysics: The Pythagoreans . . . devoted themselves to mathematics; they were the first to advance this study and having been brought up in it they thought its principles were the principles of all things. About Pythagoras himself, we are told by another

by constructive methods; the answers to these constructions were line segments whose lengths corresponded to the unknown values. The linear equation ax = bc, for example, was viewed as an equality between areas ax and bc. Consequently, the Greeks would solve this equation by first constructing a rectangle ABCD with sides AB = b and BC = c and then laying off AE = a on the extension of AB. One produces the line segment ED through D to meet the extension of BC in a point F and completes the

symbols a | b, if there exists some integer c such that b = ac. One writes a|/b to indicate that b is not divisible by a. Thus, 39 is divisible by 13, since 39 = 13 · 3. However, 10 is not divisible by 3; for there is no integer c that makes the statement 10 = 3c true. There is other language for expressing the divisibility relation a | b. We might say that a divides b, a is a divisor of b, that a is a factor of b, or that b is a multiple of a. Notice too that in the definition given there is a

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