Theres 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 meanboth in the everyday world and in math? Well, prepare to have your curiosity quenched because thats exactly what were talking about today.
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What are Coordinates?
Before we begin talking about what dimensions mean in math, lets briefly think about a simple but very important question: How do you know where you are? For example, say youre meeting friends for coffeewhat 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 , and how many blocks they need to walk in the east|west direction . Additionally, perhaps the building youre in has two competing coffee shopsone on the first floor and one on the third. If youre 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 locations5 blocks north, 3 blocks east, and the third flooryouve just employed a bit of mathematics to define whats called a coordinate system, and to give your locationyour coordinatesin 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 directionin 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 integersnegative 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 directionor one dimensionsince you only need to move in the direction from your left|to|right 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 dont be confused: these are not distinct dimensions since both movements occur along the same line. On another note, if youve ever wondered where the phrase hes so one|dimensional comes from, the origin and meaning should now be cleara one|dimensional person doesnt have a lot of depth to their character.
What Does Two|Dimensional Mean?
So thats what life in one dimension looks like. How about two? Well, if one|dimensional means you only have to move in one direction to get everywhere you could possibly go, a two|dimensional world must be one where you have to move in a minimum of two directions to get everywhere. Unless you live in a big city with lots of multi|story buildings, you practically live in 2D every day . As in our example about telling your friend how to meet you for coffee, in order to get anywhere in a city with a grid street pattern, you need to move in two directions . Mathematically, a two|dimensional object exists in a planewhich you can think of as an infinite sheet of paper. To get to any location on that plane from anywhere else, you need to know two numbers: the distance in the left|right direction from some starting locationcalled the originand the distance in the forward|backward direction from that same origin.
What Does Three|Dimensional Mean?
By now the trend should be clear and it probably wont come as a surprise that to get to every possible place in three|dimensional space, you have to move around in three different directions. As we saw in the coffee shop example, the world we live in is 3Dthats why we needed three different directions to describe the location. Another way that has become very popular in the last decade to describe our location in 3D space on Earth is to use the Global Positioning System . GPS uses a number of satellites to tell you your latitude, longitude, and altitude with very high precision. once again, GPS uses three numbers for the three locations needed to give a position in 3D space. Of course, the fact that we live in 3D space is exactly why 3D TV and 3D movies have become so trendy since, in principle, these technologies have the potential to increase the realism of our experiences with these forms of entertainment.
Wrap Up
Okay, thats all the math we have time for today. Of course, there are many more interesting things to talk about when it comes to coordinate systems and dimensionality in mathlike what it means to have four or more dimensions . Well come back to this in the future; but next week, in honor of the Math Dude podcast turning the big three|oh , were going to premier the first of a special series of secret agent math articlesthis first one will be on encryption. So be sure to check it out!
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Until next time, this is Jason Marshall with The Math Dudes Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
