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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
1 year, 10 months 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.

Staff - 1 year, 10 months ago

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.

- 1 year, 10 months ago

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.

Staff - 1 year, 10 months ago