

Some lines carry a mathematician's name. They are generally lines associated with the triangle, linked to certain notable points.



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A ruler, a compass, a sharp pencil—and the adventure has already begun! It can come as quite a surprise when three points turn out to lie on the same line. Plane geometry abounds in wondrous collinearity theorems.

Michel Chasles dreamed of it; the theory of vector spaces now makes it possible: we can do geometry without drawing a single figure. Geometric and algebraic viewpoints thus coexist, and everyone can choose whichever feels most comfortable!

The line is the simplest geometric figure imaginable. The variety of situations encountered in geometry may seem more complicated, and yet… might there be a special perspective from which the plane could be understood as a line? That is precisely what projective geometry is about!

Beyond the centroid, the orthocenter and the centers of the two circles familiar from school geometry, thousands of points can be associated with the three vertices of a triangle. These myriad points lie on hundreds of cubics with remarkable properties.
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