By Steven G. Krantz

*An Episodic heritage of Mathematics* grants a sequence of snapshots of the historical past of arithmetic from precedent days to the 20th century. The cause isn't to be an encyclopedic historical past of arithmetic, yet to provide the reader a feeling of mathematical tradition and background. The ebook abounds with tales, and personalities play a robust function. The e-book will introduce readers to a couple of the genesis of mathematical rules. Mathematical heritage is fascinating and lucrative, and is an important slice of the highbrow pie. an excellent schooling involves studying diversified equipment of discourse, and positively arithmetic is likely one of the so much well-developed and critical modes of discourse that we've got. the point of interest during this textual content is on becoming concerned with arithmetic and fixing difficulties. each bankruptcy ends with an in depth challenge set that would give you the scholar with many avenues for exploration and plenty of new entrees into the topic.

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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 the second decade of the fourth century, the Greeks resumed the pursuit of truth in earnest. It was felt that Zeno’s paradox of predication must be dealt with before there could be any discussion of the problem of knowledge and the problem of being could be resumed. Plato thus directs his serious students to the study of this question, and offers his own theory of the immanent1 idea as a solution of the paradox. 2 To Zeno, this was a declaration of the Non-ent’s absolute nullity. Thus Zeno developed the theory of the One as opposed to the theory of the Many.

This is obviously a better approximation to π than our last three attempts. It is accurate to one decimal place, and the second decimal place is close to being right. And now it is clear what the pattern is. The next step is to examine a regular polygon with 96 sides. The usual calculations will show that this polygon breaks up naturally into 96 isosceles triangles, and each of these triangles has area 2− 2+ A(T ) = 2+ 4 √ 3 . Thus the area of the polygon is 2− A(P ) = 96 · 2+ 4 2+ √ 3 = 24 · 2− 2+ 2+ √ 3.