Terminal Information
Pi
Pi is great! It can even be used to describe the dimension of actual Pie (the one everybody actually likes). It's uses are many, and when you have a better understanding of what it is, you can better appreciate it and it's uses in the world around us.
But What is Pi?
When asked, most people know that Pi is a number that is approximately 3.14, and that on or around March 14th teachers bring pie to school to try and make math class more exciting. But have you ever stopped to ask yourself why? Why is it approximately 3.14? Why is it important? What does it mean? You may have an idea of the "value" of Pi, but what is it?
Before we begin...
Pi has a lot to do with the geometry of circles, so just to be sure we're all on the same page, it's important to know what these three of the basic items are: Circumference, Diameter, and Radius. Don't worry though, these are actually very simple.
- Circumference: The length of the outside or perimeter of a circle. This is usually written as 'C'.
- Diameter: The length from one side to the other of a circle, though the center point. This usually written as d.
- Radius: The length from the center of a circle to its side. The radius is usually written as 'r'.
What Pi is
Pi is the ratio of length of a circle's circumference compared to it's diameter. This may sound complicated, but the concept is actually quite simple. It just means if you were to cut a circle's perimeter and lay it flat next to the diameter, it would be 3.14 times longer than its diameter!
Great, but now what?
Now that you know this is a ratio that works for all circles you can use it to figure out all kinds of problems! But lets start with something a little simpler to better understand this concept, and that of ratios in general.
Two ropes
Imagine you have two ropes. You know one is twice as long as the other. You know the short one is 5ft long, so what is the length of the longer rope?
The solution to this problem is pretty simple. Since the long rope is two times the length of the short rope, and we know the length of the short rope, just multiply two times the length of the short rope to get the length of the long rope. Do this and you get that the longer rope is 10ft long.
We can apply the idea of the ropes to any circle to figure out it's circumference. The diameter is the short rope, and the circumference is the long rope. Instead of being two times longer, it's a little over three times longer (3.14 to be more precise). So now just multiply 3.14 times the length of the diameter and you will have the length of the circumference!
Neat Trick is an Equation...
Our little comparison to ropes is a nice way to get a better understanding of what Pi is, but it can be simply written as Pi times the diameter of a circle equals its circumference. That's right, it's actually an equation.
πd = C
Typically, this equation is written in terms of the radius. The radius is half the length of the diameter, so we can re-write the equation as Pi times two times the radius equals the circumference.
π2r = C
One last modification, whenever you have a mix of an actual number and symbols or variables multiplied together, it's convention to put the number first, followed by the symbols and variables. This number actually even gets a special name. It is called the coefficient. When we fix this last bit we get something that may look familiar to you:
2πr = C
In the shell of a nut...
In short, Pi is just a comparison between the length of the diameter and the circumference of a circle. With this understanding and the previous equation, you can now find the circumference of any circle with just the length of it's diameter or radius and vice versa!
This is just a touch of the power of Pi though. While using Pi to find a circle's circumference is a simple way to better understand what it is and where it comes from, it's uses and abilities stretch far beyond into various fields of study. It is also used for simple things like finding the area of a circle, to complex things like describing the shape of an involute gear, and to various things such as understanding and modeling alternating current.