The Enjoyment of Mathematics: Selections from Mathematics for the AmateurRequiring only a basic background in plane geometry and elementary algebra, this classic poses 28 problems that introduce the fundamental ideas that make mathematics truly exciting. "Excellent . . . a thoroughly enjoyable sampler of fascinating mathematical problems and their solutions"—Science Magazine. |
Contents
Preface | 5 |
Incommensurable Segments and Irrational Numbers | 24 |
A Second Proof of the Same Minimum Property | 30 |
Some Combinatorial Problems | 43 |
On Warings Problem | 58 |
Is the Factorization of a Number into Prime Factors Unique? | 66 |
The FourColor Problem | 73 |
The Regular Polyhedrons | 82 |
The Theorem of the Arithmetic and Geometric Means | 95 |
The Spanning Circle of a Finite Set of Points | 103 |
Approximating Irrational Numbers by Means of Rational | 111 |
Producing Rectilinear Motion by Means of Linkages | 119 |
Perfect Numbers | 129 |
Eulers Proof of the Infinitude of the Prime Numbers | 135 |
The Figure of Greatest Area with a Given Perimeter | 142 |
A Characteristic Property of the Circle | 160 |
Common terms and phrases
a₁ alternating knot angle arithmetic mean balls chapter chord circle of radius circumference colors common multiple cone constant breadth construction convex corner countries curve of constant D. H. Lehmer decimal fraction denominator digits divide divisible divisors double point enclosing circle equal equation equilateral Euclid exactly example fact figure finite number four squares fourth powers geometric given H. A. Schwarz hence inequality infinite inscribed intersection larger least common multiple lemma length less linkage Martin Gardner mathematics obtain original P₁ P₂ pair parallel pedal triangle perfect number perimeter perpendicular plane polygon positive whole numbers possible prime factors prime numbers problem proof rational numbers regular polyhedrons relatively prime remainder Reuleaux triangle rhomboid right side segment smaller smallest solution straight line supporting lines true urns vertex vertices