Surfaces and Euler characteristic
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K-12: Materials at high school level.
Surfaces
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| A tire | A donut |
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| A double torus | A pretzel |
Note that a tire and a donut have approximately the same shape. More complicated is a so called double torua, which is made by sticking two individual torus together and for instance the surface of a pretzel. In the pretzel you see 3 "holes". The donut has only one, and the double torus has two. In mathematics we use the number of holes to identify the surface.
A fun fact is that in an area of geometry - called topology - a cup and a donut are considered to have the same shape. One can be obtained form the other by morphing the shape.
The image above shows how the mug can be morphed into a donut and back again. The main rule is that you are not allowed to cut the shape or glue pieces together.
