By Steven G. Krantz
An Episodic historical past of Mathematics gives you a sequence of snapshots of the historical past of arithmetic from precedent days to the 20 th century. The cause isn't really to be an encyclopedic heritage of arithmetic, yet to offer the reader a feeling of mathematical tradition and heritage. The e-book abounds with tales, and personalities play a powerful position. The ebook will introduce readers to a couple of the genesis of mathematical rules. Mathematical historical past is fascinating and profitable, and is an important slice of the highbrow pie. an exceptional schooling comprises studying various equipment of discourse, and positively arithmetic is likely one of the such a lot well-developed and critical modes of discourse that we've got. the focal point during this textual content is on getting concerned with arithmetic and fixing difficulties. each bankruptcy ends with a close 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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Extra resources for An Episodic History of Mathematics: Mathematical Culture through Problem Solving
17). 18). Notice that each of the central angles of each of the triangles must have measure 360◦ /6 = 60◦ . Since the sum of the angles in a triangle is 180◦ , and since each of these triangles certainly has two equal sides and hence two equal angles, we may now conclude that all the angles in each triangle have measure 60◦ . 19. But now we may use the Pythagorean theorem to analyze one of the triangles. 20. Thus the triangle is the union of two right triangles. 3 Archimedes 27 hexagon—is 1 and the base is 1/2.
Now we consider a regular 24-sided polygon (an icositetragon). As before, we construct this new polygon by erecting a small triangle over each side of the dodecagon. 27. 28 √ decagon. We first solve the right triangle with base 2 − 3/2 and hypotenuse 1—using the Pythagorean theorem, of course—to find that √ it has height 2 + 3/2. Then we see that the smaller right trian√ √ gle has base 1 − 2 + 3/2 and height 2 − 3/2. Thus, again by the Pythagorean theorem, the hypotenuse of the small right triangle is √ 2 − 2 + 3.
So our approximation is quite crude. The way to improve the approximation is to increase the number of sides in the approximating polygon. In fact what we shall do is double the number of sides to 12. 22 shows how we turn one side into two sides; doing this six times creates a regular 12-sided polygon. Notice that we create the regular 12-sided polygon (a dodecagon) by adding small triangles to each of the edges of the hexagon. Our job now is to calculate the area of the twelve-sided polygon. Thus we need to calculate the lengths of the edges.