Crazy. While the basics are pretty simple, the philosophy behind some of those very simple fundamentals can be quite profound…and even bewildering. Today we’re going to look at everything from prime numbers to infinity. So get ready because these are 25 Extraordinary Math Principles To Challenge Your Brain!

25. The equator rope

If you wrapped a rope around the equator of the Earth so that it was tightly hugging the ground, you would only need to add about 6.3 meters of rope in order for the entire thing to hover 1 meter above ground level (all the way around the Earth). This counterintuitive result works no matter how
big the sphere is. The most simple way to explain this is to remember that circumference is equal to diameter times pi. This means that if you want to make the rope hover 1 meter above the Earth, you
only need to increase the diameter by 2 meters (1 meter on each end of the globe). Therefore, you would only need to increase the circumference of the rope by 2 x pi meters (6.28318530718 meters).

24. Hippasus of Metapontum

The man who proved that irrational numbers
existed was murdered for it. His name was
Hippasus of Metapontum, and it happened
around 520 BC. Pythagoras and many Greek
mathematicians of the time believed that all
numbers were integers, or whole. It was when Pythagoras was performing his famous triangle calculations (Pythagorean theorem) that he stumbled across the square root of two. To make a long story short, he allegedly tried to keep his finding a secret and flipped out when Hippasus published it.

23. Munchausen numbers

Apart from making some assumptions about 0^0, 3435 is the only number besides 1 where you can split each digit up, raise it to its own power, sum it all together, and get the same number back. Basically, 3^3 + 4^4 + 3^3 + 5^5 = 3435 Note: 438579088 also works if you assume that 0^0 = 0.
These are called Munchausen numbers.

22. The decimal representation of the 7th's

The decimal representations of the 7th’s are the same set of numbers being repeated except always starting from a different point. 1/7 = 0.142857142857… and 2/7 = 0.285714285714… and 3/7 = 0.428571428571…

21. Binary finger counting

If you use binary, you can count to 1023 on your fingers.

20. 10!

There are exactly 10! seconds in 6 weeks. It’s easier to see this when you break it down as such:
6 * 7 * 24 * 60 * 60 = 6 * 7 * (8 * 3) * (3 * 2 * 10) * (1 * 3 * 4 * 5) = 6 * 7 * 8 * 9 * 2 * 10 * 1 * 3 * 4 * 5 = 10!

19. Graham's number

Graham’s number is so big that if you wrote every digit as small as you possibly could, it would still take up more space than is available in the observable universe. In fact, if you could hold all of the digits in your head your brain would collapse into a black hole (due to the astronomical density of neural connections you would require).

18. Repeated decimals

Any repeating decimal can be written as a fraction over an equivalent number of 9’s (as the repeating part). For example, .456456456… would be
456/999

17. Shuffling cards

Every time you randomly shuffle a deck of 52 cards, you have almost certainly arranged them in an completely unique order. What we mean by this is that in the entire history of mankind, nobody has ever shuffled a deck in the same way. How? Well, there are 52! ways that you can order the deck (52*51*50…) This leads to 8.0658 x 10^67 possibilities. In comparison, the universe is only 1 x 10^18 seconds old. Even if you shuffled one deck every second since the big bang…you’d still fall miserably short.

16. The klein bottle

If you take two Möbius strips and extend the
edges so that they connect (in effect glueing them together), you create a Klein Bottle. This “bottle” is an example of a non-orientable surface. Basically, it exists only in 4 dimensions, but can be loosely represented in 3. Like the Möbius strip, it has only 1 surface, but no edges. It’s pretty trippy.