# The Diagonal Parking Theorem

(With apologies to Georg Cantor)

Theorem: There are an infinite number of stupid ways to park.

Definition: We define as stupid any parking method that places any fender of a car outside the legal lines bounding the space.

Proof:Consider a line L through the center of a legal parking space, parallel to the lines bounding the space. Consider a point P on L. There are an infinite number of lines passing diagonally through P at an angle greater than the smallest angle θ at which a car pulled into the space will intersect each of the bounding lines once. Any car parked parallel to one of these lines is, by definition, parked stupidly.

Thus, there are an infinite number of stupid ways to park. QED.

The astute reader will note that there are an infinite number of points P on L through which stupidly parked cars might pass. The implications of this for the cardinality of the stupidity of people parking their cars is left as an exercise for the reader, while you drive in circles looking for a spot that hasn't been blocked by some goddamn idiot.

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Aw, gosh darnit Derek, I was just going to say that the first poster to use a parking lot to calculate pi wins the Internet.

By Andrew Perrin (not verified) on 16 Nov 2010 #permalink

Provided that the car is as long as the parking spot is wide. (And that the person is randomly idiotic.)

By the same logic, there are an infinite number of ways to park that are not stupid. What then become stupid are:

1) two cars may park legally but so close it is impossible to open their facing doors,

and

2) head-in parking. Whoever came up with that idea must have always had a chauffeur (since they had the power to install it as The Parking Method (tm)). If you cannot see to reverse into a slot with no obstacles you should not be driving. But when reversing out of a slot any approaching vehicles are invisible until you are already well in their path, regardless of how good you are. Yet most such vehicle drivers assume the right of way over those attempting to back out. Insane.

By GrayGaffer (not verified) on 16 Nov 2010 #permalink

So, are we talking countably infinite or uncountably infinite?

What is the ratio of stupid to un-stupid?

By Benton Jackson (not verified) on 16 Nov 2010 #permalink

There's a nice mathematical fact that (assuming I'm remembering the statement correctly) if you consider the Lie group generated by driving forward/backward and turning wheels, you find that it contains sideways translations. So in an idealized mathematical world, parallel parking is easy, because the group of motions of a car lets you just move sideways.

how does time factor into all of this?

And relativity! What about the people who scream into the parking space so fast that they are relativistically contracted enough to fit between the lines, and then just don't notice that they don't fit any more once they stop moving relative to the parking lot?

Is space/distance/position not quantized? Surely there aren't actually infinite possible positions between 0.005mm over the line and 0.006mm?

Ender, even if space is quantized, that does not mean there cannot be an infinite number of points even within a quantum of space. Since a point is of infinitely small size, many points can dance on a quantum of space.

Gaffer, head in parking has become so dominate that a lot of parking lots are now designed, very badly, so that's all you can do.

Head-in parking is actually mandatory on our college campus and the local military base. Too many TX jackaholes with extra-long pickups don't know exactly how long they are until they back right into your vehicle. Anyway, people here have enough trouble parking straight when you are looking right at the spot, let alone while eyeballing the mirrors.