Wednesday, November 29, 2006

Way beyond being random...

How to Calculate Pi by Throwing Frozen Hot Dogs

Throwing a pie in someone's face is good. Throwing food at pi is better. Believe it or not, of all the countless ways to approximate the most prolific irrational number in the universe, there are none quite as interesting or as surprisingly satisfying as throwing perfectly good food around your kitchen. In fewer steps than it takes to circumscribe your house in a circle of baguettes, you, too, can easily add a slice of pi into your dinner menu tonight. The best part is...it really works!

Steps

  1. Select your food item to throw. There are a couple of qualifications. First, it must be long, thin, and straight, like a frozen hot dog, for example. There are lots of other items that fit this criterion including Otter Pops, celery sticks, and churros. (If you simply can't come to grips with throwing perfectly good food, see the Tips section for some additional ideas.) Second, it must be a reasonably stiff item. Third, it should be somewhere between six and eighteen inches long. The experiment can be performed otherwise, but read on, and you will see why this size is optimal.
  2. Select the spot from where you will throw your mathematical cuisine. You will probably need about 6-10 feet in front of you as you will be throwing straight ahead.
  3. Clear the area. The place at which you are throwing should be devoid of objects that your food item could possibly run in to. So, if you are throwing in your kitchen, consider moving the table into another room or at least throwing in such a way that your food won't hit the table during its flight.
  4. Measure the length of your projectile (i.e. your frozen hot dogs). A tape measure should do the trick. Be as accurate as you can, even down to the millimeter, for best results.
  5. Lay down masking tape in parallel strips across the floor as far apart as your projectile is long. The strips should be perpendicular to the direction you will be throwing (see picture below). Do about 6-10 strips if your item is 6-18 inches long; fewer, if longer; more, if shorter.
  6. The throwing set-up
    Enlarge
    The throwing set-up
    Get a piece of paper and across the top make a column for “Tosses” and another column for "Crosses." The "Tosses" column is to keep track of how many times you throw your food item. The "Crosses" column is to keep track of how many times your item, once it lands and stops moving, is laying across one of the lines.
  7. Now, get into position, and THROW YOUR FOOD! Throw just one item at a time. Once it is at rest, observe whether or not it is crossing one of the lines. If it is, put a tick under "Crosses" and a tick under "Tosses." If it isn't, just put a tick under "Tosses." Repeat this as many times as you like. You should start seeing some interesting results by around 100 to 200 throws (it doesn't take as long as it sounds, especially if you use a pack of 10 frozen hot dogs so you're not out retrieving the one hot dog after every throw).
  8. Once you are done throwing your food, multiply the number of tosses by two and divide by the number of crosses. For example, if I threw 500 times, and it crossed 320 times, I would calculate 500 x 2 / 320. And, as if a miracle has occurred, you will have an approximation for pi! Now, don't you feel less stressed?


Tips

  • For those who are troubled by throwing perfectly good food, consider throwing sticks, dowels, bats, or a very stiff person. In fact, any item will do so long as it is long, thin, straight, and stiff.
  • If room is a concern, consider just drawing lines on a piece of paper and dropping toothpicks onto the paper from about three feet up. This definitely is not as refreshing as throwing food across the room, but it works.
  • The more the merrier! If two or three throw food together, you will get a better approximation faster because you will be able to get more throws in a shorter amount of time.
  • As long as you have your calculator, you could just press the "pi" key.
  • For the mathematically-inclined, this experiment is actually real! The proof and other details can be found at mathworld.wolfram.com: Buffon Needle Problem


Warnings

  • Remember that this is an experiment, so the idea is not to TRY and get the food to land on one of the lines. Just throw it randomly towards the lines. It should still land amongst them, but don't jinx the experiment by encouraging your dinner to land onto the tape.
  • Resist the temptation to use bananas. Not only are they not really straight, but they really won't last more than 50 throws before creating a big mess. Really.


Things You'll Need

  • Pen and Paper
  • Masking Tape
  • Calculator
  • Long, Thin, Straight, Stiff Food. Preferably a pack of frozen hot dogs

5 comments:

Zenka said...

eww... Hot dogs. Not even going to read it. Plus, it's too long anyway.
enjoy the snow. I'm enjoying the sunshine, especially when I'm sick. Like right now. Blech.

cinia said...

basically, I didn't read it either!:P

Erin said...

Holy my goodness, to quote a dear older brother.

Madeline said...

I didn't read it either... ha ha! We're such goofs.

cinia said...

yep, pretty much