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 .

Archimedes, the great ancient mathematician from Syracuse, determined that the value of pi was between 3 (3.1408) and 3 (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 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 . 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.)

On the ORC Website and the Web

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.

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.

Adding Up Reciprocals of Perfect Squares (ORC #10155) challenges students in grades 10 to 12 to use the computational power of their computer to convince themselves that the sum of reciprocals of perfect squares, 1/1 + 1/4 + 1/9 + 1/16 + . . . , is equal to (pi)2/6.

Circles and Their Areas (ORC #9712) is a hands-on investigation in which students find the area of a circle or other curved region. The activity will appeal to students in middle school and higher with possibilities for engaging all students in discussions related to trigonometric and limit concepts.

The rich problem Adding up Reciprocals of Perfect Squares (ORC #10155) takes a different look at pi and allows students in grades 10 to 12 to examine the numerical relationship between the square of pi and the sum of the reciprocals of perfect squares.

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