Editing 2706: Bendy

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| titletext = Squaring the circle is really easy with some good clamps.

 

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).

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.

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.

:[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.]