** Here are some amazing facts about math: **
* ** Main set of spheres **: The set of main spheres in algebraic topology states that there is no continuous tangent vector field on non-dimensional n-spheres.
In simple terms, it is impossible to comb all the hair of a tennis ball in the same direction without creating a cowlick.
* Isaac Newton's ** Principia Mathematica ** contained a simple calculation error that went unnoticed for 300 years.
- * If you write Pi out to two decimal places, "** Pie **" is written backwards.
- * The spiral shapes of the sunflowers follow a ** Fibonacci sequence. **
- There, add the two previous numbers in order to get the next one. So it starts 1, 1, 2, 3, 5, 8, 13, 21 etc.
* The Fibonacci sequence is encoded in number 1/89.
1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034 etc.
- * The word hundred is derived from the word "** hundrath **", which actually means 120 and not 100.
- 111,111,111 × 111,111,111 = 12,345,678,987,654,321.
- * In a room of only 23 people, there is a 50% chance ** that two people have the same birthday.
It's called the birthday problem. In a room of 75, there is a 99% chance ** that two people will match.
- * If you shuffle a deck of cards correctly, there is a chance that the exact order in the entire history of the universe has never been seen before.
0 is an even number
Googolplex and other large numbers written out
- * Number 4 is considered unfortunate in large parts of Asia.
- * Take any four digit number, follow these steps and you will get ** 6174 **.
1. Dial a four-digit number (the only condition is that it has at least two different digits).
2. Arrange the digits of the four-digit number in descending, then ascending order.
3. Subtract the smaller number from the larger one.
4. Repeat.
Finally, you end up at 6174, which is called Kaprekar's constant. If you repeat the process, you will always get 6174.
- * A circle has the largest area of all shapes with the same circumference.
- * A circle has the shortest circumference of all shapes with the same area
- * Multiply any number by nine (9) and then add all the individual digits of the result (product) to make them one-digit. The sum of these individual digits would always be nine (9).
- * If the number 1 is divided by 998.001, the answer will be in a complete order of 000 to 999. Try it out and be ready to waste an entire notebook!
- * According to mathematicians, there are 177,147 ways to tie a tie.
- * ** Arabic numerals ** as we use them in English today were invented in India.
- * ** The Millennium Prize ** is a $ 1 million award given to anyone who can solve 1 out of 7 math problems. So far, only 1 problem has been solved.
- * The most accurate calculations at NASA use only 15 decimal places of Pi.
- * If you set Pi to 39 digits, you can measure the size of the observable universe across the width of a single hydrogen atom.
- * If you divide a number by 7 and the answer is not an integer, the sequence 142857 ends.
1/7 = .142857142857
3/7 = .428571428571
2/7 = .285714285714
6/7 = 0.857142857142
4/7 = .571428571428
5/7 = 0.714285714285
- * International paper sizes (e.g. A4) use a ratio of 1: √2. If you halve them across, the same ratio is maintained. It's great for scaling up or down.
- * ** The problem with the Monty Hall. ** You are on a game show. There is a main prize that you can win, but it is hidden behind one of the three closed doors. The other two doors have nothing. You will be asked to choose one of the three closed doors. Once you've chosen a door, the host opens one of the remaining two doors that don't include the fabulous price. The host will then ask if you want to change your choice to another unopened door. Are you changing
Statistically speaking, you should do this because the probability that the other door is correct is 66.6% and only 33.3% that your door is correct. Most people will argue vehemently that there is a 50/50 chance of making the right choice, so switching is irrelevant. But you actually had a 66.6% chance of choosing the wrong door.
- There are 3D objects which have an infinite surface area, but a limited volume, like the 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 ..
- * ** The Banach-Tarski paradox **: You can cut a ball into pieces and then reassemble these parts to get two balls that correspond exactly to the first ball.
- * When you fold a normal sheet of paper in half 103 times, its thickness is larger than the size of the observable universe.
- * The math used in Futurama's body switching episode is a real sentence created by Futurama writer Ken Keeler, who has a PhD in applied math.
- According to the Friendship Paradox, your friends have more friends than you.
Source: quora German