An introduction to surfaces | Differential Geometry 21 | NJ Wildberger

Описание: We introduce surfaces, which are the main objects of interest in differential geometry. After a brief introduction, we mention the key notion of orientability, and then discuss the division in the subject between algebraic surfaces and parametrized surfaces. It is very important to have a balanced view between these two aspects; most texts are oriented, following Gauss, to the parametrical side: we will at least initially compensate by providing more detail on the algebraic surfaces.

Important examples of surfaces include quadrics, such as spheres, or more generally ellipsoids, or hyperboloids. We also mention some more unusual examples, including the Oloid, discovered by Paul Schatz in 1929.

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