This post follows on from Non-Euclidean Geometry – An Introduction – read that one first! Non Euclidean Geometry IV - New Universes The 19th century saw mathematicians finally throw off the shackles of Euclid's 5th (parallel) postulate - and go on to discover a bewildering array of geometries which no longer took this assumption about... Continue Reading →
The Riemann Sphere
The Riemann Sphere The Riemann Sphere is a fantastic glimpse of where geometry can take you when you escape from the constraints of Euclidean Geometry - the geometry of circles and lines taught at school. Riemann, the German 19th Century mathematician, devised a way of representing every point on a plane as a point on... Continue Reading →