So Many Variables

Sometimes you are in a class that is really easy to talk about with other people. For example, a few of my friends are in a class where they study global warming, and the stuff that they learn makes it really easy to talk about their class. The people they talk to find it interesting, and many a good discussion has been sparked by someone asking which class they were in.

Now, I write a lot about the classes I take in the blog. Not only do I find it important to give people a sense for what Quest is really like, but the way your life is structured at Quest is that the class you are in becomes a huge part of your life. So whenever I think about a good topic to tell you guys about, my classes I take come up quite a bit, because they are just so exciting!

Now, if the first paragraph and the title didn’t give it away, I am clearly not in an easy-to-talk-about class. In fact, whenever people ask what course I am in and I tell them, I usually get a “wow”, sometimes a slight gasp, and almost always a look of disbelief or pity. You see, I am in Multivariable Calculus, also known as Calc 3.

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For some reason, this seems to be a big deal for a lot of people. And I think that this comes from how our society views math. There is this kind of attitude present that says that math is esoteric, boring, difficult, and not worthwhile. And while certainly not everyone thinks that,  I think it would be fair to say that math often gets a bad rap.

If you’ve read any of my other blog posts, you know that I have written about classes such as Logic and Metalogic and Object Oriented Programming. Although these courses border on the math, and sometimes do involve quite a bit of math, they are definitely not math courses. I’ve found that, although these kind of courses can seem esoteric, they tend not to suffer from a preconceived negative view of them in the same way that math does.

I’ve tried my best to convey my excitement about these different courses before, and I think I’ve done so with a reasonable degree of success. So, now comes the big trick. If you’ve read this far already, thank you. The actual subject of the blog post will start soon. I’m gonna write about my class, and tell you how cool math really is…

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Multivariable calculus explores calculus in higher dimensional space. For example, if you take a look at the picture above, we have a function in not only the x-y plane, but with a z component as well. If this sounds like nonsense to you, think of it like this: if you are exploring objects in two dimensions, then all you need are two numbers to describe where something is. That is what the 2 in 2D means. If you are in a three dimensional space, you need three numbers to describe where something is.

This means that instead of just talking about lines and areas, we can talk about lines, surfaces, and volumes. And that’s only in three dimensions! Using the tools we learned in this class, we can talk about things like 7 dimensional hyper volumes, 4 dimensional spheres, and find the angle between two points in a hyper cube with an infinite amount of dimensions.

Now, if this kind of stuff doesn’t immediately strike you are particularly cool or noteworthy, just think about it. If we try to picture what something in higher dimensions would look like, our minds usually can’t do it. But using the language of mathematics, we can uncover different characteristics of higher dimensional objects.

If even that didn’t get you excited about this kind of things, just wait for the next section.

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One of the really interesting things that we did in this course was explore polar coordinates. Most people are used to the regular Cartesian plane, that is, describing the position of a point using an x coordinate and a y coordinate. However, in polar coordinates, we describe a point by using an angle, and then a distance from the origin. So, in polar coordinates, the point (1,1) would be expressed as (1,45°). Using this kind of coordinate system, we were able to create very interesting and simply beautiful pieces of art. For example, the flower-like picture above is the function r=sin(t)*(1/3)*cos(πt), in radians as opposed to degrees.

I hope that this post has helped you see that, even if at first a field or area of study may seem uninteresting, once you delve a bit into it and start looking at the concepts, that field can be quite beautiful.

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