25 Cool and Interesting Facts About Maths

Amazing and weird facts about Math.

1. Potato paradox. Fred brings home 100 lbs of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then leaves them outside overnight so that they consist of 98 percent water. What is their new weight? The surprising answer is 50 lbs.

Water weight: 99% = 99 lbs.
Not water weight: 1% = 1 lb.
You can't suddenly gain more lbs of the portion that is not water weight, so:
Not water weight = 2% = 1 lb
New water weight = 98% = 49 lb
49+1= new total weight = 50 lbs

2. Futurama theorem. The math used in the body switching episode of Futurama is a real theorem created by the Futurama writer Ken Keeler, who has a PHD in applied mathematics. READ MORE

3. The Monty Hall problem. You're on a gameshow. There is one grand prize that you can win but it's hidden behind one of three closed doors. The other two doors have nothing. You are asked to select one of the three closed doors. Once you choose a door the host opens one of the remaining two doors that does not contain the fabulous prize. The host then asks if you'd like to switch your choice to the one other unopened door. Do you switch?

Statistically, you should because there is a 66.6% chance the other door is correct and only a 33.3% chance your door is correct. Most people will argue, vehemently, that there is a 50/50 chance of having the correct choice so switching is irrelevant. But you actually had a 66.6% chance to choose the wrong door, to begin with.

4. Hairy Ball Theorem: The hairy ball theorem of algebraic topology states that there is no non-vanishing continuous tangent vector field on even-dimensional n-spheres.

In simple terms, it’s impossible to comb all the hairs on a tennis ball in the same direction without creating a cowlick.

5. International Paper Sizes (e.g. A4) use a 1:√2 ratio. If you cut them in half crosswise, the same ratio will be maintained. It's great for scaling up or down.

Amazing and weird facts about Math.

6.  1 + 1/2 + 1/4 + 1/8 + 1/16 + … equals 2 but

1 + 1/2 + 1/3 + 1/4 + 1/5 + … is infinite.

7. If you fold a standard piece of paper in half 103 times, the thickness of it will be greater than the size of the observable universe.

Some other milestones: 23 folds ~ 1km. 42 folds ~ distance to the moon. 53 folds ~ distance to the sun. READ MORE.

8. There are 3D objects which have an infinite surface area, but a limited volume. Like the above pictured Gabriels Horn. You can fill it with paint, but it will never have enough to cover the outside. It extends forever, so there is no end to its surface. The only reason you can fill it with paint is because, since the object becomes narrower as it extends to the right, the volume is approaching a finite number.

9. This is more of a statistics fact, but if there is a 1 in x chance of something happening, in x attempts, for large numbers over 50 or so, the likelihood of it happening is about 63%.

1-(1-1/x)^x

For example, if there's a 1 in 10,000 chance of getting hit by a meteor if you go outside, if you go outside 10,000 times, you have a 63% chance of getting hit with a meteor at some point. If there's a 1 in a million chance of winning the lottery and you buy a million (random) lottery tickets, you have a 63% chance of winning.

10. According to the Friendship Paradox, your friends have more friends than you.

In spite of its apparently nature, the phenomenon is real, and can be explained as a consequence of the general mathematical properties of social networks. The mathematics behind this are directly related to the arithmetic-geometric mean inequalityCauchy–Schwarz inequality.

Amazing and weird facts about Math.

11. There is no evidence that Pythagoras worked on or proved the Pythagorean theorem, or, for that matter, any mathematical problems at all.

12. There are exactly 10!(factorial) seconds in six weeks.

Let’s figure this one out. So, 6 weeks is 1 second x 60 x 60 x 24 x 7 x 6. Straight away there we have our 1, 7 and 6 – now we just need the rest.

60 = 2 x 3 x 10
60 = 5 x 4 x 3
24 = 8 x 3

We have 2 extra 3s here, so take two of them: 3×3 =9. Now we have 1x2x3x4x5x6x7x8x9x10 and that's 6 weeks.

13. There isn't enough room in the universe to write down the number googolplex, even if each 0 was the size of an atom.

Googol: A very large number!  A "1" followed by one hundred zeros.

10,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Googolplex: The world's second largest number with a name. A "1" followed by a googol of zeros.

Googolplexian: The worlds largest number with a name. A "1" followed by a googolplex of zeros.

A typical book can be printed with 10⁶ zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10⁹⁴ such books to print all the zeros of a googolplex (that is, printing a googol zeros). If each book had a mass of 100 grams, all of them would have a total mass of 10⁹³ kilograms. In comparison, Earth's mass is 5.972 x 10²⁴ kilograms, and the mass of the Galaxy is estimated at 2.5 x 10⁴² kilograms.

Impressive?

14. Birthday Problem. Select at random 23 people and put them in a room. There is roughly a 50% chance that 2 people in that room will share the same birthday.

15. Over 2000 years ago, Eratosthenes estimated the Earth's circumference using good old math, without ever leaving Egypt, and he was accurate to within 2%.

Amazing and weird facts about Math.

16. If you divide any number by 7, and the answer isn't an integer, you end up with the sequence 142857 recurring.

1/7 = .142857142857
3/7 = .428571428571
2/7 = .285714285714
6/7 = .857142857142
4/7 = .571428571428
5/7 = .714285714285

17. The Banach-Tarski Paradox. You can cut a sphere up into pieces, and then reassemble those pieces to get two spheres which are exactly the same as the first sphere.

18. 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3 and in binary 73 is a palindrome, 1001001, which backward is 1001001. 73 is also the best number. Itself and its mirror and 100 plus both numbers are all primes (73, 37, 137, 173).

If you take 73 and 100 more than its mirror, 37 (137) and multiply them together you get 10,001. Which leads to a calculator trick I learned when I was young: Take any four-digit number and multiply it by 73, then multiply the result by 137, your result is the four-digit number repeated twice.

19. Ancient Babylonians did math in base 60 and not base 10, giving us 60 seconds in a minute, 360 degrees in a circle, etc. Babylonian numerals

20. 2⁶⁷ -1 was thought for a long time to be a prime number (suggested by Mersenne) until a mathematician named Frank Nelson Cole proved that it wasn't by devoting 3 years worth of Sundays to the problem.

At a mathematicians conference in 1903, during a lecture that he was supposed to give, he walks up to the chalkboard in front of a room full of his fellow mathematicians. In total silence, he writes 147,573,952,589,676,412,927 which is 2⁶⁷ -1 and then moves to the other side of the chalkboard. He writes 193,707,721 x 761,838,257,287 and then does the entire calculation by hand... which equals the same number as 2⁶⁷ -1.

He puts the chalk down and silently returns to his seat while receiving a standing ovation.

Amazing and weird facts about Math.

21. According to Zipf's law: in a large, enough sample of text from any language, the most frequent word will occur twice as much as the second, three times as much as the third, four times as much as the fourth and so on.

22. The false Positive Paradox describes a situation where a "highly accurate" test is worthless if the testing condition is rare enough. Example: If 10 people in a city of 20 million are "bad guys" and a surveillance program identifies them with 99% accuracy, then 99.995% of positives will be false

23. You can almost perfectly convert miles and kilometers using the Fibonacci sequence.

1 1 2 3 5 8 13 21 34 55 89 ....

Skip the first few terms and...

Miles	Exact km	Approx km
3	4.83	5
5	8.04	8
8	12.87	13
13	20.92	21
21	33.80	34
34	54.71	55
55	88.51	89

24. There are 52! (factorial) ways to shuffle a deck of cards or

80658175170943878571660636856403766975289505440883277824000000000000 ways.

How big is that number?

Start by picking your favorite spot on the equator. You shuffle the deck of cards once every second. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. After you complete your round the world trip, remove one drop of water from the Pacific Ocean.

Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.

Do this until the stack of paper reaches from Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e67 seconds remaining. You’re just about a third of the way done.

25. Finger binary. Using binary you can count to 31 on one hand 1023 on two.