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Sunday, January 3, 2016

Tangent Surface?

This post is more like a question than an answer, I really just wanted to document my doubt.

To me, the tangent surface to a curve is a really strange concept.

The book defined the tangent surface as the union of all tangent lines as follow:



Suppose I take a circle and take all the tangent lines, that should give the whole plane except the interior of the circle, and that's the tangent surface of a circle?

What is so interesting about the tangent surface of a curve anyway? Except of course the surface does contain the curve itself.


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