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.

#Geometry #CylindricalSurfaces

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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

Calvin Lin Staff - 5 years, 6 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.

Hobart Pao - 5 years, 6 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.

Calvin Lin Staff - 5 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$