What Is Pi? - Number & Usage

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  • 0:00 Definition of Pi
  • 0:43 Approximations for Pi
  • 2:03 Uses of Pi
  • 2:55 An Example Using Pi
  • 4:21 Lesson Summary
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Lesson Transcript
Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

Learn where the number pi comes from, how mathematicians estimate it, and some of the many uses of the number in the worlds of science and mathematics. In the end, you can test your knowledge with a quiz.

Definition of Pi

Imagine drawing a pencil line across a circle so that it cuts the circle in half. Now imagine cutting a string the length of that line across the circle, or its diameter. If you took that string and tried to wrap it around the outer edge of the circle, or its circumference, you would find the string went a little less than a third of the way around.

No matter how big or little your circle is, the ratio, or fraction, of the circle's circumference to its diameter is a little more than three. The exact ratio, however, is irrational. It can't be written exactly as a fraction or decimal number, and we call this ratio pi (𝝅) (𝛑).

Approximations For Pi

You may have heard that pi is about 3.14, 22/7, or 333/106. While those numbers are close to the true value of pi, they are not exact. The true value of pi is an unending decimal number. This picture shows you the first 1000 digits of pi.

Even the early Greeks were fascinated with trying to get correct digits for pi. Archimedes came up with a clever approach. He showed that if you draw two polygons, or figures with at least three straight sides, one inside the circle and one outside it, then pi would be somewhere in between. He imagined creating polygons with more and more sides until you got an approximation for pi that was precise enough.

Since then, scientists and mathematicians have come up with a variety of ways that make it possible to calculate pi to trillions of decimal places. One approach can be visualized by a continued fraction - a fraction that has nested layers that go on forever.

In modern days, computers are used to find more digits of pi. Practically speaking, there is no need for us to know pi to trillions of digits. But, mathematicians find it fun to break records by finding more digits.

Uses of Pi

Pi is not just theoretically interesting, but also useful to mathematicians. The simplest place pi is used is in finding the circumference or area of a circle. These formulas are probably familiar from math class:

The first formula tells you that the circumference, or the distance around, a circle can be found by multiplying the circle's diameter, which is 2 times the radius, by pi. The second formula shows you how to find the area of a circle by multiplying pi by the radius squared.

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