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What are 1D, 2D, and 3D Coordinates?

Learn what 1D, 2D, and 3D (one, two, and three-dimensionality) means in math and how coordinate systems can describe locations in 1D, 2D, and 3D.

By
Jason Marshall, PhD
Episode #29

http://www.shutterstock.com/pic-132560180/stock-vector-glossy-compass-vector-illustration.html?src=2FJhcC2hU1Tc2KFVCJ3aEQ-1-13There’s been a lot of talk about 2D versus 3D in the television and movie industries lately. But what exactly does one, two, and three-dimensionality really mean—both in the everyday world and in math? Well, prepare to have your curiosity quenched because that’s exactly what we’re talking about today.

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What are Coordinates?

Before we begin talking about what dimensions mean in math, let’s briefly think about a simple but very important question: How do you know where you are? For example, say you’re meeting friends for coffee—what directions do you need to tell them so they can find you?

There are a number of ways to describe your location, but one way is to tell your friend how many blocks from their house they need to walk in the north-south direction (let’s say 5 blocks north), and how many blocks they need to walk in the east-west direction (let’s say 3 blocks east). Additionally, perhaps the building you’re in has two competing coffee shops—one on the first floor and one on the third. If you’re in the third floor coffee shop, you need to give your friend that piece of information too. Believe it or not, by giving these three locations—5 blocks north, 3 blocks east, and the third floor—you’ve just employed a bit of mathematics to define what’s called a coordinate system, and to give your location—your coordinates—in it. Think of it as yet another example that math is quietly ever-present in the everyday world.

What Does “One-Dimensional” Mean?

What does the term “one-dimensional” mean? Well, we know what the “one” part means, but what about the word “dimensional?” The number of dimensions describes the minimum number of directions you can move in and still get to everywhere you could possibly go. For example, something that is one-dimensional only exists along a single direction—in math, this one-dimensional object exists along a line. To see what I mean, imagine again the number line that we first talked about in the article on negative numbers and integers—negative numbers span out to your left, zero is in the middle, and positive numbers go on forever to your right. Notice that this line runs in only one direction—or one dimension—since you only need to move in the direction from your left-to-right (or vise versa) along the line to get to every single possible point on the line. Of course, you can move in the positive or negative “direction” along the line; but don’t be confused: these are not distinct dimensions since both movements occur along the same line. On another note, if you’ve ever wondered where the phrase “he’s so one-dimensional” comes from, the origin and meaning should now be clear—a one-dimensional person doesn’t have a lot of depth (in other words: multiple dimensions) to their character.