Geometry and Soccer ballsDate: 10/29/98 at 10:50:00 From: Megan Monaghan Subject: Geometry/Soccer balls Hi, We are studying geometry right now. I am supposed to make a math project or display for our bulletin board. Since I love soccer, I would like to do something fun about the shapes on a soccer ball. Do you have any ideas? Thank you for your help, Megan Monaghan Date: 10/29/98 at 15:57:48 From: Doctor Tom Subject: Re: Geometry/Soccer balls Here are a couple of ideas. First, look carefully at a soccer ball and you'll see that it's the intersection of two Platonic solids - the icosahedron and the dodecahedron. In fact, like the dodecahedron it has 12 5-sided faces, and like the icosahedron it has 20 6-sided faces. You might look at Euler's formula, which relates the number of faces, edges, and vertices of a solid. For example, a cube has 6 faces, 12 edges, and 8 vertices (corners). The tetrahedron has 4 faces, 6 edges, and 4 vertices. If you take ANY solid without holes that's made of flat faces like this, and F = number of faces, E = number of edges, and V = number of vertices: F - E + V = 2 For the cube: 6 - 12 + 8 = 2 For the tetrahedron: 4 - 6 + 4 = 2 Find the numbers for some other shapes, and for your big example, do the soccer ball. - Doctor Tom, The Math Forum http://mathforum.org/dr.math/ |
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