There was once a cone

It all begins with Apollonius of Perga, whose monumental treatise laid the foundations of a geometry that would not be surpassed for two millennia. The xvii th century will overturn everything: Descartes, Pascal and Desargues seize upon conics and transform them, blending algebra, perspective and theory. Kepler – a genius astronomer but also a prodigious mathematician – is undoubtedly one of the first to unify the concept of a conic into a coherent object which he explores both in the study of polyhedra and in that of celestial orbits. Finally, projective geometry, by bringing infinity to the same status as the finite, reveals that behind the diversity of curves lies a profound unity.