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Circles (A Mathematical View)

It gives me great pleasure that the Mathematical Association of America is republishing my book on circles, and I have been happy to adopt their suggestion that I write an introductory Chapter Zero to introduce and discuss the geometrical terms which may not be familiar to a new generation of students. This additional chapter is based on lectures I have given in India and Australia entitled “Geometry and the Pleasure Principle,” and I hope that my enthusiasm may be shared by others. I cannot think of any possible moral disapproval which can be held to be valid if one enjoys geometrical activity, and perhaps one of the beliefs of my youth that excellence in geometry leads to excellence in other branches of mathematics may once again become current. For this criterion to be tested, of course, geometry must not be excluded, as it has been for too many years, from school and college curricula. Fortunately there are many signs of a revival of interest in geometrical teaching, and the MAA is one of the leaders in this very heartening activity. Boldface numerals in parentheses, such as (n) which appear in Chapter Zero refer to the list of references which appear at the end of Chapter Zero. These articles and books can be consulted, of course, for further and more detailed information.D. P. Minneapolis, Minnesota June, 1994

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