866: Compass and Straightedge

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Compass and Straightedge

Title text: The Greeks long suspected this, but it wasn't until April 12th of 1882 that Ferdinand von Lindemann conclusively proved it when he constructed himself the most awesome birthday party possible and nobody showed up.

Explanation

Compass and straightedge constructions are a class of problems in classical geometry. They take the form "Using only a compass and a straightedge, construct X", where X is a geometric figure such as a regular pentagon. The subject is typically covered in high school mathematics. Three such constructions remained unsolved for thousands of years before being shown impossible with the use of modern algebraic techniques.

The comic begins as if it were stating a problem in classical geometry but veers into an observation that no amount of technical knowledge can substitute for human companionship. An additional layer of humor is that Cueball is a stick figure so technically it is possible to create friends with a straightedge and a compass.

Ferdinand von Lindemann was a German mathematician who showed in 1882 that pi is not a zero of any polynomial with rational coefficients, i.e. it is a transcendental number. Transcendental numbers cannot be constructed with straightedge and compass.

Transcript

I learned in high school what geometers discovered long ago:

[Cueball, holding a compass and straightedge, looks sad.]

Using only a compass and straightedge, its impossible to construct friends.

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Discussion

No, the comic is funny because many geometrical theorems prove something along the lines of "With a compass and straightedge you cannot construct..." (e.g. a square and a circle with the same area) If you have knowledge of this type of proof, the humor is that you think he's about to talk about something that is impossible in geometry, but really he's talking about the inapplicability of geometry to real life. This is often a difficulty with nerds and brainy people, they try to apply their theoretical knowledge to human relationships and fail. 75.103.23.206 19:53, 13 December 2012 (UTC)