Nets in a Geometrical Sense
Date: 03/07/99 at 19:15:11 From: Abby Shields Subject: Nets in a "geometrical" sense In our geometry project, we are supposed to draw the "net" of various shapes. What is the net of a shape? Thank you.
Date: 03/08/99 at 12:00:14 From: Doctor Rick Subject: Re: Nets in a "geometrical" sense The net of a polyhedron (a 3-dimensional shape made up of flat faces) is a plane diagram that shows how the edges of the polyhedron are connected. The edges in the net should not intersect. You can picture making a net by making a hole in one face of the polyhedron, then stretching the hole out as if the polyhedron were made of very stretchable rubber, and flattening the whole shape onto your paper. It does not matter if the edges change their length; sometimes they even have to curve, and that is okay too. You just want to show which other edges each edge meets. For example, here is a cube: D_____________ C / /| / : / | / : / | /___:________/ | A| : |B | | : | | | .........|...| | . H | / G | . | / |.___________|/ E F Here is a net of the cube, with the vertices labeled. I put the "hole" in the bottom face, EFGH. H_________________________ G |\ /| | \ / | | \ / | | \ / | | \_______________/ | | D| |C | | | | | | | | | | | | | | | | | | | | | | | | | | A|_______________|B | | / \ | | / \ | | / \ | | / \ | |/_______________________\| E F You can see that these lines divide the plane into 6 regions, matching the 6 faces of the cube. Five of these are quadrilaterals like EADH. The sixth is the region outside the figure (that is, the whole plane except what is inside EFGH). This matches the face that I put the hole in. I hope this helps you complete your project. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 03/09/99 at 09:12:58 From: Doctor Peterson Subject: Re: Nets in a "geometrical" sense Hi, Abby. I saw Doctor Rick's answer to your question, and want to add something to it. I think the kind of net your teacher wants may be slightly different from what Dr. Rick told you about, which is the "topological" version of a net (that is, it allows you to stretch things and ignores the actual shape and size of the faces of the polyhedron). Here is a page that shows you several nets in a "geometrical" sense: the shape is flattened out not by stretching, but by cutting apart along the edges. You can cut these nets out and actually build the shape. Doctor Rick and I (twin brothers!) used to make a lot of these when we were kids: http://mathforum.org/alejandre/workshops/net.html There is a lot on the Web about making polyhedron models, but it is hard to search because the word "net" is a little too common! But this is probably enough to get you going. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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