what is mathematics

On the direction of the cross product of vectors

One of my math professors always told me:

Understand the concept and not the definition

A lot of times I have fallen into this pitfall where I seem to completely understand how to methodically do something without actually comprehending what it means.

And only after several years after I first encountered the notion of cross products did I actually understand what they really meant. When I did, it was purely ecstatic!

Why on earth is the direction of cross product orthogonal ? Like seriously…

I mean this is one of the burning questions regarding the cross product and yet for some reason, textbooks don’t get to the bottom of this. One way to think about this is :

It is modeling a real life scenario!!

The scenario being :

When you try to twist a screw (clockwise screws being the convention) inside a block in the clockwise direction like so, the nail moves down and vice versa.

i.e When you move from the screw from u to v, then the direction of the cross product denotes the direction the screw will move..

That’s why the direction of the cross product is orthogonal. It’s really that simple!

Another perspective

Now that you get a physical feel for the direction of the cross product, there is another way of looking at the direction too:

Displacement is a vector. Velocity is a vector. Acceleration is a vector. As you might expect, angular displacement, angular velocity, and angular acceleration are all vectors, too.

But which way do they point ?

Let’s take a rolling tire. The velocity vector of every point in the tire is pointed in every other direction.

BUT every point on a rolling tire has to have the same angular velocity – Magnitude and Direction.

How can we possibly assign a direction to the angular velocity ?

Well, the only way to ensure that the direction of the angular velocity is the same for every point is to make the direction of the angular velocity perpendicular to the plane of the tire.

Problem solved!

Neil deGrasse-Tyson gives a great answer to the question math teachers so often get: WHEN WILL I EVER USE THIS?!?

“Whether or not you ever again use the math you learned in school, the act of having learning the math established a wiring in your brain that hadn’t existed before, and it’s the wiring in your brain that makes you the problem solver.”


What is Math?

Mathematics is everywhere and we all learned it at some point, but what is mathematics, really? A search on the internet will yield many different interpretations. According to Google, mathematics is “the abstract science of number, quantity, and space.” Here is a collection of how some of history’s greatest minds described mathematics.

An intellectual game
“Mathematics is a game played according to certain simple rules with meaningless marks on paper.”—David Hilbert

“Pure mathematics is the world’s best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It’s free. It can be played anywhere—Archimedes did it in a bathtub.”—Richard J. Trudeau

“Mathematics is about making up rules and seeing what happens.”—Vi Hart

“Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.”—Plato

“Mathematics is an independent world created out of pure intelligence.”—William Woods Worth

A tool for the sciences
“Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.”—Paul Dirac

“Our physical world doesn’t have just some mathematical properties, it has only mathematical properties.”—Max Tegmark

“Mathematics serves as a handmaiden for the explanation of the quantitative situations in other subjects …”—H. F. Fehr

“In order to understand the universe, you must know the language in which it is written. And that language is mathematics.”—Galileo

A search for pattern, order, and structure
“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”—G. H. Hardy

“Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.”—Joseph Fourier

“Go down deep enough into anything and you will find mathematics.”—Dean Schlicter

Logic and reasoning
“All Mathematics is Symbolic Logic.”—Bertrand Russell

“Pure mathematics is, in its way, the poetry of logical ideas.” –Albert Einstein

“Mathematics is the supreme judge; from its decisions there is no appeal.“—Tobias Dantzig

Which do you believe best describe math?

 and It Is Done! :D The sewing, pattern, framing, photos– every bit! 

I began work on this sampler at the same time as the space one, but it took a lot longer for it to come together. I’m very happy with what it ended up becoming; I think it says all the things I hoped it would.

If you’d like to make your own, I’ve got the pattern up on my Etsy now. :)

BTS Fic: The Devil Himself pt. 1 -

Kim Namjoon X Reader 


Genres: tutor!Namjoon AU, angst, smut (in later chapters)

Summary: You’re failing math class and are forced to see a private tutor by your teacher. “It can’t be that bad,” or so you thought before you met the strikingly attractive tutor from hell with seemingly sweet personality. Little did you know that Mr. Kim’s charming smile was simply a facade for the real devil that resided within. 

Word Count: 3.1k

A/N: IM BACK!!! So I decided to make this into an actual fic with parts and everything so this will have smut in it, but in a later part, so stay tuned if you wanna read that~ I’m super excited to write this because I love love love the idea of strict Namjoon so I hope you all like it too

“I don’t get it!” You groaned in frustration as you stared down at the test Mr. Park handed back to you. The page was covered in red marks where you had gotten each question wrong and at the top was the result, circled with angry, crimson ink to remind you of just how terrible you were at math. You ran a hand through your hair, tugging at the strands as you scowled at the paper before you. This was the fourth math test you’d failed and by now, there was no way you were going to pass this class. No wonder Mr. Park had asked you to stay after class so he could tell you just how much of a dimwit you were at the subject.

“Mr. Park, I don’t know what went wrong, I just can’t understand this stuff.” You whined, turning to face your teacher who stood across from you with an equally frustrated expression plastered to his face. He rubbed at his temples, furrowing his eyebrows as he stared down at your calculations and shrugged his shoulders.

“Y/N…you’ve been consistently failing these tests, and I really don’t know what to tell you except that I suggest you see a trained tutor.” Mr. Park tried to put it lightly, but you knew he was hinting at the fact that you were a complete dimwit when it came to mathematics.

“What? No!” You shoved the failed assessment back at Mr. Park as you cried out, being unable to bear to looking at the jumble of letters and numbers on the page any longer. “No, Mr. Park I just don’t think that’s a good idea.”

“Why not?” Mr. Park gave you a questioning look upon hearing your sudden outburst.

“N-no…I just-” you stuttered. It didn’t matter how badly you needed the help, you didn’t want a tutor. A tutor would be a waste of your time, time that you could spend doing much more important things rather than sitting at a desk and being forced to that pretend you understood the concepts. Besides, what good would a tutor do other than judge your intelligence based on your ability to solve a mathematical equation?

“Look, Y/N,  I’d offer to help you myself, but I’m tied up with other commitments, so I would strongly suggest that you see a tutor. I actually have a friend who works as a private tutor and I could get you some lessons with him.” Mr. Park sighed as he stared back down at your test, “It’s either that, or you fail the class and retake it next semester. Would you like to do that?”

You felt adamant to argue with Mr. Park, to tell him that you didn’t want a tutor and to convince him that you’d try to learn it on your own. However, if you wanted to pass this class, you needed the help. Perhaps if you proved that not even a tutor could improve your nonexistent ability in math, Mr. Park would take pity on you and allow you to pass the class.

“Is there really no other choice, Mr. Park?” You asked desperately.

“I’m afraid not, Y/N.” He gave you a reassuring smile as he patted your back consolingly, “I’ll talk to my friend and let you know when you can start your lessons.” You huffed and nodded before turning around and exiting the classroom with slumped shoulders.

“Well, what did he say?” you snapped your head up to see a familiar figure moving alongside you, completely forgetting that he was waiting outside during your meeting with Mr. Park.

“He said I have to get a tutor…I don’t want a tutor!” You cried, your voice ringing throughout the quiet hallway as you watched Taehyung’s confused expression twist into a mocking smile.

“A tutor? C’mon a tutor can’t be that bad.” Taehyung tried to suppress his laughter, miserably failing as he let out a small giggle at your frustration.You rolled your eyes as he found amusement in your agony and gave him a slight shove to the shoulder as you trudged back home.

“That’s what you think, you don’t even need one. Why can’t you just tutor me?” You asked hopefully turning to Taehyung as he quickly wiped his grin off his face.

“You know…I don’t think that’s a good idea,” you shot him a questioning look before gesturing for him to elaborate, “Well…I have no idea how to tutor and I just think you ought to learn from someone more professional because-”

“Because I’m unteachable, right? Thanks. You’re a real pal, Taehyung.” You rolled your eyes at your friend’s excuse as he shot you an innocent smile before you stormed off. He was right, you were unteachable, which is exactly why a tutor was a waste, but it was no use arguing with Mr. Park. You continued home, kicking the pavement with your shoes as you dragged them along, dreading what would be in store for you.

Keep reading

Physicists may have fallen prey to a false dichotomy between mathematics and physics. It’s common for theoretical physicists to speak of mathematics providing a quantitative language for describing physical reality… But maybe… math is more than just a description of reality. Maybe math is reality.
—  Brian Greene, The Hidden Reality
Stop aliens are evil tropessss

I firmly believe that any species that looks upwards and sees the stars and is filled with wonder and curiosity can’t all be evil.

You assume bug and lizard aliens must be out to conquer other planets.

But look at our piece of shit imperialist species, our asses have barely scraped space.

Our corporate assholes are so tightly clenched that we’ll never waddle out too far.

I swear, the urge to dominate and conquer will never get us off this fucking planet.

Our mega businesses don’t care about seeing beyond their financial gains and exploitation of their fellow beings. They’re JUST thinking about being rich. They can’t see BEYOND the fact that money is a concept and a symbol, an element the same as any other, and look and see a whole universe out there.

They don’t see their own species as their people. They see them as disposable.

And I don’t think a species that only wants to dominate can go to space, I really don’t.

Think about the resources it takes to get to space.

You NEED social cohesion for that.

You COULD enslave or dominate your own people for that goal, I guess, but I again return to the point that it’s difficult for people to look up when they’re too busy looking down on their fellows.

Delusions of grandeur aside, even an asshole would have a hard time NOT being excited to meet another species.

We keep assuming aliens will be hostile but stop it. That’s geocentric.

Any species that’s out there might not be hostile.

No matter what they look like, if they’ve acquired space travel, then who knows? Maybe. JUST MAYBE. They’re really interested in SPACE. They’re SCIENTISTS.

They might be CURIOUS first and foremost about us.

I don’t get why Stephen Hawking, smartest man in the world or whatever, says aliens will automatically be evil and imperialist and want to take over our resources because it’s only “logical.”

Stephen I may not be an expert or anything close, and I may not be as smart as you or anything close.

But how many aliens have you met? You don’t KNOW they have a culture like ours.

Full of the absolute assholish desire to claim every patch of rock they find.

Space is fucking huge. Even if they were looking for resources, maybe they would see we need ours and they would just go looking for another uninhabited planet.

The point is.

I’m tired of aliens as imperialist enemy themes.

I get that it’s fun to make anything other than humans out to be the “ugly enemy” but this is some bullshit right here.

You just naturally ASSUME that capitalism exists everywhere. That every species must live under a rigid hierarchy of the rich and powerful over the poor. That every species follows our system of domination.

Get off with it.

r u ever doing a math problem and u are hard the fuck at work doing all these fucking math backflips and you have got this and you end up with a fucking monster of an answer that looks like it belongs in a movie on the supergenius theoretical physicist’s board like aw man look at this tough as nails problem with the long answer look how well i managed dealing with all these numbers

then u look in the back of the book and the answer was like fucking 3 or something