#PhysicsFactlet (Math edition)
A circle is the set of points equidistant from a center. But the meaning of "distance" depends on the metric used.
The p-norm on the plane (given by \( (|x|^p+|y|^p)^{1/p}\) can produce circles that look like squares, depending on the p you choose.
In particular:
* For p=2 one recovers the common Euclidean metric.
* For p=1 and p=\(\infty\) the circles looks like squares.
* for p<1 the p=norm doesn't satisfy the triangle inequality.
#Visualization #Geometry
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It is interesting that for cases other than L² the continuous symmetry is lost and the orientation of the figure depends on the coordinate system (I guess).
