Curvature of Surfaces (Geometry and the Imagination)
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|Conway, Doyle, Gilman, Thurston; The Geometry Center|
|If you take a flat piece of paper and bend it gently, it bends in only one direction at a time. At any point on the paper, you can find at least one direction through which there is a straight line on the surface. You can bend it into a cylinder, or into a cone, but you can never bend it without crumpling or distorting to the get a portion of the surface of a sphere. If you take the skin of a sphere, it cannot be flattened out into the plane without distortion or crumpling. This phenomenon is familiar from orange peels or apple peels...|
|Levels:||Elementary, Middle School (6-8), High School (9-12)|
|Resource Types:||Lesson Plans and Activities|
|Math Topics:||Differential Geometry, Topology|
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