Dandelin Cone


Biography of Germinal Dandelin



What is Dandelin Cone?


     Dandelin Cone is the theorem that Germinal Dandelin discovered in 1822 and named after him. The theorem shows that if a cone is intersected by a plane in a conic, then the foci of the conic are the points where this plane is touched by the spheres inscribed in the cone. In 1826, he generalized his theorem to a hyperboloid of revolution, rather a cone, relating Pascal's hexagon, Brianchon's hexagon and the hexagon formed by the generators of the hyperboloid.


What is Pascal's Theorem?


     Pascal's famous Mystic Hexagram Theorem states that if an arbitrary hexagon is inscribed in a conic, then the interesection points of the three pairs of the hexagon opposite sides are collinear, and conversely.


What is Brianchon's Theorem?


     Brianchon's Theorem states that In a hexaon circumscribing a conic section, the three opposite diagonals all intersect in a single point.



Created by: Aaron Yuen
Created for: Mrs. McDougall