Edges, Vertices, Surfaces
Date: 04/22/2003 at 21:37:37 From: Katie Subject: Edges, vertices, and surfaces I need help with edges, vertices, and surfaces. How can a shape have 8 edges and 5 vertices? How can a shape have 12 edges, all the same length? How can a shape have 3 surfaces, one curved? The one with three surfaces could be a cylinder, but that has 4 surfaces (I think). Thanks!
Date: 04/22/2003 at 22:36:44 From: Doctor Peterson Subject: Re: Edges, vertices, and surfaces Hi, Katie. You're right about the cylinder; it is like a soup can, with two flat ends and one curved "side." Probably the biggest difficulty here is to try to visualize the shapes and count their edges. I think these problems all relate to familiar, ordinary shapes like prisms and pyramids, so if you can find pictures of those, you can just count the sides. There are pictures of a lot of shapes in the Dr. Math Geometric Formulas FAQ: Formulas: Geometric http://mathforum.org/dr.math/faq/formulas/ Then you need an orderly way to count everything. Let's take a simple example, the cube: +------+ / /| / / | +------+ | | | + | | / | |/ +------+ You can't see all the edges and surfaces, but you can still think about them. First, think about the surfaces. We can group them into top, bottom, and sides: there is 1 top, 1 bottom, and 4 sides, making a total of 6 surfaces. Now, how about the edges? There are 4 on the top, 4 on the bottom, and 4 standing upright between the sides, making a total of 12 edges. Hmmm ... they are all the same length, too, so you might have an answer here. Try doing this for other basic shapes, and see if you find one that fits the other question. You might be able to see a pattern that lets you find the number of parts of any prism or pyramid when you know the number of sides in the base. If you need more help, please write back and show me how far you got. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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