Quiet Day
I haven't done much today. Got up and went to breakfast, after which I talked to Hannah, which was lovely as usual. Then on to uni. We had our morning Japanese lesson, which I followed with a bowl of ramen. Then we had Seb's history lesson. Today we did the Kamakura period.
I taught at Linden Hall in the afternoon with Katherine. We sat in the room whilst the children did their homework on shapes. Paul was there and we had a little discussion about how many sides a circle has. The children have been taught that it has zero sides, as in it has no straight edges. I however say that it has an infinite number of edges since the circle is the limit of the regular polygons. We then talked about what a vertex was, though he stumped me with a particular shape. Turns out that there are two definitions of a vertex: one is about polygons, and the other about graphs. Fun stuff.
Quick quiz: Take a cone ad remove it's base so that it is hollow. Now cut down one edge of the open cone and flatten it. What shape is it? Answers on a postcard...
posted by Edd @ Wednesday, November 02, 2005
5 Comments:
Edd:
A Circle, obviously, has two sides in a one dimensional world .... an inside and an outside!
People just complicate these things .....
S 'n D.
I was under the impression that a circle with an infinite diameter was a straight line.
Further to the circle's edges conundrum, I read a very convincing argument proposing that it has one edge. If you are interested, you can find it here.
I think the main argument that swayed me was that if a circle has an infinite number of edges, then so does a semi-circle, but I'd say that had 2.
Can a circle have an infinite diameter? If one part of a circle goes one way, then surely musn't there be another part of it going back to complete it?
However, if you project a grand circle (one going through the north pole) onto the plane, it will be a line. This is how one can define the complex plane plus a point called "infinity". Mmmm... third year complex analysis.
Children often arrive in school having been taught at nursery that a circle has no sides. I always say it has 1. Not least because when you play a die game where you collect a shape each time you throw a number you need something for number 1 !!
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