This Polar Coordinate System Flower Pendant was created for Ultimaker's Design Engine Challenge Week 7. The challenge was to design an object that expresses the beauty of math. The parameter cards for this challenge are “complex” and “private”, while the gameplay card is “reverse” which means that one of these parameters can be expressed as its opposite.

Many people think of math as right or wrong, a utilitarian function. I think of math as a beautiful, elegant way to understand and describe the world around me. Graphing the equation,

r = 4cos(2ϴ)

in a polar graph yields a plot that resembles a flower. I use these as small trinkets on a charm bracelet. The derivative is

r = -8sin(4ϴ)

which yields a bigger plot which I use as a pendant for a necklace.

This solution is “complex” because a graph of the derivative was used to generate the larger necklace pendant. Applying the “reverse” gameplay card to the “private” parameter card gives a twist, the pieces generated are worn as jewelry in public.