Notneimanmarcus - Seriously Though. It Isn't.

Somebody should have told me this two years ago when I could have saved myself.

Tips for Having an Enjoyable 10th Grade Year

Don’t take all PreAP classes.  

I know you think you can.  

BUT YOU CAN’T

DONT FUCKING DO IT

I SWEAR

Visual Representation of a Fourier transform whoaaaa hyo

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

(via brittbutterfly21)

Bedruthan Steps, Cornwall | England (by Ian Percival)

Joel Tettamanti - Greenland

The relationship between sine and cosine.

If you like this check out “How a Fourier series approximates a square wave.”

Just something to think about:

"Look again at that dot. That’s here. That’s home. That’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there-on a mote of dust suspended in a sunbeam." - Carl Sagan

Lagrange's theorem

Theorem: The size of a subgroup of finite group is divisible by the group’s size. That is, if H is a subgroup of G, |H| is a divisor of |G|.

Proof: Let’s start by saying we have a group G and a subgroup H.

This proof will count cosets. Specifically, I’ll use left cosets, but right cosets work the same way. Also, this proof will rely on a few properties of the integers.

I’ll prove this through lemmas, which are theorems used to prove other theorems. The distinction between a lemma and a theorem is only based on how we use them, and so historical reasons might leave some theorems as “lemmas.”

Keep reading

The traditional Le Mans-start of the 12 Hours of Sebring, 1964.