Odd-looking circle

Question

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 09:47 — CJ Dennis, Feb 11 '18 at 09:47

Faruk D. · Answer 1 · 2018-10-20T08:05:54.367

53

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.

edited Oct 20 '18 at 08:05

answered Feb 11 '18 at 17:25

Faruk D.

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

score 48 · Accepted Answer · edited Feb 12 '18 at 21:00

48

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.

edited Feb 12 '18 at 21:00

ibrahim mahrir

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answered Feb 11 '18 at 04:03

phenomist

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score 29 · Answer 3 · answered Feb 11 '18 at 14:22

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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 $p$:

answered Feb 11 '18 at 14:22

Rand al'Thor

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So he could also be in L^inf space, just with is head tilted? – Dale C Feb 12 '18 at 02:10
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@Tilefish Well yes. – Rand al'Thor Feb 12 '18 at 02:11

score 0 · Answer 4 · answered Nov 08 '19 at 00:02

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

answered Nov 08 '19 at 00:02

user118161

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Odd-looking circle

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