Trifolium Rose Curve via Parametric Gear Coupling Gear ratio 3:1. A fixed point on the linkage traces a perfect periodic path in the rotating frame of the larger gear. Orthogonal projections (blue) physically realize: r = a cos(3θ)

The blue dotted line is the imaginary part. It's the VERY real product of imaginary numbers in graphic detail. It is the fingerprint of ecological coupling. This is a simple proof of imaginary numbers being the other side of the coupling rather than abstract operations that work.

When you switch perspective into the rotating frame of the bigger gear, everything suddenly becomes super clean and predictable. The motion loops perfectly, like it’s following an invisible script.

I am now imagining a power fan that self-cleans its own blades

What is it used for?

Adobe Acrobat?

I bet every shape human species can be draw circle.. 💯

🍴... 🥘🍲 🍜🍛 ...🍽 Oof... thanks. I needed some math.🫂