Geometric loci

What do the perpendicular bisector of two points, an ellipse, a strophoid or a caustic have in common? These are geometric loci satisfying predefined conditions stemming from purely mathematical considerations or problems drawn from physics. The introduction of analytic geometry followed by differential calculus revolutionized the methods for finding such loci. Ingenious scholars designed mechanisms, specific machines to draw them. The advent of computers transformed the landscape and gave rise to new geometric questions.

The "Pascal's triangle" is a strange array of numbers, imagined long before the French philosopher and mathematician: from India to China through the Arab-Muslim world, it has fascinated generations of scientists. We acknowledge the French scholar for giving it its full importance and for justifying many unexpected formulas that interact between its elements. We know the use of this combinatorial object in probability theory, in the binomial expansion. Perhaps we are unaware of all the corners where it hides…