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Facts About Pi

Pi is the ratio of the circumference of any circle to its diameter. In the Greek alphabet, the sixteenth letter is pi and is represented by the symbol pi.

Archimedes, the great ancient mathematician from Syracuse, determined that the value of pi was between 31/7 (3.1408) and 310/71 (3.1429). As you can see, he was very close. By today's calculations, the approximate value of pi to four decimal places is 3.1416.

For the new world record for computer calculation of pi, see 5 Trillion Digits of Pi—A New World Record. And see Visualizing Pi for some interesting observations about the arrangement of digits in expansions of pi.

Pi is a never-ending number. To get an idea of what a never-ending number looks like, see One Million Digits of Pi.

Pi is an irrational number, meaning it cannot be written as a ratio of two rational numbers. The familiar ratio of 22/7 is only a fractional approximation for pi.

Pi is a transcendental number, meaning that it is not the root of any algebraic equation with rational coefficients.

For more information about the mathematics related to pi, see a mathematics history book such as Mathematicians Are People, Too by Luetta Reimer and Wilbert Reimer, go online to Archimedes for information, or visit the Exploratorium's A Brief History of pi. Also, NOVA has some very good information about the history and development of pi. (Please be aware that the applet on the NOVA site incorrectly states the value of pi as being a terminating decimal—which we, of course, know it is not.)


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On the ORC Website and the Web

With this ORC best practice lesson Exploring c/d = pi (ORC # 5811), students in grades 5 and 6 measure circular objects to investigate the relationship between the circumference of any size circle and its diameter.

The best practice lesson Square Circles (ORC #7864) has two creative twists. Students in grades 6 to 8 measure squares to find a simpler constant ratio (4) of perimeter to length of a side and then go on to study the circle. In addition, students measure with a variety of units to see that the ratio of measurements remains constant.

With the lesson Pi Line (ORC #7834), students in grades 8 to 10 measure circumference and diameter, plot graphs, and relate the slope of the line to pi.

The problem in Circles and Their Areas (ORC #9712) is a hands-on investigation that can lead to a discussion of the important mathematical idea of limit.

Make pi visible for students in grades 7 to 12 with Computing Pi (ORC #13765), an online learning tool that allows the user to approximate pi using inscribed and circumscribed polygons.

Finally, Your Piece of the Pi is a Thinkquest site featuring everything pi including history, uses, and pi fun like "An Ode to pi," the Shakespearean sonnet.