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Can you draw something on a piece of paper that looks like a square and a circle at the same time? ( without using Math or 3-d visualisation techniques)

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  • $\begingroup$ How about this one petapixel.com/assets/uploads/2011/08/circles.jpg $\endgroup$ – Hubble07 Sep 17 '14 at 6:46
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    $\begingroup$ If you use the Chebyshev norm on $\mathbb{R}^2$ rather than the Euclidean one, then circles are squares. $\endgroup$ – Julia Hayward Sep 17 '14 at 9:18
  • $\begingroup$ First guess: draw a squircle. Second guess: the answer to the question is "no, such a task is impossible" $\endgroup$ – Kevin Sep 17 '14 at 12:06
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You can draw a cylinder, which (a real 3D object, not the 2D drawing) can look like a square and like a circle, depending on how you turn it.enter image description here.

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    $\begingroup$ nice Also you can cut that cylinder into a shape which can give a triangle as the third projection. $\endgroup$ – Hubble07 Sep 17 '14 at 13:43
  • $\begingroup$ The problem however, is that if you draw it on a piece of paper, you only have the one perspective. $\endgroup$ – Tim Couwelier Sep 18 '14 at 6:49
  • $\begingroup$ @TimCouwelier, if you draw an elephant on a post mark, does it become a small animal? $\endgroup$ – klm123 Sep 18 '14 at 7:06
  • $\begingroup$ No, it becomes a small drawing of the animal. $\endgroup$ – Tim Couwelier Sep 18 '14 at 7:20
  • $\begingroup$ @TimCouwelier similarly cylinder does not lose other perspectives if you draw only one. $\endgroup$ – klm123 Sep 18 '14 at 7:57
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Here is one possible answer ( like Marylin Vos Savant said try to find many possible useful answers to one problem ) ;just draw a circle on a piece of paper , it 'looks' like a circle , it also looks like a 'zero' which is a square integer....

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Here is an edge-view picture of a square or a circle: |

It looks like both at once, or indeed like any other planar polygon viewed edge-on. It is fairly easy to draw, using a pencil, ruler, and piece of paper.

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