Fractured Theorems


The Bovino-Weierstrass Theorem:  In any bounded pasture containing an infinite number of cow pies, you can stand in one location where no matter how close you look, there are an infinite number of cow pies near your feet.

 Surely there must be more such fractured theorems lurking out there in our collective imagination… If you come up with any new ones, share them in the comments.

6 Responses to “Fractured Theorems”

  1. Ξ Says:

    Puck’s Theorem: If you create a polygonal hockey arena on a lattice and put hockey pucks at each of the grid intersections, the area of the arena will be one less than the number of hockey pucks in the middle plus half the number of pucks on the boundary.

    Edited to add that WikiHow has an example of the Buffon Hot Dog Problem (how to estimate Pi by throwing frozen hot dogs). Essentially you draw vertical lines, spaced one hot-dog apart, and then throw a hot dog 100-200 times, marking down whether it lands on a line or not. The equation 2x(the number of throws)/(the number of times a hot dog touches or crosses one of the lines) is a pretty good approximation for Pi.

  2. TwoPi Says:

    Oiler Path: Route driven by a road maintenance crew spraying a single layer of fresh oil on each of the roads in a given region.

  3. Batman Says:

    Instead of an “Oiler path”:

    Yuler path: The route taken by holiday carolers singing exactly once on every block.

    (Because let’s face it – if you’re going to fracture Euler, you might as well go all the way.)

  4. Batman Says:

    Wait, wait, wait…

    Would that be a compound fracture?


  5. Batman Says:

    Oh, no. Are you going to revoke my math license, now?

  6. mbork Says:

    Not sure whether this fits here, but do you know the “local genius theorem”?
    “For each mathematician there exists a neighbourhood in which he is the most prominent one.”

    And one stupid joke: what is yellow, curved and complete? A Bananach space, of course.

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