Most people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in short, fun! As veteran math educators Posamentier and Lehmann demonstrate, when you realize that doing math can be enjoyable, you open a door into a world of unexpected insights while learning an important skill.

The authors illustrate the point with many easily understandable examples. One of these is what mathematicians call the "Ruth-Aaron pair" (714 and 715), named after the respective career home runs of Babe Ruth and Hank Aaron. These two consecutive integers contain a host of interesting features, one of which is that their prime factors when added together have the same sum.

The authors also explore the unusual aspects of such numbers as 11 and 18, which have intriguing properties usually overlooked by standard math curriculums. And to make you a better all-around problem solver, a variety of problems is presented that appear simple but have surprisingly clever solutions.

If math has frustrated you over the years, this delightful approach will teach you many things you thought were beyond your reach, while conveying the key message that math can and should be anything but boring.

nearer segment. Therefore, , or BC2 = AB ⋅ BD and a2 = c ⋅ p. By substitution: (r + p)2 = a2. Since we know the lengths are positive, we get r + p = a, or r = a – p. With p = , it follows that: , which is what we sought, namely, to get the value of r in terms of the sides of the triangle. Analogously, we can find the radius of the other circle. Thus, we now have the two radii that we sought: SANGAKU PROBLEM 3 We are given a Reuleaux triangle3 with three congruent circles inscribed in it as

typical solution to this problem could be to simulate the actual tournament by beginning with twelve randomly selected teams playing a second group of twelve teams—with one team drawing a bye. This would then continue with the winning teams playing each other as shown here. Any 12 teams versus any other 12 teams, which leaves 12 winning teams in the tournament. 6 winners versus 6 other winners, which leaves 6 winning teams in tournament. 3 winners versus 3 other winners, which leaves 3 winning

and three presidents died on the Fourth of July (John Adams, Jefferson, and Monroe). Above all, this demonstration should serve as an eye-opener about relying on intuition too much, and, at the same time, trusting probability even if it sometimes seems counterintuitive. SOLUTION FOR PROBLEM 71 For those who insisted on using a calculator and avoided seeing the beauty of mathematics that leads to an elegant solution, we offer this result: Therefore, . Using an algebraic method to establish

Amazement and Surprises, which show a variety of other peculiarities of this very visual aspect of mathematics. Problem solving is a key component of mathematics. Naturally, there are countless very challenging mathematical problems that did not guide our selection for inclusion. In chapter 3, we selected ninety problems, each of which has a curious aspect to it. Some were selected for the nature of the question asked—which may seem overwhelming at times. Others were selected to show how a

Book of Numbers, pp. 152–54. Page numbers in italic indicate solutions for word problems in chapter 3. SYMBOLS . See arithmetic mean () . See Chuquet addition () . See contraharmonic mean () . See controidal mean () !. See factorials (!) . See Farey, John, Sr., and Farey sequences of order () . See geometric mean () Φ. See golden ratio (Φ) . See harmonic mean () . See Heronian mean () ∞. See infinity (∞) π. See pi (π) . See root-mean-square () NUMBERS 0 times ∞, 120 1/7,