# Define a circle in two dimensions in the L3 norm

So this is straight from my homework so please don't all out answer it but maybe point me in the right direction.

We are learning about dimensionality and clustering algorithms and this is one question.

Where I'm currently at is:

This is the way I think a norm is defined is as follows:

$$L_n(a,b)=\sqrt[n]{(a_1−b_1)^n+(a_2−b_2)^n+\dots+(a_i−b_i)^n}$$

So the $L3$ norm is easy enough to compute. So for the circle part do I have to parametrize it? Or can someone point me in the proper direction?

• Please take a look at this one: math.stackexchange.com/questions/254620/… – Guangliang Mar 23 '17 at 17:21
• Firs of all, consider all $a_i=0$, i.e., try to understand the unit ball or unit sphere centered at the origin. Then work in dim. 2: in this way you can take advantage of a polar representation. – Jean Marie Mar 23 '17 at 17:27