What is pi?
Briefly, pi is the circle constant. If you find a random circle somewhere around, take the circumference of the circle (the distance around) and divide it by the diameter of the circle (distance across), you always get the same number. The magic of pi is that it doesn't matter how big the circle is.Another magical quality of pi is that it isn't a whole or counting number, like the numbers you learn about in kindergarten. It isn't a fraction, like the things you learn about in 3rd grade. It isn't even an algebraic number like the solution to x^2=2. It is something called a transcendental number. The name makes it sound like transcendental numbers are hard to find, but it turns out that if you are looking at a number line, most of the space is taken up by transcendental numbers. Only a few of them have names, though, and one of the named ones is pi.
History
Back in the day ancient societies used pi for various tasks, even if they didn't know what it was. (I know about the ancient Egyptians and the ancient Greeks, but I assume most ancient cultures discovered the basics of pi) . They may have used a fraction, 22/7, which is accurate to 2 decimal places. Frankly, that's all most of us ever need.There are two people I associate most strongly with the history of pi. The first was Archimedes, who estimated pi by "trapping" a circle between two polygons. You know that the circumference of the circle is bigger than the perimeter of the inside polygon, but smaller than the perimeter of the outside polygon. The more sides you have, the better the estimate! Archimedes used a 96-side polygon for his calculations, which is really something in the days before calculators (even the days before using the Hindu-Arabic number system...) (Of course, another significance of his calculations was the idea of the limit...but we'll save that for Calculus Day.)
Archimedes is also famous for shouting "Eureka!" and running down the street in his birthday suit after making a discovery while taking a bath. He invented several war weapons for his kingdom of Syracuse. When the Romans did invade Syracuse, they had instructions to take Archimedes alive. The story goes, however, that a soldier came upon Archimedes making math drawings in the sand (no white boards) and messed up his pictures. When Archimedes complained, the soldier ran him through.
The other person I associate with pi is the Swiss mathematician Euler. Euler (say it, "oiler") popularized the use of the Greek letter "pi" to mean the circle constant. Euler popularized many other notations as well (e, i, f(x), trigonometric functions, etc.). He thousands of papers and over 900 books, despite the fact that he was blind in the later part of his life.
There are many useful websites for the history of pi, including
http://www.techhive.com/article/191389/a-brief-history-of-pi.html
http://www.piday.org/learn-about-pi/
Activities
Here are some things I like to do on pi day:- Buffon's needle: estimate pi using needles and parallel lines. (https://vimeo.com/38580856, http://www.numberphile.com/pi/pi_matches.html, http://www.mathsisfun.com/activity/buffons-needle.html) Note: some people use frozen corn dogs and tape on the floor.
- Estimate pi directly. measure the circumference of a round object, Then measure the diameter. Find the ratio. How close did you get? (http://illuminations.nctm.org/lesson.aspx?id=1849 there is a PDF worksheet for recording your answers.)
- make pi bracelets: You can use different numbers of beads with spacers (3 black beads, 1 white, 1 black, 1 white, 4 black, 1 white, and so on) or choose a color for each number (3=red, 1=blue, 4=tan, and so on) (http://cheerstoschool.blogspot.com/2012/03/pi-day-and-teachers-notebook.html)
- Learn to draw circles (surprisingly difficult!) (https://www.youtube.com/watch?v=QncgmzH6yQU)
- search for numbers within pi (http://www.facade.com/legacy/amiinpi/)
- memorize pi using fun mnemonics (http://en.wikipedia.org/wiki/Piphilology)
- recite pi
- and of course, eat pie (and other round foods).
Videos
Some of my favorites:- Danica McKellar (includes a song): https://www.youtube.com/watch?v=8-cazxAL_tU
- Vi Hart: Anti pi rant, (I am going to memorize all the digits of 1/3!) https://www.youtube.com/watch?v=5iUh_CSjaSw
- More Vi Hart: pi is still wrong: https://www.youtube.com/watch?v=jG7vhMMXagQ
- (There are many other Vi Hart videos you want to see. Trust me on this)
- Estimating pi with pies: https://www.youtube.com/watch?v=ZNiRzZ66YN0
- (There are lots of other Numberphile videos that are fun, but some of them are very serious mathematics. Try the one on math in the Simpsons https://www.youtube.com/watch?v=K305Vu7hFg0).
Music
What pi sounds like: https://www.youtube.com/watch?v=wK7tq7L0N8EPi, pi, mathematical pi...https://www.youtube.com/watch?v=_BwKZEp2K_0
The Pi rap (Lose yourself in the digits): http://teachpi.org/music/rap/
Vi Hart's singing pi gram: https://www.youtube.com/watch?v=4C9PALaDh2U
Vi Hart and John Sims: https://www.youtube.com/watch?v=NsKH5h7j2_o
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