The Story of Pi


Video Segments

1.
What is the number pi?
2.
Some uses of pi
3.
Early history of pi
4.
A discovery of Archimedes
5.
Computation of pi
6.
Further uses of pi
7.
Recap

Contents

The program opens with a reporter interviewing young people, asking "What can you tell me about the number pi?" Each person gives a different answer, some of which are only partially correct.

The program defines pi as the ratio of circumference to diameter of a circle, and shows how pi appears in a variety of formulas, many of which have nothing to do with circles. After discussing the early history of pi, the program invokes similarity to explain why the ratio of circumference to diameter is the same for all circles, regardless of size. This ratio, a fundamental constant of nature, is denoted by the Greek letter pi, so that 2 pi r represents the circumference of a circle of radius r.

Two animated sequences show that a circular disk of radius r can be dissected to form a rectangle of base pi r and altitude r, so the area of the disk is pi r squared, a result known to Archimedes. Animation shows the method used by Archimedes to estimate pi by comparing the circumference of a circle with the perimeters of inscribed and circumscribed polygons.

The next segment describes different rational estimates for pi obtained by various cultures, and points out that pi is irrational. After demonstrating the appearance of pi in probability problems, the program returns briefly to the reporter, who interviews the students again, asking, "Now what can you tell me about pi?" This time, each student gives a different correct statement about pi. The concluding segment explains that major achievements in estimating pi represent landmarks of important advances in the history of mathematics.


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