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L^p norm balls
di christianlp
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Props made to accompany a course in linear analysis. Each of these shapes shows a unit ball in a different Lᵖ norm, stretched in the _x_ axis.
* Ellipsoid: (x/2)² + y² + z² ≤ 1 (the L² norm)
* Cuboid: max(|x/2|,|y|,|z|) ≤ 1 (the L∞ norm)
* Stretched octahedron: |x/2| + |y| + |z| ≤ 1 (the L¹ norm)
* Squircle-oid: (x/2)⁴ + y⁴ + z⁴ ≤ 1 (the L⁴ norm)
* Ellipsoid: (x/2)² + y² + z² ≤ 1 (the L² norm)
* Cuboid: max(|x/2|,|y|,|z|) ≤ 1 (the L∞ norm)
* Stretched octahedron: |x/2| + |y| + |z| ≤ 1 (the L¹ norm)
* Squircle-oid: (x/2)⁴ + y⁴ + z⁴ ≤ 1 (the L⁴ norm)
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