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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 non-Euclidean systems have been invented in the past with non-standard properties.
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.
The title-text talks about "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 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.
- [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 catheti appearing like longer but bent lines with about three wiggles each near the right angled corner. As with the first the side lenghts are denoted around it, but they are not the same as for the first. Around this triangle are a red line circling about two times around it.]
- Left triangle: 3 4 5
- Right triangle: 5 5 5
- [Caption below the panel:]
- Huge geometry breakthrough: Turns out those lines we make triangles out of are bendy!
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