Somebody Should Have Told Me This Two Years Ago When I Could Have Saved Myself.

I made a gif animation of the Binomial Cube. :D

http://en.wikipedia.org/wiki/Montessori_sensorial_materials

http://hyrodium.tumblr.com/post/85901458594/do-you-know-the-maria-montessori-method-of-education

Visual Representation of a Fourier transform whoaaaa hyo

my teacher could give me a year to do an assignment and ill still end up doing it the night before

On the back roads of Glacier National Park, Montana With Andrea

Iceland

Eleven Interactive Fractals in 2D & 3D

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

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.

Minimalist Posters of Great Mathematicians.