Graphing in Three Dimensions: Method & Formula

Graphing in Three Dimensions: Method & Formula
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  • 0:00 Two-Dimensional Graphs
  • 0:53 A Three-Dimensional World
  • 1:47 The Z-Axis
  • 2:30 An Example
  • 3:41 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

Graphing in three dimensions can be a tough thing to visualize, but once you get that part down it makes geometry much more useful. In this lesson, we learn how to graph using the z-axis as well.

Two-Dimensional Graphs

Chances are you're pretty familiar with graphing something on a coordinate plane. You take the first number as the x-coordinate, which refers to the horizontal distance from the origin, while the second number is the y-coordinate, which refers to the vertical distance from the origin. However, we don't live in a two dimensional world. If you want to only use math to calculate movement across a flat plane, then there, you've got the tools you need.

On the other hand, if you want to calculate location in three dimensions, whether out of personal interest or the fact that your geometry teacher tells you that it will be on the next exam, then this lesson is exactly what you're looking for. First, we'll make sure that you fully conceptualize the need for a three-dimensional plane. From there we'll learn about the new points we have, how to graph the points, and then look at an example of this in action.

A Three-Dimemsional World

But wait, why do we care about three-dimensional motion? Aren't two dimensions enough? Well, like I said earlier, we live in a three dimensional world. In fact, there are even some mathematicians who do work in a world with even more dimensions than that, dealing with an object's location through time as a dimension.

However, don't worry about that. Look up from this lesson. Go ahead, look. Chances are you're in a room. Now imagine that there was a ball floating by itself somewhere in the room. How would you describe its location so that you can describe exactly where it was when people start to assume you've gone crazy for seeing a floating ball. More likely, imagine that you're describing the location of a bunch of different planes over an airport. You'd want to make sure that you know their coordinates as well as their altitude, right? That's why we have to know how to use three-dimensional graphs.

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