Skip to main content

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)╭



Image source 
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.


Mind.


Blown.


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.

Image source 


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.


Image source 

Comments

  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.

    ReplyDelete

Post a Comment

Popular posts from this blog

When Plans Go Wrong

Quote of the day:
"Sometimes on our way to our dreams, we get lost and find a better one." - Unknown


When Plans Go WrongOh! The wonders of Junior year! Kids all across the nation from the class of 2018 are stressing over SAT scores, ACTs, NMSQTs, IB classes and harder APs. The homework piles in and GPA is now more decisive than it had ever been. The words of the adults pile in on the subconscious mind of stressed out teenagers. They play over and over in the back of their heads, like this: 
"You're not an underclassman anymore, huh?"
"Better get those SAT scores in before Senior year!"
"So... How many IB/AP classes do you plan to have?"
"Keep that GPA in check!"
"Where are you planning to go to college?"
"Graduation is so close!"
And finally, the most stressful question for a Junior that has too many interests and no idea what to do with them:
"What do you plan to major in?"
While this is something that happens …

Who are we? God, Science, and Humanity

Quotes of the day:

"The human brain is a most unusual instrument of elegant as yet unknown capacity" - Stuart Seaton

"The greatness of humanity is not in being human, but in being humane" - Gandhi

"A human being is a single being, unique and unrepeatable" - Eileen Caddy


God, Science, and Humanity 
This blog is a response to the following knowledge question:

“Knowledge gives us a sense of who we are.” To what extent is this true in the human sciences and one other area of knowledge?


For the past century,  scientists had been using animals for medical trials, surgical procedure practices, and cosmetic testing. This brought about many new benefits for the human race, including insulin treatments for diabetes patients, and heart valve transplants from pigs to humans. However, with the new scientific era came new ethical, social, and scientific questions for humanity. Do animals have feelings? As human beings, what are our responsibilities to other living creatures?…