Joel Tettamanti - Greenland

Fifty years of space exploration. Well, American space exploration at least. Originally published by National Geographic back in 2008, a few things have changed:

Several new missions have embarked to our Moon since 2008, including the Lunar Reconnaissance Orbiter, GRAIL (mission complete, RIP) and LADEE, just launched last week.

The Mars Curiosity rover, duh!

Juno, launched in 2011, is only halfway to Jupiter today. That big planet is far away.

The Solar Dynamics Observatory has given us beautiful solar spectra to stare at.

New Horizons is set to be the first spacecraft to fly by Pluto and its moons in 2015. It rode on the fastest launch vehicle ever in order to begin its epic journey.

And Voyager has left the building …

Embigginate this beautiful piece of work here.

as seen here in katherines and paper towns, you are very opinionated on subdivisions. what are your feelings about them and why?

I really hated subdivisions as a teenager because to me they represented sameness and the bloated, intellectually disengaged, wretchedly average 21st century America.

I felt like all these identical houses were architectural crimes committed against the land, and like we would pay for our crimes with these stretched out, sprawling cities that human beings of the future would see as proof of the insanity that accompanied our national prosperity.

Now I live in that very suburbia. So….yeah.

A mathematics course is much more than a thrice-weekly regurgitation of algorithmic tools. It is a distilled presentation of centuries of concentrated effort by fellow humans, men and women motivated both by real-world problems and a sense of beauty and consistency

Charles Doran (via ixxra)

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

0.207879576350761908546955619834978770033877841631769608075135…

Visualizing sine and cosine waves from a circe.

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.”

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