Graph Of Sine/cosine From Unit Circle. [via]

Hand drawn hypercube animation. I’ve been facinated by the fourth dimension for really quite long, this gif goes between a hypercube in 0,1,2,3,4 dimensions and back again.  

1. Take a circle and draw some points on the boundary. For every point you draw, you must also draw its antipode (point on the opposite side of the circle).

2. Draw some points in the interior wherever you want.  3. Label the points either +1, -1, +2, or -2 as you wish. The only stipulation is that antipodes must have opposite sign.

4. Draw triangles however you want without crossing lines.

Tucker’s Lemma says that you will ALWAYS end up with at least one line that has endpoints of either +1 and -1 or +2 and -2. Try it! More info and proof here.

“The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such.“

“There is surely no more reliable way to kill enthusiasm and interest in a subject than to make it a mandatory part of the school curriculum.”

“No mathematician in the world would bother making these senseless distinctions: 2 ½ is a “mixed number,” while 5/2 is an “improper fraction.” They’re equal for crying out loud.”

“All metaphor aside, geometry class is by far the most mentally and emotionally destructive component of the entire K-12 mathematics curriculum. Other math courses may hide the beautiful bird, or put it in a cage, but in geometry class it is openly and cruelly tortured. (Apparently I am incapable of putting all metaphor aside.)“

“A proof, that is, a mathematical argument, is a work of fiction, a poem. Its goal is to satisfy. A beautiful proof should explain, and it should explain clearly, deeply, and elegantly. A well-written, well-crafted argument should feel like a splash of cool water, and be a beacon of light— it should refresh the spirit and illuminate the mind. And it should be charming.“

“A proof should be an epiphany from the Gods, not a coded message from the Pentagon.“

“Students learn that mathematics is not something you do, but something that is done to you.“

This guy gets it

It’s a big, nasty differential equation. But don’t worry, someone smarter than you has solved it.

Physics professor (via mathprofessorquotes)

Don’t drink and derive.

AP Calculus teacher (via mathprofessorquotes)

“You ask me if an ordinary person by studying hard would get to be able to imagine these things like i imagine. Of Course!..I was an ordinary person who studied hard. There is no miracle people. It just happened they got interested in these things and they learned all these stuff. They’re just people!!There is no talent special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields that comes without practice and reading and learning and mathematics. So if you say you take an ordinary person whose willing to devote a great deal of time on studying and thinking and mathematics and so on. Then he’s become a scientist!” -Richard Feynman

A list of math books

…to read in lieu of an actual math class. So far I have

- Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter

- I am Strange Loop by Douglas Hofstadter

- Chaos by James Gleick

- Category Theory by Steve Awodey

What do you call a snake that’s exactly 3.14 feet long? 

Calculus was created to predict the rotation of the planets. I think you can bother to simplify your fractions.

Calculus professor (via mathprofessorquotes)