What are some mind-blowing facts about mathematics?

 Someone hacked my account last night. He was from United States. I’ve answered that already but my last account has been deleted by that hacker. So, I am again answering.

I bet you’ll be amazed and your mind will be blown after that.

#10. Number Theory

Have you ever wondered why one two three is written like 1 2 3 ???

The numbers we write are made up of algorithms (1,2,3,4,etc) called Arabic algorithm to distinguish between Roman algorithms (I ,II ,III ,etc) .
the Arabs popularize these algorithms but their origin goes back to the Phoenician merchants that used them to count and do their commercial count ability .

#9. 0.99999.... = 1

No, the above written is not an approximation. It is a solid proved truth in mathematics. There are many proofs for this statement, but the one that's easiest to understand and absolutely genius is this:

#8. Deck Of Cards

You will never look at a deck of cards the same way after reading this.

How many ways can a deck of cards be arranged?

Any mathematician will tell you that it’s a simple calculation - the answer is 52!

But how big is this number really?
52 Factorial has found a creative way to visualize this number. I have simplified it for better readability.Set a timer so that it would take 52!seconds for it to reach 0.Choose any spot on the equator. You have to walk around the Earth along the equator. But there’s a the catch — you can only take one step every billion years.(Did I leave the stove on?)After you complete one journey around the equator and reach the point where you started, remove one drop of water from the Pacific Ocean.(No peeking at the timer!)Now repeat the whole process — walk around the Earth at one billion years per step, removing one drop of water from the Pacific Ocean every time you circle the globe. Continue until the ocean is empty.(How long has it been?!)After you have emptied the Pacific Ocean, take one sheet of paper and place it flat on the ground.Fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack every time you empty the ocean. Do this until the stack of paper reaches the Sun.(You’re almost there!)Once the stack reaches the Sun take it down and do it all over again.One thousand times more.(Is there a point to this?)Surely the timer must have reached 0 by now?Nope.You’re only done with one-third of the time!
*52! = 806581751709438785716606368564037669752895054408832778240000000000000

I know you didn't even read the whole number.

#7. Surface Area Of Sphere

Well ever wondered how the Surface Area of a Sphere was derived?

Well here is a great visualization to alter your perception.

Step 1: Cut the sphere in the following way.

Step 2: Spread the cut out part across the paper.

Step 3: Collate the pieces together in the following way

Step 4: Spread the areas out separately to form a sine curve

Step 5: The area of the sine curve is the surface area of the sphere.

#6. Can You Prove 1+1=2?

If you have 1 apple and someone gives you 1 apple you have 2 apples right?

Yet the proof that 1 + 1 = 2 is many pages long.

Alfred North Whitehead and Bertrand Russell wrote The Principia Mathematicia, a three-volume work on the foundations of mathematics.

When they started in 1903 they thought they'd be finished in one year but it took them 10 years.

Only in the second volume, after 362 pages they come to the conclusion that 1 + 1 = 2.

Learning addition now really made things easier, didn't it?

#5. Most Beautiful Number

Ever heard of the world’s most beautiful number?
It’s φ=1.61803399.

This number is known as the Golden Ratio, Golden Proportion, Divine Number, Divine Section and Golden Mean. In Mathematics, two numbers are said to be in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two.

Using this concept, here is a golden rectangle:

A golden rectangle (in pink) with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship a+ba=ab≡φ

.

Additionally, the ratio of two successive Fibonacci numbers is very close to the golden ratio.

So what’s so special about this number? The golden ratio has been used for centuries in paintings, architecture, in preparing artificial designs, as maintaining proportions conforming to the golden ratio has always proved to be attractive and visually appealing. This ratio is found everywhere in nature, from the arrangement of branches on trees and veins in leaves to the human body.

Here are some examples:

Taj Mahal, India

CN Tower, Toronto

Notre Dame, Paris

Human Face

Google

Now who was not agreeing to Mathematics Being Everywhere...?

#4. The Black Hole Number

Did you know that the number 4 is designated as the black hole number?

Think of any word, name, thing etc.

For e.g. the word ‘‘mathematics”, has eleven letters.

Now ‘eleven’ in turn has six letters.

‘Six’ has three letters.

‘Three’ has five letters.

‘Five’ has four letters.

And how many letters does ‘four’ have?

FOUR!

Think of any other word and you’ll arrive at the same dead end.

Black hole number, people.

#3. Special Number

The number is 6174.
Wait, are you thinking this a randomly generated number?

You will know soon enough.

Try this:

1. Take any four-digit number, using at least two different digits. Repeated digits, such as 1111, will not work, because you will just end up with 0 after step 3.
2. Arrange the digits in ascending and then in descending order, adding leading zeros if necessary. Add leading zeros if necessary – for example, 4560 in ascending order is 0456 and 6540.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2 and repeat the process.

This process, known as the Kaprekar routine, will always reach the number 6174, within 7 iterations. Once 6174 is reached, the process will continue yielding 6174 because 7641 – 1467 = 6174.

For example, choose 6532:
6532 – 2356 = 4176
7641 – 1467 = 6174

Another example, choose 4906:

9640 – 0469 = 9171
9711 – 1179 = 8532
8532 – 2358 = 6174
7641 – 1467 = 6174

6174 is known as Kaprekar’s constant, named after Indian mathematician D. R. Kaprekar.

#2. Logic Fails Before Mathematics Sometimes

What if I say,

1+2+3+4+5+6+7....=−1/12

Yes, sum of all positive integers up to infinity is negative, sounds crazy?

It's not.

I am going to prove the above equation. Bear with me.

Don't worry, I am not the one behind this magic, its Mr. Srinivasa Ramanujan.

#1. The Still Unsolved...

A prime number, to refresh your memory, is a number that can only be divided by 1 and itself.

Let's try out the conjecture on the even number 4. 4 can be expressed as 2 + 2. 2 is a prime, so the conjecture holds up.

Same goes for a larger number like 28. You can express 28 as the sum of the prime numbers 5 and 23, or 11 and 17.

You can go even higher—why not try something crazy like 12,345,678? That can be expressed as the sum of prime number 20,297 and 12,325,381.

(You can try it yourself on this Goldbach calculator.)

There you have it, Top 10 Mind Blowing Facts About Mathematics that most people are unaware of.

I hope you liked this collection of amazing mathematics fundamentals, logic thoughts, proofs, theorems etc. and if you did don't forget to share this with your friends to blow their mind too!

What are amazing facts about mathematics?

 ** 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.

MW - Shuffling Cards

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