As p increases from 1 to 2 to infinity, the Lp norm ball becomes more spherical
Image: Created by Wolfgang Beyer with the program Ultra Fractal 3., CC BY-SA 3.0, via Wikimedia Commons
the Lp norm ball shape changes as p goes from 1 to 2 to infinity
As p increases from 1 to 2 to infinity, the Lp norm ball becomes more spherical
Related concepts
Norm (mathematics)
L∞ norm equals max absolute value
the L1 unit ball is a diamond shape and the L2 unit ball is a circle
L1 ball: Manhattan distance, L2 ball: Euclidean distance. Diamond shape for L1 reflects Manhattan geometry, circle for L2 reflects Euclidean geometry
List of unsolved problems in mathematics
Random points in high dimensions are nearly equidistant due to the uniform distribution of volume in high-dimensional space
the volume of a unit ball approaches zero as dimensions increase
As dimensions increase, the volume of a unit ball approaches zero due to the formula V = (π^(d/2) / Γ(d/2 + 1))^(1/d), where d is the dimension
the L1 norm is not differentiable at zero
The L1 norm is not differentiable at zero because the absolute value function has a kink at zero
Surface tension
High surface tension in water
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