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==Explanation==
 
==Explanation==
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Geometry usually represents 2D polygons with simple straight lines. In the comic, the lines are compared to a physical object, and are shown to have the property of bendiness. Randall claims this simplifies geometry as now triangles can have arbitrarily defined side lengths by merely stretching the lines, but it is unclear what benefits this may have over current Euclidean geometry. These lines cannot have Euclidean properties, but other {{w|Non-Euclidean_geometry|non-Euclidean systems have been invented in the past with non-standard properties.}} One such non-Euclidean space can be modelled as the surface of a sphere. If the sphere had a circumference of 20, the triangle with three sides of length 5 would be right angled (at all three vertices).
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{{incomplete|Created while BENDING OVER PULLBACKWARDS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
  
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This comic may be a reference to axis breaks in graphs, which shrink large segments and enhance readability and are denoted by a wiggly line on the axis in question, though this is more frequently done with angular zig-zags than the smoother curves as depicted.
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The original triangle, without bendy lines, is an example of a {{w|Pythagorean triple}}. Randall 'simplifies' this by adding squiggles to the two sides in order to make them longer and therefore match the length of the hypotenuse (longest side). The idea is that this would allow one to arbitrarily define side lengths and therefore avoid doing calculations to figure them out, but in practice this is not possible in geometry as the sides will no longer be lines and the shape would be by definiton no longer a triangle. The way these calculations are used in real life also render this method unusable, as the point of the calculations Randall is trying to avoid is typically to determine the length of an already-existing side. The joke here is that Randall is trying to solve a geometric problem (that is actually already solved, in this case) with non-conventional methods unrelated to the problem's application.
  
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The title-text talks about "{{w|Squaring the circle}}" (not to be confused with {{w|Tarski's circle-squaring problem|circle-squaring}}), a famous geometry problem based around constructing a square with the same area as a given circle, using a compass and straightedge, which was proven to be impossible (even with more powerful forms of construction, such as marked straightedges or origami) in 1882 as pi is a transcendental number. However, it then goes on to describe a way to literally turn one of these bendy shapes from a circle into a square - namely using clamps.
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This comic may be a reference to axis breaks in graphs, which shrink large segments and enhance readability and are denoted by a wiggly line on the axis in question.
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The title-text talks about "{{w|Squaring the circle}}", a famous geometry problem based around constructing a square with the same area as a given circle with a compass and straightedge, which was proven to be impossible (even with more powerful forms of construction, such as marked straightedges or origami) in 1882 as pi is a transcendental number (Not to be confused with {{w|Tarski's circle-squaring problem|circle-squaring}}.) However, it then goes on to describe a way to literally turn one of these bendy shapes from a circle into a square, namely using clamps.
  
 
==Transcript==
 
==Transcript==
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:[There are two right triangles. The one to the left is a standard right triangle with the right angle denoted by a small square at that corner. The lengths of the sides are denoted around it, but it has been scribbled out with red lines. The triangle to the right has the same general shape as the first one, but with the legs appearing longer but bent with about three wiggles each near the right-angled corner. As with the first triangle, the side lengths are denoted around it, but they are not the same as for the first. Around this triangle is a red line circling about two times around it.]
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{{incomplete transcript|Do NOT delete this tag too soon.}}
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:Left triangle: 3 4 5
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:[There are two right triangles. One triangle has side lengths of 3, 4, and 5, and is scribbled out in red. The other triangle has the same general shape but with the catheti appearing like longer but bent lines, so that all the side lengths equal 5 if straightened.]
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:Right triangle: 5 5 5
 
  
 
:[Caption below the panel:]
 
:[Caption below the panel:]
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{{comic discussion}}
 
{{comic discussion}}
  
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[[Category:Math]]
 
[[Category:Comics with color]]
 
[[Category:Comics with color]]
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[[Category:Comics with red annotations]]
 
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[[Category:Math]]
 
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[[Category:Geometry]]
 

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