Quod Erat Demonstrandum

2010/04/28

Net of cylinder

Filed under: Junior Form Mathematics — johnmayhk @ 11:58 上午

Just forward a movie clip showing the way of making a cylinder from its net:

http://www.yenka.com/file/videopopup.action?quick=13x

It is good as a demonstration in junior form or primary school mathematics lesson.

Question: Is there any universal definition of ‘net’ of a 3-dimensional figure?

As asked by students, I’d found the statement

“A net is a two-dimensional figure that can be cut out and folded up to make a three-dimensional solid."

at http://mathforum.org/~annie/gsp.handouts/box.net/

1. My colleague, Mr. C, said that “net of cylinder" does not exist, because there is only a touching point between a circle and a rectangle and it is impossible to “fold up" and form a solid. Is it true?

2. Also, we can fold two different nets N1 and N2 to form two solids S1 and S2 (say), and we can “glue" S1 and S2 into one signle 3-dimensional figure S. The question is, can we say N1 union N2 (even they are disjoint) is a net of S?

3. We can fold up something to fold a 3-dimensional figure, but is it a must to say that something is a net of the figure? As for example, should the following be a net of a cube?

I have not thought about questions above in details when making up the instructions of a school math project. Sorry students.

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