Download An Episodic History of Mathematics: Mathematical Culture by Steven G. Krantz PDF

By Steven G. Krantz

An Episodic historical past of Mathematics promises a chain of snapshots of the background of arithmetic from precedent days to the 20 th century. The reason isn't really to be an encyclopedic heritage of arithmetic, yet to offer the reader a feeling of mathematical tradition and historical past. The ebook abounds with tales, and personalities play a powerful function. The e-book will introduce readers to a few of the genesis of mathematical rules. Mathematical historical past is fascinating and worthwhile, and is an important slice of the highbrow pie. a superb schooling comprises studying assorted tools of discourse, and definitely arithmetic is likely one of the so much well-developed and demanding modes of discourse that we've got. the focal point during this textual content is on becoming concerned with arithmetic and fixing difficulties. each bankruptcy ends with an in depth challenge set that might give you the scholar with many avenues for exploration and lots of new entrees into the topic.

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Extra resources for An Episodic History of Mathematics: Mathematical Culture through Problem Solving

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And their scientific beliefs were intertwined with their religious beliefs. For example, 43 44 Chapter 2: Zeno’s Paradox and the Concept of Limit Pythagoras was not simply a person. “Pythagoras” (or “the Pythagoreans”) was the name for a society of people who developed the ideas to which we now attach his name. And that society was both a religious organization and a scientific laboratory. One of the overriding Greek philosophical concerns was whether everything in the universe was “one”, or whether the universe contained independent entities.

The argument here is not answered by the well known infinite sum 1 1 1 + + + ··· = 1 2 4 8 On the one hand Zeno can argue that the sum 1/2 + 1/4 + 1/8 + . . never actually reaches 1, but more perplexing to the human mind is the attempts to sum 1/2 + 1/4 + 1/8 + . . backwards. Before traversing a unit distance we must get to the middle, but before getting to the middle we must get 1/4 of the way, but before we get 1/4 of the way we must reach 1/8 of the way etc. 1. This argument makes us realize that we can never get started since we are trying to build up this infinite sum from the ”wrong” end.

Our job now is to calculate the area of the twelve-sided polygon. Thus we need to calculate the lengths of the edges. 23). We use the Pythagorean theorem to calculate the length x of a side of the new dodecagon. It is √ 2 √ √ 3 1 2 3 1 x= + 1− 3+ + 1− = = 2 − 3. 24). We have just calculated that each side √ of the dodecahedron has length 2 − 3. If we can calculate the area of each of the congruent subtriangles, then we can obtain the area of the entire dodecahedron (by multiplying by 12). 25. This is one of the 12 triangles that makes up the dodecahedron.