If you're building your own game, bookmark this.
- https://t.co/Mwagc3de7i Indie game assets
- https://t.co/ig4BYLHvfF Community game art
- https://t.co/TRL9lYnUvy Game asset packs
- https://t.co/d6Y13aHEW9 Game interface icons
- https://t.co/hv6ZhkfftA Character rigging and animation
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- https://t.co/CWxDt7F5fY Library Godot plugins and assets
What did I miss?
Each coordinate of a closed outline has its own real Fourier series: x(t) = ∑ (aₖ cos kt + bₖ sin kt), and the same for y.
A cosine and sine of frequency k make one arm of length √(aₖ² + bₖ²) turning k times per lap. One chain sets x, one sets y, and the pen sits where their guides cross. With N harmonics per axis the knight is off by 30.2 % of its height at N = 1, 0.70 % at N = 50.
At N = 1 both coordinates are pure sinusoids: an ellipse.
Cut a bar magnet in half and you get two smaller magnets, never a lone north pole. One equation says why.
∇·B = 0. By the divergence theorem, ∮ B·dS = ∫ ∇·B dV = 0 for every closed surface.
So every magnetic field line that leaves a surface must come back in. The lines of a current loop close on themselves.
A monopole would act as a source, giving nonzero flux like an electric charge does: ∇·E = ρ/ε₀.
Physicists still search for one. None has ever been seen.