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Full Description
What is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? Are there more whole numbers than even numbers? These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this book leads the reader into some of the most fundamental ideas of mathematics, the ideas that make the subject exciting and interesting. Explaining clearly how each problem has arisen and, in some cases, resolved, Hans Rademacher and Otto Toeplitz's deep curiosity for the subject and their outstanding pedagogical talents shine through. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions.
The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Contents
*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Introduction, pg. 1*1. The Sequence of Prime Numbers, pg. 9*2. Traversing Nets of Curves, pg. 13*3. Some Maximum Problems, pg. 17*4. Incommensurable Segments and Irrational Numbers, pg. 22*5. A Minimum Property of the Pedal Triangle, pg. 27*6. A Second Proof of the Same Minimum Property, pg. 30*7. The Theory of Sets, pg. 34*8. Some Combinatorial Problems, pg. 43*9. On Waring's Problem, pg. 52*10. On Closed Self-Intersecting Curves, pg. 61*11. Is the Factorization of a Number into Prime Factors Unique?, pg. 66*12. The Four-Color Problem, pg. 73*13. The Regular Polyhedrons, pg. 82*14. Pythagorean Numbers and Fermat's Theorem, pg. 88*15. The Theorem of the Arithmetic and Geometric Means, pg. 95*16. The Spanning Circle of a Finite Set of Points, pg. 103*17. Approximating Irrational Numbers by Means of Rational Numbers, pg. 111*18. Producing Rectilinear Motion by Means of Linkages, pg. 119*19. Perfect Numbers, pg. 129*20. Euler's Proof of the Infinitude of the Prime Numbers, pg. 135*21. Fundamental Principles of Maximum Problems, pg. 139*22. The Figure of Greatest Area with a Given Perimeter, pg. 142*23. Periodic Decimal Fractions, pg. 147*24. A Characteristic Property of the Circle, pg. 160*25. Curves of Constant Breadth, pg. 163*26. The Indispensability of the Compass for the Constructions of Elementary Geometry, pg. 177*27. A Property of the Number 30, pg. 187*28. An Improved Inequality, pg. 192*Notes and Remarks, pg. 197
