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

By Steven G. Krantz

An Episodic heritage of Mathematics offers a chain of snapshots of the heritage of arithmetic from precedent days to the 20 th century. The purpose isn't really to be an encyclopedic heritage of arithmetic, yet to provide the reader a feeling of mathematical tradition and historical past. The ebook abounds with tales, and personalities play a robust function. The publication will introduce readers to a couple of the genesis of mathematical principles. Mathematical heritage is intriguing and worthwhile, and is an important slice of the highbrow pie. a great schooling contains studying various equipment of discourse, and positively arithmetic is among the such a lot well-developed and significant modes of discourse that we have got. the point of interest during this textual content is on getting concerned with arithmetic and fixing difficulties. each bankruptcy ends with an in depth challenge set that would give you the pupil with many avenues for exploration and lots of new entrees into the topic.

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It has base √ 2 − 3. Each of the two sides has length 1. Thus we may use the Pythagorean theorem to determine that the height of the triangle is  h= 2− 12 −  2 √ 2 3 √ 2− 3 1− = 4 = √ 2+ 3 . 4 We conclude that the area of the triangle is 1 1 A(T ) = · (base) · (height) = · 2 2 √ 2− 3· Hence the area of the dodecagon is A(D) = 12 · 1 = 3. 4 √ √ 1 2+ 3 4−3 = = . 26, and thinking of the area inside the dodecahedron as an approximation to the area inside the unit circle, we find that π = (area inside unit circle) ≈ (area inside regular dodecahedron) = 3 .

In fact Plato claimed that Zeno’s book was circulated without his knowledge. Proclus goes on to say . . Zeno elaborated forty different paradoxes following from the assumption of plurality and motion, all of them apparently based on the difficulties deriving from an analysis of the continuum. The gist of Zeno’s arguments, and we shall examine them in considerable detail below, is that if anything can be divided then it can be divided infinitely often. This leads to a variety of contradictions, especially because Zeno also believed that a thing which has no magnitude cannot exist.

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. Indeed this is a clever argument which still puzzles the human mind today.

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