I am working on a project for my Calculus class in which I have to rotate a curve about some axis and 3-d print a model of the curve (using any type of cross-sectional areas). At first, I tried to model a colosseum using the curve $y=0.5x^2$, but I was wondering if anyone had any other cool ideas.
Thanks!
The topologist's sine curve $$y = \sin(1/x)$$ or its continuous friend $$y = x\sin(1/x)$$ (for $0 \le x \le 1/pi$, say) should be fun. You'll have to do a bit of design work to deal with the discontinuity of $\sin(1/x)$ at $x = 0$.