It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. Its purposes are to collect many trisections in one place, inform about trisectors, to amuse the reader, and, perhaps most importantly, to reduce the number of trisectors. This book includes detailed information about the personalities of trisectors and their constructions. It can be read by anyone who has taken a high school geometry course.

It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. Its purposes are to collect many trisections in one place, inform about trisectors, to amuse the reader, and, perhaps most importantly, to reduce the number of trisectors. This book includes detailed information about the personalities of trisectors and their constructions. It can be read by anyone who has taken a high school geometry course.

Fur viele Menschen besitzen die Zahlen eine Bedeutung, die uber den Zahlenwert hinausgeht, sie haben eine innere Natur und einen magischen Charakter. So weisen Numerologen und Zahlenmystiker den Zahlen eine aussergewoehnliche Macht uber Ereignisse zu. Ein Pyramidologe zum Beispiel vermisst seine Pyramide und schliesst aus den Zahlen, dass die Welt am 20. August 1953 untergeht. Die Boersenkurse schwanken auf und ab, weil die Fibonaccizahlen sie dazu bringen, die Bibel ist voller Siebener und Dreizehner, weil Gott es so gewollt hat, und Biorhythmiker behaupten, die Menschen oszillieren in Zyklen von 23, 28 und 33 Tagen, und folglich sei unser Verhalten von diesen Ziffern bestimmt. Es findet sich kaum ein Bereich, auf den nicht irgendwelche Zahlen angeblich Einfluss haben. Underwood Dudley hat sich ihren Geheimsinn naher angesehen und begleitet in seinem unterhaltsam zu lesendem Buch den Leser auf eine historische Tour durch die Numerologie. Angefangen mit Pythagoras, uber die Neupythagoraer, die Pyramidologen, die biblischen und Shakespeares Zahlen, wird der Bogen bis hin zu modernen Zahlenmystikern gespannt, die eine geheimnisvolle Zahlenfolge etwa auch im UPC-Strichcode zu finden glauben. Dabei lasst Dudley den Leser nicht im Zweifel, wie die Mathematik die Numerologie sieht: Diesen Aberglauben mit den Mitteln der Vernunft zu bekampfen, ist fur sie und den Autor die vordringlichste Aufgabe.

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Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems--some computational and some classical, many original, and some with complete solutions.
The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.