Another Open University oldie. This one's a bit more hxc (and considerably older - the 1970s public were apparently considered far smarter than we are today!), but it's mostly easy enough to grasp if you put your mind to it. <br /> <br />Euclidean Geometry describes the world we're all familiar with in our daily lives. Non-Euclidean Geometry is relevant for the Riemann curvature of space-time in General Relativity and all that. It's also interesting to watch logic (or a bearded professor) decimate what was once considered to be a fundamental truth of mathematics and reality, if you're into that sort of thing. (maybe that's a bit over-dramatic).