Editing 2706: Bendy
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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). | 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). | ||
| β | 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 | + | 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 "{{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. | 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. | ||
