Calculate Pi by Throwing Frozen Hot Dogs

Throwing a pie in someone's face is good. Throwing food to discover 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

Calculation Chart

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Calculating Pi by Throwing Frozen Hot Dogs

  1. Select a food item to throw. There are a couple of qualifications. First, it must be long, thin, hard, and straight, like a frozen hot dog, for example. Second, it must be a reasonably stiff item. Third, it should be somewhere between 15 to 20 cm (6-8 inches) long; the experiment can be performed otherwise, but read on, and you will see why this size is optimal. There are lots of other items that fit these criteria including Otter Pops, celery, and churros. (If you simply can't come to grips with throwing perfectly good food, see the Tips section for some additional ideas.)
  2. Select the spot from which to throw your mathematical cuisine. You will probably need about 180-300 cm (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. A tape measure should do the trick. Be as accurate as you can, even down to the millimeter, for best results. Since length is a factor, it’s best to choose food items that are all the same size. If you’ve chosen something that isn’t naturally uniform, such as celery sticks, cut them evenly beforehand.
  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. If your item is 15-45 cm (6-18 inches) long, lay down about 6-10 strips; lay down fewer if longer and more if shorter.
  6. On a piece of paper, make a column for “Tosses” and another column for "Crosses." The "Tosses" column is where you’ll keep track of how many times you throw your food item. The "Crosses" column is where you’ll keep track of how many times your item lands across one of the lines. (Note that landing is not the same thing as bouncing.)
  7. 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." When you’ve run out of hot dogs, pick them up and re-use them, making sure to throw from the same position. Repeat this as many times as you like. You should start seeing some interesting results by around 100 to 200 throws. (This doesn't take as long as it sounds.)
  8. When you’re done, divide the number of crosses by 2 and divide the number of tosses by that. For example, if you threw 300 times, and it crossed 191 times, you would calculate 300/(191/2). And, to your amazement, you will now have an approximation for pi!

Tips

  • For those who are troubled by throwing perfectly good food, consider throwing sticks, dowels, or pencils. In fact, any item will do so long as it is long, thin, straight, stiff and hard. The thinner the better.
  • For the mathematically-inclined, this experiment is actually real! The proof and other details can be found at mathworld.wolfram.com: Buffon Needle Problem.
  • A quick estimation of pi is 22/7; a much better one is 355/113 (note the memorable pattern of the digits); Or, you could just press the "pi" key on your calculator.
  • 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.
  • Craft sticks (popsicle sticks) would meet the requirements listed above, are inexpensive, and of uniform length.
  • This type of approach (essentially, using random numbers to experimentally solve a problem) is also known as Monte Carlo Simulation.
  • If room is a concern, consider just drawing lines on a piece of paper and dropping toothpicks onto the paper from about 90 cm (3 feet) up. This definitely is not as refreshing as throwing food across the room, but it works.

Warnings

  • Hitting someone in the eye with a hot dog, especially if it is frozen, even if very funny, is generally not a good idea.
  • 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.
  • If you have a pet (e.g. dog or cat), they may feel inclined to eat the hot dogs, and thus ruin your experiment. Try putting your critters outside (or in another room if they have to stay inside) for this experiment.
  • Though there is no food that is more fun to throw than hot dogs, the math buff will note that greater accuracy will be found the thinner the lines of tape and the thinner the food. Try uncooked spaghetti sticks, for example, for greater accuracy.
  • Remember that this is an experiment, so the idea is not to try to 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.

Things You'll Need

  • Pen and Paper
  • Masking Tape
  • Calculator
  • Long, thin, straight, stiff food items, preferably a pack of frozen hot dogs

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Sources and Citations

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