Video:What Is Pi?with Bassem Saad
In math, pi may be more familiar to you as 3.14, but this is just an estimation. Watch this About.com video to see how pi works as a variable and how to use the pi symbol to solve equations exactly.See Transcript
Transcript:What Is Pi?
Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate a U.C. Davis, and I'm here today for About.com to answer the question: “What is Pi?”
Pi Cannot Be Written as Specific Number
Pi is not the number 3.14. Pi is a transcendental number, which basically means it cannot be represented as a decimal or as a fraction. So 3.14 is actually just an approximation of the exact number pi. If you ever want to write down the exact number, all you can use is the symbol π. What this means is if you ever want to add, subtract, or multiply a number to pi and get the exact answer, you have to treat pi like it's a variable. Let me show you what I mean.
Pi in Equations
Say we had two times pi. Well, you can just write that as two pi, where two is the coefficient. Or say we want to add three plus pi. If we want to express this exactly, there's only really one simplified way we can write this, and that's just as three plus pi. Now, say we wanted an approximation of two pi. We can use this approximation over here and multiply two – that is, 6.28. Or if we want an approximation of three plus pi, we can again use 3.14 and get 6.14.
Pi is Common in Geometry and Trigonometry
The fact that pi, which is really just a number, has a name and a symbol to represent it, should give you a clue to its importance. You'll probably first encounter pi in geometry when you calculate the area or perimeter of a circle. Remember, the radius of a circle is a line that extends from the center to the edge. Then the area of the circle is just given by pi r squared. And the perimeter is just given by two pi r.
Pi is also an important number when measuring angles in radians. For instance, this angle (for the sharp angle over here) is pi over two. You can imagine if you went all the way around you would be measuring two pi.
In trigonometry, a periodic function is a function that repeats after a certain period. Some important periodic functions are sine of theta and cosine of theta; both these functions have a period of two pi. Tangent of theta is also another periodic function, but this time it has a period of pi.
And those were some of the basics of pi. Thanks for watching, and to learn more, visit us on the web at About.com.