Conic Sections

Take a double cone — two ice-cream cones tip-to-tip — and slice through it with a flat plane. Astonishingly, four completely different shapes emerge depending on the angle of the cut: a circle, an ellipse, a parabola, or a hyperbola. The Greeks studied these 'conic sections' purely for beauty, yet 2000 years later Kepler used them to prove planets move in ellipses, and engineers still design satellite dishes as parabolas. Four shapes, one geometric origin, and a starring role in the laws of motion.