In Search of Infinity pp 71-116 | Cite as

# Remarkable functions and curves, or a stroll through a mathematical hall of wonders

## Abstract

The whole history of the evolution of mathematics is marked by dialectical opposition and unity of its two parts devoted to the study of numbers and figures, respectively. The natural numbers differ from one another by their properties: some are even and some odd, some are prime and some composite, some can be written as sums of two squares and some can not. This infinite variety of properties that change so strikingly upon addition of just one unit to a number endows number theory with a special charm. Of course, geometric figures are just as varied — triangles and squares, circles and parabolas, astroids and cardioids. But each curve by itself, a straight line or a circle, is composed of points with identical properties.

### Keywords

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