# Odd-looking circle

A man is told to make a circle

He makes this: Where is the man?

• And this is an even-looking circle: ⃝. – CJ Dennis Feb 11 '18 at 9:47
• In a US public school? – Chowzen Feb 20 '18 at 12:15

In Manhattan, because that is what a "circle" (defined to be the set of points of a certain set distance d away from a given point) looks like when using the taxicab (or Manhattan) metric.

He has made a rapid escape from the scene because he actually didn't know what a "circle" was.

No wait.

He makes it.
Well, he draws a circle. And then he makes the diamond... So where is the man?
Think what I have just done.
I am that man.

• That's a..... cheeky ..... answer :) – Brian J Feb 12 '18 at 13:53
• But we still don’t know where you are!   :-)   ⁠ – Peregrine Rook Feb 13 '18 at 16:11

Clearly the man is

in $L^1$ space.

He was asked to draw a circle, namely the set of all points at distance $1$ from a fixed centre.

We imagine this as looking round, because we live in Euclidean $L^2$ space. But this man lives in $L^1$ space, in which the unit circle is a square box because the concept of 'distance' is defined differently. More generally, unit circles in $L^p$ space look like this for assorted values of $p$: • So he could also be in L^inf space, just with is head tilted? – Dale C Feb 12 '18 at 2:10
• @Tilefish Well yes. – Rand al'Thor Feb 12 '18 at 2:11

He's in another distance metric, one where distance is determined by the addition of coordinates, instead of pythagorean theorem.