HOW ACCURATE IS THIS?

I had to share this with you guys because I know most of you can relate (even all you high schoolers!).

I was absolutely Ariel and Tiana in college lmao.

I’m Aurora and Rapunzel all the way lol

Ohhh, I remember my Tiana days.

Can I change the drugs (in Merida’s) to food…..cuz I did that a lot too…

(via ululato)

Pick any natural number (whole numbers ≥ 1)

1. If the number is even, divide by two (n/2).
2. If the number is odd, multiply by three and add one (3n+1).
3. Repeat until you reach the number one

This is called the Collatz Conjecture, an unsolved problem in mathematics, that states that for any natural number you start off with, you will eventually get to one by following this process.

It’s also a great way to kill time.

Perfect numbers are positive integers who equal the sum of their proper integers (their aliquot sum). An well-known example is 6. Indeed, the proper divisors are 1, 2 and 3, and they sum up to 6. Another example is 28: 1+2+4+7+14.

• 6
• 28
• 496
• 8128
• 33550336
• 8589869056
• 137438691328
• … (?)

Only the first four perfect numbers were known to the ancient Greek mathematicians. Euclid could proved the following generating formula:

$\dpi{120} p \text{ and } 2^p-1\text{ prime }\quad\Rightarrow\quad2^{p-1}(2^p-1)\text{ perfect}$

Two millennia later Euler proved that all even perfect numbers are of the form described by Euclid’s recipe. This means that every Mersenne prime generates an even perfect number and vice-versa.

However, what about odd perfect numbers; do they exist? No one knows. All of the 48 perfect numbers known today (see this list) happen to be even. It’s unknown as well whether there exist infinitely many perfect numbers.

De izquierda a derecha la derivada de Sec(x)
De derecha a izquierda la integral de Tan(x)*Sec(x)

From left to right the derivative of Sec (x)
From right to left the integral of Tan (x) * Sec (x)

(via visualizingmath)

### THE TEN COMMANDMENTS OF MATHEMATICS

1: Thou shalt not divide by zero
2: Thou must show thy work
3: Thou must do unto one side of the equation what thou dost unto the other
4: Thou shalt not forget to carry the 1
5: Thou must honour the order of operations
6: Thou must flex the hexaflexagon with caution and never to cause hexaflexaperplexia
7: Thou must properly indicate ye unit of measurement, lest ruin befall thee
8: Thou must set thy calculator to radians or degrees, as is fit for the situation
9: Thou must sketch and graph as the situation demands
10: Thou shall not apply the commutative property to non-commutable groups

(a collaboration between grumpyotter, 14-inox and myself)

(via minutemath)

"There is much pleasure to be gained from useless knowledge." -Bertrand Russell

Intersection of a rotating hexacosichoron (600-cell) and a hyperplane.

And with that, I am done