Playing with Infinity: Mathematical Explorations and Excursions

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Courier Corporation, 1976 - Mathematics - 268 pages
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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
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