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Something that just clicked for me - In the same way that dividing by distance-to-origin (L2 norm) projects a point onto the unit circle/sphere: Dividing by L1 norm projects onto the unit diamond/octahedron Dividing by L-infinity norm projects onto the unit square/cube cont.

Mike Turitzin

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25,848 views • 2 months ago •via X (Twitter)

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Euler's formula states that e^(iθ) = cos θ + i sin θ. As the angle θ increases, e^(iθ) traces the unit circle in the complex plane. Plotted against θ, that rotation becomes a helix. The real part of the helix projects as the cosine wave Re(z) = cos θ. The imaginary part projects as the sine wave Im(z) = sin θ.

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