# Get PDF How Mathematics Happened: The First 50,000 Years

Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history.

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The authors take the reader on a fascinating tour of the many ramifications of the Fibonacci sequence--the most ubiquitous, and perhaps the most intriguing, number pattern in mathematics. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it 1, 1, 2, 3, 5, 8, 13, 21, ad infinitum. Far from being just a curiosity, this sequence recurs in structures found throughout nature -- from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world.

The authors begin with a brief history of their distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. With separate chapters devoted to the remarkable Egyptian and Babylonian mathematics of the era from about to BCE, when all of the basic arithmetic operations and even quadratic algebra became doable, Rudman concludes his interpretation of the archeological record.

Since some of the mathematics formerly credited to the Greeks is now known to be a prior Babylonian invention, Rudman adds a chapter that discusses the math used by Pythagoras, Eratosthenes, and Hippasus, which has Babylonian roots, illustrating the watershed difference in abstraction and rigor that the Greeks introduced.

He also suggests that we might improve present-day teaching by taking note of how the Greeks taught math.

Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history. Read more Read less. Frequently bought together. Add both to Cart Add both to List. These items are shipped from and sold by different sellers. Show details. Ships from and sold by Prodigal Products.

## Mathematics

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From Booklist Anyone who has ever wondered why an hour is divided into 60 minutes has much to learn from Rudman, student of the ancient mathematics of the Babylonians, Egyptians, and Mayans. Read more. Don't have a Kindle? Try the Kindle edition and experience these great reading features:.

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There was a problem filtering reviews right now. Please try again later. Format: Hardcover Verified Purchase. Many books have been written on the history of mathematics, but much of what is written seems to focus almost entirely on the mathematical traditions beginning with the Greeks and extending into modernity with only passing mentions of the more ancient systems that existed in many parts of the world long before Pythagoras, Archimedes, or Euclid.

It's refreshing to read a book that largely reverses this trend by devoting the majority of its attention to what I've seen described as the pre-history of mathematics. By the nature of this exercise, however, one can't simply trace the development of theorems through time but must instead focus equally on mathematical concepts and archaeological ones. Because the subjects of both mathematics and archaeology are so vast, it would be impossible to give even a cursory treatment to either topic in a single volume of only pages.

Instead, it's best to consider this book a very broad survey of the development of ancient mathematics, occasionally narrowing its focus to discuss a concept or result of particular interest but generally maintaining its position as a cursory overview of an entire field of inquiry.

Approximately the first half of the book is devoted to the origin of various number systems. Many readers are likely already familiar with the fact that our decimal system is not the only or even the oldest number system, but even those who already know a little bit about ancient mathematics will likely find it interesting to learn about Torres-Strait body-parts counting or the Babylonian sexagismal system. However, for the reader whose undergraduate mathematics education did not include as mine did significant time spent performing operations with unit fractions sometimes written in Egyptian Hieroglyphics , this first part of the book might seem to drag on a bit longer than it needs to.

The book begins to obtain a broader general interest in the second half when it moves on from counting systems and the most basic concepts of arithmetic into the early history of algebra, spending a good amount of time discussing the algebraic problems from ancient Egypt recorded in the Rhind Papyrus. The author does an excellent job of communicating, in relatively few pages, the depth of mathematical understanding possessed by the ancient Egyptians, including concepts of geometric series, algebraic geometry, and precursors to integral calculus.

## How mathematics happened: the first 50, years - Peter Strom Rudman - Google книги

The following chapter traces an alternate lineage of mathematics in Babylon covering similar but distinct mathematical territory including a rather stunning approximation of the square root of 2 and a special case of the Pythagorean theorem. Arguably the most interesting mathematics is found in relatively few pages toward the end of the book where the author describes the development of rigorous proof. Illustrative examples include one of my own favorite stories from mathematical history: Eratosthenes, whose sieve can be used to locate prime numbers and whose knowledge of geometry allowed for a remarkably accurate calculation of the Earth's circumference as early as some BCE.

While this chapter does include a few of the "greatest hits" of early Greek mathematics, as well as a brief description of our own mathematical lineage it can, after all, be argued that we are all the mathematical descendants of the Greeks , it's not the strongest point of the book because the description is, frankly, far too brief to allow for any real depth of understanding.

## Mathematics Happened

The book concludes with a brief but important plea for improved education in mathematics. While this certainly isn't the message you buy this book to hear, it remains a message that more people interested in mathematics need to start thinking about. He then traces the evolution of number systems from finger counting in hunter-gatherer cultures to pebble counting in herder-farmer cultures of the Nile and Tigris-Euphrates valleys, which defined the number systems that continued to be used even after the invention of writing.

With separate chapters devoted to the remarkable Egyptian and Babylonian mathematics of the era from about to BCE, when all of the basic arithmetic operations and even quadratic algebra became doable, Rudman concludes his interpretation of the archeological record. Since some of the mathematics formerly credited to the Greeks is now known to be a prior Babylonian invention, Rudman adds a chapter that discusses the math used by Pythagoras, Eratosthenes, and Hippasus, which has Babylonian roots, illustrating the watershed difference in abstraction and rigor that the Greeks introduced.

He also suggests that we might improve present-day teaching by taking note of how the Greeks taught math. Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history. Rudman Haifa, Israel is professor ret. See All Customer Reviews. Shop Books.