Development (differential geometry)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In classical differential geometry, development refers to the simple idea of rolling one smooth surface over another in Euclidean space. For example, the tangent plane to a surface (such as the sphere or the cylinder) at a point can be rolled around the surface to obtain the tangent-plane at other points. The tangential contact between the surfaces being rolled over one another provides a relation between points on the two surfaces. If this relation is (perhaps only i...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In classical differential geometry, development refers to the simple idea of rolling one smooth surface over another in Euclidean space. For example, the tangent plane to a surface (such as the sphere or the cylinder) at a point can be rolled around the surface to obtain the tangent-plane at other points. The tangential contact between the surfaces being rolled over one another provides a relation between points on the two surfaces. If this relation is (perhaps only in a local sense) a bijection between the surfaces, then the two surfaces are said to be developable on each other or developments of each other. Differently put, the correspondence provides an isometry, locally, between the two surfaces.
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