# Playing with Infinity: Mathematical Explorations and Excursions

Courier Corporation, Jan 1, 1976 - Mathematics - 268 pages

This popular account of the many mathematical concepts relating to infinity is one of the best introductions to this subject and to the entire field of mathematics. Dividing her book into three parts ? The Sorcerer's Apprentice, The Creative Role of Form, and The Self-Critique of Pure Reason ? Peter develops her material in twenty-two chapters that sound almost too appealing to be true: playing with fingers, coloring the grey number series, we catch infinity again, the line is filled up, some workshop secrets, the building rocks, and so on.
Yet, within this structure, the author discusses many important mathematical concepts with complete accuracy: number systems, arithmetical progression, diagonals of convex polygons, the theory of combinations, the law of prime numbers, equations, negative numbers, vectors, operations with fractions, infinite series, irrational numbers, Pythagoras' Theorem, logarithm tables, analytical geometry, the line at infinity, indefinite and definite integrals, the squaring of the circle, transcendental numbers, the theory of groups, the theory of sets, metamathematics, and much more. Numerous illustrations and examples make all the material readily comprehensible.
Without being technical or superficial, the author writes with complete clarity and much originality on the whole range of topics from counting to mathematical logic. Using little algebra and no mathematical formulas, she has written an unusual book that will interest even mathematicians and teachers. Beginning mathematics students and people in the humanities and other fields will find the book particularly outstanding for their purposes.

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### Contents

 THE SORCERERS APPRENTICE 1 The temperature charts of the operations 6 The parcelling out of the infinite number series 14 The Sorcerers Apprentice 21 Variations on a fundamental theme 29 We go through all possibilities 42 Colouring the grey number series 56 I have thought of a number 66
 The charts get smoothed out 126 Mathematics is one 140 Write it down elements 160 Some workshop secrets 177 Many small make a great 196 THE SELFCRITIQUE OF PURE REASON 211 The building rocks 225 Form becomes independent 233

 THE CREATIVE ROLE OF FORM 77 Limitless density 88 We catch Infinity again 99 The line is filled up 112
 Awaiting judgement by metamathematics 243 What is Mathematics not capable of? 255 Copyright