Rollgebra · Maths you can play
Polar curves: draw with radius and angle
Polar coordinates describe a point using its distance from the origin, r, and an angle, θ. The curve r=2cos(5θ) creates a five-petal rose when traced over a full turn.
From angle to track
Rollgebra converts each sampled polar point to Cartesian coordinates with x=r cos(θ) and y=r sin(θ). The resulting connected points make a visible and collidable track.
Try a simpler example
r=3 makes a circle centred at the origin. r=2+cos(4θ) creates a wavy circular shape. You can adjust the minimum and maximum θ in Advanced settings.
What are the limits?
Physics and rendering use finite sampling: extremely oscillatory curves may show approximations. Polar experiments are unscored and not part of the ranked daily challenges.