# Difference between revisions of "Euler Characteristic"

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− | In 1750, the Swiss mathematician Leonhard Euler discovered a remarkable formula involving the number of faces | + | 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=== | ===Tetrahedron=== | ||

+ | |||

+ | [[Image:Tetrahedron-labeled.svg|500px]] | ||

+ | |||

+ | 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=== | ||

+ | |||

+ | [[Image:Octahedron-labeled.svg|500px]] | ||

+ | |||

+ | 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? ______ |

## Revision as of 10:44, 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

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

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? ______