High School How do you create a + and π sign using multivariable (x,y,z)

[JessicaHelena]

I am taking a high school multivariable calculus class and we have an end-of-semester project where we trace out some letters etc., except that they all have to be connected, continuous and differentiable everywhere. My group's chosen to do Euler's formula, but so far we are having problems making $\pi$ and the + sign. For the + sign, we thought that we could do rose curves, but it seems that the equations for rose curves in 2D don't really work in a 3D environment. Could someone give us hints as to how to approach these problems? Any help would really be appreciated!

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[andrewkirk]

You can use piecewise-defined curves, for which each piece is either a straight line or a quarter or half circle. Provided the circle pieces join the circle segments to which they connect as a tangent, the curve will be continuous and differentiable everywhere. It will even be twice-differentiable everywhere except at points where a straight and curved segment connect.

It's easy to make a pi and a plus sign using that approach. Both drawings will have a hollow 'inside', but if the radii of the circles are made small enough, that will not be visible to the naked eye.