Visualizing Sine And Cosine Waves From A Circe.

Minimalist Posters of Great Mathematicians.

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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Having been lucky enough to travel on numerous roads like this last summer, I'm pretty sure I remember being genuinely and irrationally afraid of this exact thing happening. I have no clue why.

So the universe is not quite as you thought it was. You’d better rearrange your beliefs, then. Because you certainly can’t rearrange the universe.

Isaac Asimov (via wordsnquotes)

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Inside a Neutron Star

Credit: Karl Tate, via SPACE.com

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.

Iceland’s sublime silence

A Canadian photographer turns her fascination with Iceland into a series celebrating the country’s raw and wondrous landscape

Convair F2Y Sea Dart seaplane at rest on the water