Curvature Behavior of a Parametric Curve in R3

[aesailor]

Homework Statement

Find a parametric curve in R3 that has zero curvature at the origin and infinite curvature as the parameter t goes to infinity.
2. The attempt at a solution

I was thinking it would look like a spiraled cone with the radius getting infinitely bigger, but I didn't know what the parametric curve would be

 

[tiny-tim]

haello aesailor!

I was thinking it would look like a spiraled cone with the radius getting infinitely bigger, but I didn't know what the parametric curve would be

wouldn't it be easier with the radius getting smaller?