At the root of numbers

Extracting a root, for the famous scholar Cosinus, is a calculation session… at the dentist's. In maths, the methods for extracting square roots are multiple: exact or approximate, using sequences or functions, a calculator – it has become the modern reflex –, but also by hand, like at school for divisions, except that it's a bit more complicated. This will be an opportunity to discover a little-known technique for manually extracting cube roots! One can then easily generalize to complex roots, thanks to Euler, always him: their definition, the regular polygons they allow to draw, and what are called primitive roots with the concept of cyclotomic polynomial.

Appeared with the Babylonians, highly developed in Antiquity but also during the Renaissance, astrology long tempted astronomers and mathematicians when the origin of gravitational forces was unknown. Although sometimes based on learned calculations, we now know it has no theoretical foundation and is based on astronomical considerations that are most often erroneous… Classified today by scientists as an obscurantist discipline, it still attracts numerous followers. Why? This is undoubtedly the domain of psychology and… probabilities. Because its only art is to make one believe in the reality of its affirmations.

In its arithmetic version, Bézout's theorem is a true invitation to the discovery of "pleasing and delectable" problems, that Bachet de Meziriac had devised and that Tangente continues to offer you. Many elementary arithmetic results follow from it, and will allow you to exercise your sagacity. Bézout's theorem also comes in a polynomial version. This time, it has applications extending into integral calculus and plays a particular role in studying the intersection of algebraic curves.