Difference between revisions of "Euler Characteristic"
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===Tetrahedron=== | ===Tetrahedron=== | ||
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| + | A tetrahedon is a simple shape that is made up of 4 triangles. Below you see a picture with labels on the vertices (V) and edges (E). | ||
[[Image:Tetrahedron-labeled.svg|400px]] | [[Image:Tetrahedron-labeled.svg|400px]] | ||
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===Octahedron=== | ===Octahedron=== | ||
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| + | A tetrahedon is a simple shape that is made up of 8 triangles. Below you see two pictures, the one on the left is given with labels on the vertices (V) and edges (E). | ||
[[Image:Octahedron-labeled.svg|500px]] | [[Image:Octahedron-labeled.svg|500px]] | ||
Revision as of 10:46, 6 May 2009
K-12: Materials at high school level.
In 1750, the Swiss mathematician Leonhard Euler discovered a remarkable formula involving the number of faces F, edges E, and vertices V of a polyhedron:
He found that V - E + F = 2
Let's check this formula on some of the shapes below.
Tetrahedron
A tetrahedon is a simple shape that is made up of 4 triangles. Below you see a picture with labels on the vertices (V) and edges (E).
How many vertices ("corners") V do you see? _______
How may edges E do you see? ______
How many faces ("sides") F do you see? ______
Now find V - E + F = ___ - ___ + ___ =
Did the answer come out to 2? ______
Octahedron
A tetrahedon is a simple shape that is made up of 8 triangles. Below you see two pictures, the one on the left is given with labels on the vertices (V) and edges (E).
How many vertices ("corners") V do you see? _______
How may edges E do you see? ______
How many faces ("sides") F do you see? This may be easier to count in the figure on the right. ______
Now find V - E + F = ___ - ___ + ___ =
Did the answer come out to 2? ______
