01. 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.
02. 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
03. 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%
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.
04. 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
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- 3/7 = .428571428571
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- 2/7 = .285714285714
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- 6/7 = .857142857142
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- 4/7 = .571428571428
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- 5/7 = .714285714285
05.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.
06.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.
Image and Description Source : 25 Kickass and Interesting Math Fact
