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Flat like a pancake: let's talk about curves

Quotes of the day

"Out of nothing, I have created a strange new universe."
- Janos Bolyai

"It's not what you look at that matters. It's what you see."
-Henry David Thoreau

Flat like a pancake: let's talk about curves

Oooooohh do we get to talk about VS models or Kim K's (recently hidden) butt today? Or better yet, can we talk about Kylie Jenner's recent photos with Tyga? Ha! No... but we do get to talk about something even more deceptive (and probably way cheaper) than her half empty lip kits all of the YouTube makeup gurus have been ranting about. Today we are talking about.... MATH!!!

* crowd booing and throwing tomatoes*

I'm sorry... have I deceived you? Well guess what? So have all your math teachers! About what? you may ask... well... lots of things... but today, we will be taking about parallel lines.

Apparently... they aren't a thing... ╮(O_o)╭

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When we were first told this in TOK, I was so confused. I mean, you're telling me that those things I've been (painfully) graphing since junior high aren't real? Well... it's actually a lot more complicated than that. They do exist... but they don't

If we define parallel lines as two lines that never intersect, this is possible in a completely flat surface, like, say, a sheet of paper. If you drew two perfectly straight lines on a flat sheet of paper, they would never touch, even if the paper went on forever and ever.

But imagine a spherical surface, like say a beach ball, or planet earth. Pick any two points on the beach ball, call them point A and point B. Now imagine drawing a "straight" line passing through them(which will be curved because the surface of the baseball is curved, and thus called a "great circle"). Now, extend that straight line so that it surrounds the whole beach ball.

Now, draw another line, parallel to the line that passes through points AB. In order for it to be parallel, there must be a perpendicular line that creates a 90-degree angle when it intersects both lines. Make the parallel line surround the whole beach ball, and you will find that eventually, the lines that were once parallel, will, in fact, touch.

Crazy right? Especially because it's something so simple , that we see every day in things such as models of the earth, but we don't really think about them.

Image Source 

Also, because in a sphere two parallel lines can intersect, it is also possible to have a triangle with more than 180 degrees.



There's also another type of geometry called hyperbolic which is exactly the opposite of spherical geometry, and in which triangles have less than 180 degrees and parallel lines get farther away from each other, but I think we've had enough math for today.

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So.... why does any of this matter?

It matters because it teaches us that, in the real world, not everything is perfect. The world is full of curves and bends, and answers are never really cookie cutter, one size fits all. This means that we can't just stick to one single idea to fix the deepest problems in society. We must instead realize that as crazy and weird as certain ideas may seem, and as uncomfortable as they may make us, they could be right. It is up to us to open our minds and try to understand where others are coming from. After all, not even the most perfect pancakes are really flat.

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  1. Excellent work here! Very funny tone, and very good job explaining a potentially obscure topic. Thanks for geeking out on math for a while.

    Good work linking this to a broader understanding of the world, too! I might have gone further to critique the ideology of the Euclidean hegemony. Whenever I see this sort of thing, I think "Who benefits from my continued misinformation?" But that's just me.


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