balls in 2D
Oct. 18th, 2009 12:49 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslThe L1 ball in 2D is shaped like a diamond (L1 is also known as the Manhattan norm). The L∞ ball is shaped like a square (L∞ is also known as the supremum norm). They are similar, i.e. have same shape. The L2 ball is shaped like a circle.
Hypothesis: For all n in the interval (1,2), there is m>2 such that the m-ball and the n-ball are similar.
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In case you need the mathematical background:
The Ln ball is the set of points whose Ln norm is < 1.
If we call our coordinates x and y, then the Ln norm is defined as (|x|n + |y|n)1/n (for n=-1, we get the formula for resistance in a parallel circuit)
Hypothesis: For all n in the interval (1,2), there is m>2 such that the m-ball and the n-ball are similar.
---
In case you need the mathematical background:
The Ln ball is the set of points whose Ln norm is < 1.
If we call our coordinates x and y, then the Ln norm is defined as (|x|n + |y|n)1/n (for n=-1, we get the formula for resistance in a parallel circuit)