What is a surface of revolution?

What is a surface of revolution? Here are some definitions.

  1. (mathematics) A surface formed when a given curve is revolved around a given axis. If the resulting surface is a closed one, it also defines a solid of revolution.
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He drew the two straight sections as two cylinders and then used a surface of revolution to create the bend between them.
The model was obtained on the surface of revolution of a tractrix about its asymptote.
The only surface of revolution having this property is the catenoid formed by the revolution of a catenary about its directrix.

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