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Full Description
This book is a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general math enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking. The essays are self-contained and rely only on tools from high-school mathematics (with only a few pieces that ever-so-briefly brush up against high-school calculus).
The gist of each essay is easy to pick up with a cursory glance--the reader should feel free to simply skim through some essays and dive deep into others. This book is an invitation to play with mathematics and to explore its wonders. Much joy awaits!
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Contents
Dragons and poison
Folding tetrahedra
The arbelos
Averages via distances
Ramsey theory
Inner triangles
Land or water?
Escape
Flipping a coin for a year
Coinciding digits
Inequalities
Gauss's shoelace formula
Subdividing a square into triangles
Equilateral lattice polygons
Broken sticks and Viviani's theorem
Viviani's converse?
Integer right triangles
One more question about integer right triangles
Intersecting circles
Counting triangular and square numbers
Balanced sums
The Prouhet-Thue-Morse sequence
Some partition numbers
Ordering colored fractions
How round is a cube?
Base and exponent switch
Associativity and commutativity puzzlers
Very triangular and very very triangular numbers
Torus circles
Trapezoidal numbers
Square permutations
Tupper's formula
Compositional square roots
Polynomial permutations.
