projective geometry
Two lines in a plane always intersect in a single point ... unless the lines are parallel. This annoying exception is constantly inserting itself into otherwise simple mathematical statements. Burkard Polster and Marty Ross explain how to get around the problem.
Runner up in the schools category. Dusty books, chalky blackboards and checked shirts are all things usually associated with maths. But according to Jonathan Tims, pubs, hot chocolate and cats can be far more inspirational. Join him on a trip through shadow land.
In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.
Imagine stepping inside your favourite painting, walking around the light-filled music room of Vermeer's "The Music Lesson" or exploring the chapel in the "Trinity" painted by Masaccio in the 15th century. Using the mathematics of perspective, researchers are now able to produce three-dimensional reconstructions of the scenes depicted in these works.