Dandelin's father, who was an administrator, was French but his mother came from Hainaut, now in Belgium. Dandelin studied at Ghent, then in 1813 he entered the Ecole Polytechnique in Paris. However his career was to be very much influenced by the political events of these turbulent times. In 1813 Dandelin had volunteered to fight the British.
In March 1814 the Treaty of Chaumont united Austria, Russia, Prussia and Britain in the aim of defeating Napoleon. When the allied armies arrived near Paris on 30 March 1814, Dandelin was in the opposing French army and was wounded on that day. Napoleon abdicated on 6 April, but in the following year he returned for the 100 days. During Napoleon's time back in control of France, Dandelin worked at the Ministry of the Interior under the command of Carnot. After Napoleon was defeated at Waterloo, Dandelin returned to Belgium. He became a citizen of the Netherlands in 1817.
Back in Belgium Dandelin continued his military career as an engineer. From 1825 he spent five years as professor of mining engineering at Liège. Then, in 1830, he was back in the thick of the Revolution which erupted that year. From 1835 he was in the Belgium army, assigned posts in charge of building fortifications in Namur, Liège and, later, in Brussels.
Dandelin's early mathematical influence was Quetelet, who was two years younger than him, and his early interests were in geometry. Dandelin has an important theorem on the intersection of a cone and its inscribed sphere with a plane, discovered in 1822, named after him. This 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 generalised his theorem to a hyperboloid of revolution, rather than a cone, relating Pascal's hexagon, Brianchon's hexagon and the hexagon formed by the generators of the hyperboloid.
Dandelin also worked on stereographic projection of a sphere on a plane (1827), statics, algebra and probability. He gave a method of approximating the roots of an algebraic equation, now named the Dandelin-Gräffe method. The history of the Dandelin-Gräffe method is discussed in  and .
Among the honours which Dandelin received was election to the Royal Academy of Sciences in Brussels in 1825.
References (5 books/articles)
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You can find a colour picture illustrating Dandelin's theorem at the Free University of Brussels, Belgium and another picture at University of Virginia, USA
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