Is Adobe Acrobat's icon a special function?

Question

It looks like a function in polar coordinates.

Is it a special function ?

Answer 1

The logo dates back to Adobe Reader v1.0. (link) I always thought it was chosen simply because it looks like the letter A for Acrobat.

A parametric function that approximates the logo is: $$x(t)=5\cos(t)\times \left(\sin(t+.5)+\cos(3t+.5) \right) \\ y(t)=5\sin(t)\times \left(\sin(t+.5)-\cos(3t+.5) \right) $$

Answer 2

It bears a strong resemblance to (in cartesian coordinates) $ x = \cos(t) + 3 \cos(2 t)/4, y = \sin(t) - 3 \sin(2 t)/4$ but not quite as symmetric.

Answer 3

It looks a bit like a deltoid, which belongs to the family of Kakeya sets. It was thought to be the solution to the problem of finding the minimal area you need to rotate a needle in the plane.

Answer 4

Thanks you guys! Very grateful for this discussion. This is just what I was looking for. It's a Cinema4D Formula Object. Did a little Z tweaking to make it loop like Acrobat Logo. Apologies for my home made Z formula, kinda hacked at it. Sure there is a better solution.

• $X= 300 \cdot \cos(t) \cdot (\sin(t+.5) +\cos(3t+.5))$
• $Y= 300 \cdot \sin(t) \cdot (\sin(t+.5) -\cos(3t+.5))$
• $Z= 10 \cdot \cos(t) \cdot 10 \cdot \sin(t)$
• TMin $=-1.571$
• TMin $=1.571$