By SHERMAN STEIN

Math fans usually are not inevitably the number-crunching geeks we have a tendency to think. in reality, they be aware of that math is ready even more than numbers; it's a profoundly philosophical recreation, in addition to a stimulating psychological workout. In How the opposite part Thinks, Sherman Stein emphasizes the artistic component of arithmetic by means of exploring a few major mathematical discoveries via easy, intuitive manipulations. With an creative technie that makes use of no algebra or trigonometry, and just a minimal of mathematics, Stein takes us during the proposal approach in the back of a few of math's nice discoveries and purposes. each one bankruptcy starts with an easy query approximately strings made of the letters a and b, which results in different, extra profound questions. alongside the best way, we familiarize yourself with strategies from such fields as topology and likelihood, and find out how they've got resulted in functions comparable to codes and radar, computing, or even baseball facts. leisure and instructive, How the opposite part Thinks will entice die-hard math fanatics (of which there are lots of) in addition to these "right-brainers" who're trying to find the way to comprehend and luxuriate in math.

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**Example text**

That implies that there is at least one complete triangle, for zero is an even number.

A Depending on how a b a b their corners are labeled, a a b there are 10 types of triangles that may appear in the polygon, as is shown below. c a b a c b a c a a c c a c b b b c b b a a a b a b c b c c In only one of the 10 types do all three letters appear. Call such a triangle complete. Six types have two different letters, and three types have only one letter. 49 How the Other Half Thinks The complete triangle has exactly one edge with the letters a and b, a complete edge. ) The triangle with two a’s and a b has two complete edges; so does the triangle with two b’s and an a.

9990 to four-decimal-place accuracy. It looks as though the sums are approaching 1. A glance at the diagram to the right of a square cut into an infinite number of rectangles will show that the sum of the series is indeed 1. Unfortunately, only a few of the rectangles can be shown. The 33 How the Other Half Thinks square has area 1. The shaded rectangle has area 1/2, leaving an area of 1/2 unshaded. The next rectangle fills half the unshaded area, namely, 1/4. That leaves an area of 1/4 that is not covered by those two rectangles.