I think I mentioned the two '50 ideas...' books I bought at the fête a while ago. I've been working through the Maths one – Chris has the Physics book; I'll be looking at that later so watch out. The sections on number sequences were fascinating but yesterday I got to non-Euclidean geometry. This was equally intriguing. Until I had read this, I thought that the angles of any triangle always added up to 180°. But that's only in Euclidean geometry. You can make a triangle with three right angles! You'll need an orange. Another spherical fruit will do, I suppose, but an orange is best. You'll also need a sharp knife. I guess at this point I should warn you about the dangers... so be careful! Hold the orange upright. Now cut a horizontal line around the centre of the orange – the equator – and go a quarter of the way round. Now make two cuts at right-angles to this cut towards the top of the orange, one at each end, and continue these till they meet. They will meet at right angles, too. So you have made a triangle with three 90° angles – the total is now 270° not 180.
I think I mentioned the two '50 ideas...' books I bought at the fête a while ago. I've been working through the Maths one – Chris has the Physics book; I'll be looking at that later so watch out. The sections on number sequences were fascinating but yesterday I got to non-Euclidean geometry. This was equally intriguing. Until I had read this, I thought that the angles of any triangle always added up to 180°. But that's only in Euclidean geometry. You can make a triangle with three right angles! You'll need an orange. Another spherical fruit will do, I suppose, but an orange is best. You'll also need a sharp knife. I guess at this point I should warn you about the dangers... so be careful! Hold the orange upright. Now cut a horizontal line around the centre of the orange – the equator – and go a quarter of the way round. Now make two cuts at right-angles to this cut towards the top of the orange, one at each end, and continue these till they meet. They will meet at right angles, too. So you have made a triangle with three 90° angles – the total is now 270° not 180.
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