
The definition of the straight line through the ages
You thought you knew what a straight line is? Read on, and you may well start to doubt it…


You thought you knew what a straight line is? Read on, and you may well start to doubt it…


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By drawing infinitely many conclusions from a single principle, proof by induction is one of mathematics’ great achievements. Constructing recursively defined sequences makes it possible to model objects of practical interest and solve a wide variety of problems.

Complex numbers, born of impossible calculations, found an unlikely geometric interpretation. This meeting of algebra and geometry is beautifully illustrated by theorems about the roots of a complex polynomial.

Mathematical writings contain words, but also signs, symbols and figures. Texts are therefore meant to be looked at as much as read, as works of geometry from antiquity to the present day attest.

In mathematics, every proof starts from premises assumed to be true. What particular form must these premises take to become axioms, the foundation of all our current theories?
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