In mathematics, physics, and art, Moiré patterns are geometrical designs that results when a set of straight or curved lines is superposed onto another set.

(Source: trigonometry-is-my-bitch, via trigonometry-is-my-bitch)

Some people argue that the golden ratio is a divine number. It appears to pop up everywhere in nature, so it must be God’s architectural fingerprint, right? I’m curious what these people would say about the following equation, relating the golden ratio to the number of the Beast:

$\sin(666^\circ)=-\dfrac{\phi}{2}$

Finite Simple Group (of Order Two), by the Klein Four.

The path of love is never smooth
But mine’s continuous for you
You’re the upper bound in the chains of my heart
You’re my Axiom of Choice, you know it’s true

But lately our relation’s not so well-defined
And I just can’t function without you
I’ll prove my proposition and I’m sure you’ll find
We’re a finite simple group of order two

I’m losing my identity
I’m getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we’re one-to-one you’ll see what I’m about
'Cause we're a finite simple group of order two

Our equivalence was stable
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
To have a finite limit, in some sense

I’m living in the kernel of a rank-one map
From my domain, its image looks so blue
'Cause all I see are zeroes, it's a cruel trap
But we’re a finite simple group of order two

I’m not the smoothest operator in my class
But we’re a mirror pair, me and you
So let’s apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let’s be a finite simple group of order two

I’ve proved my proposition now, as you can see
So let’s both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q.E.D.

Exactly 20 years ago, Andrew Wiles had the final insight to solve the enigma that had been Fermat’s Last Theorem. He presented his first attempt in 1993 after seven years of secret work, but an error was found. One year later, on September 19, 1994, in what he would call “the most important moment of his working life,” Wiles stumbled upon a revelation, “so indescribably beautiful… so simple and so elegant,” that allowed him to correct his proof and ultimately break the back of Fermat’s conundrum.

Exactly the same day is my birthday! 😃

A graph representation of the Erdös number network.

A hyperbola of one sheet can be traced by a straight line, making it a ruled surface. You can make a beautiful real-life model by connecting two circles with some elastic strings, and rotating one of the circles; here’s a virtual Wolfram Demonstration.

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

(Source: curiosamathematica)

Launching Today: Mathematica Online!
The Book Bucket Challenge

Repeated barycentric subdivision results in a gorgeous fractal-ish pattern.

(Source: mathani)

A fully operational Turing machine built in LEGO Mindstorms, by Jeroen van den Bos and Davy Landman at Centrum Wiskunde & Informatica (Centrum Mathematics & Computer Science, CWI) in Amsterdam. They built it for an exposition “Turing’s Legacy” in honor of Alan Turing’s 100th birthday.

A collection of beautiful mathematics: attractive pictures and fun results