The Beauty of Geometrical Curves

The path traced out by a given point on the rim of a circle as you roll it along a straight line is a beautiful curve called a cycloid, whose appeal to mathematicians has had it dubbed “the Helen of Geometry”. This curve is known in geometry as a roulette, which is a curve you get by rolling one curve along another, and there are many more with an amazing range of applications, from clockwork toys to nuclear reactors. This lecture will provide a guided tour of the beauty of geometrical ...