A man is told to make a circle

He makes this:

enter image description here

Where is the man?

  • 6
    $\begingroup$ And this is an even-looking circle: ⃝. $\endgroup$
    – CJ Dennis
    Feb 11 '18 at 9:47
  • 1
    $\begingroup$ In a US public school? $\endgroup$
    – 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. enter image description here And then he makes the diamond... enter image description here
So where is the man?
Think what I have just done.
I am that man.

  • 6
    $\begingroup$ That's a..... cheeky ..... answer :) $\endgroup$
    – Brian J
    Feb 12 '18 at 13:53
  • 3
    $\begingroup$ But we still don’t know where you are!   :-)   ⁠ $\endgroup$ 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 $p$:

unit discs

  • 7
    $\begingroup$ So he could also be in L^inf space, just with is head tilted? $\endgroup$
    – Dale C
    Feb 12 '18 at 2:10
  • 3
    $\begingroup$ @Tilefish Well yes. $\endgroup$ 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.


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