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Cylindrical surfaces problem

Find all possible equations for a cylindric surface (extending infinitely) with radius 1 using rectangular coordinates in 3-space, such that the surface is tangent to the Z-axis.

Note by Hobart Pao
2 years ago

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Hm, you might have to clarify what "tangent to the z-axis" means, esp at the "corners" of the cylinder.

Calvin Lin Staff - 2 years ago

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No corners on this cylinder, any of these cylinders extend infinitely. Maybe I should have said cylindric surface that extends infinitely? For example, if I have an equation \(x^{2} + y^{2} = 1\) in 3-space, that's a cylinder that extends infinitely in both directions concerning the z-axis.

Hobart Pao - 2 years ago

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Ah, I was thinking of it having a finite height because I only read "cylinder". I agree that "cylindrical surface" means what you say, though adding in "extends infinitely" will help clarify the situation.

It's an interesting question. Somewhat easy to visualize, but hard to describe completely.

Calvin Lin Staff - 2 years ago

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