Hello, maths lovers! What? You don't love maths. Then don't worry, after knowing these amazing facts about maths, you will love mathematics in a way that you have never done before. So without wasting a little time lets go to our first intresting fact of maths :)
This beautiful equation of maths is made up of three mathematical operations and five constant numbers. You probably know about these five mathematical constant numbers which are:
Pi(π>); π = 3.14
Euler's number(e); e = 2.71
Imaginary Unit(i); i2 = −1
The number 0
The number 1
And the equation is :
eiπ + 1 = 0
This equation is also known as Euler's Identity. Here Pi(π) and Euler's number(e) are an irrational numbers i.e. they cannot be represented as ratio of integers. Whereas i is known as imaginary unit which represent i2 + 1 = 0, giving i2 = -1.
The number 0 is the smallest whole number and does not have any sign, i.e it is neither positive nor negative. And the number 1 is the smallest natural number, and the factor of every number.
Why this is beautiful? As you can see we used three completely ridiculous numbers and added 1 to it and they together makes 0 forming such a simple equation. And that's why it is the most beautiful equation in mathematics.
The number we are talking about is 6174 which is also known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. D. R. Kaprekar showed that if you carry out a procedure with any four digit number(excluding repdigits like 1111) you will end up getting this number. And that procedure is:
- Take any four-digit number, using at least two different digits. (Leading zeros are allowed)
- Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
- Subtract the smaller number from the bigger number.
- Go back to step 2 and repeat.
The above process, known as Kaprekar's routine. And will always reach at its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding 7641. For example choose 2453:
- 5432 - 2345 = 3807
- 8730 - 0378 = 8352
- 8532 - 2358 = 6174
So what are you waiting for go ahead take a pen and paper, and try this fun facts of maths by yourself.
Perhaps you are aware of the Palindrome numbers. And if I do not know, then I tell you, A palindromic number is a number that remains the same when its digits are reversed. For example 198891. As it will be same if we write it in backwards.
Now, What I mean by the above statement Every Number is a Sum of Three Palindrome numbers is that each and every positive number can be written as the sum of three palindrome numbers. Let's do an example for this by taking a number 22121887 and it can be represented as:
Now the question arises that, how will you find those three pallidrome numbers which gives a the required number on adding them. So for this a 40-page algorithm has been written by three mathematicians named Javier Cilleruelo, Florian Luca, and Lewis Baxter, after reading and remembering this 40-page algorithm you can show any number as the sum of three palindrome numbers. But reading and remembering that 40-page algorithm and be boring and tough too, that's why we have an alternative for this and it is a website designed by Christian Lawson-Perfect. Visit his website and try it out by your self.
Website that does the work of 40-page algorith: https://somethingorotherwhatever.com/sum-of-3-palindromes/
Link to the 40-page Algorithm: https://arxiv.org/abs/1602.06208v2
It's hard to believe but it is true that 1 is equals to 0.9 followed by infinite numbers of 9. This equation is really simple to understand and yet fascinating. At first many people don't believe it can be true, that's why here is a simple proof for this:
Let n = 0.999... ------- Equation 1
Now multiply both sides by 10, then you will get:
10n = 9.999... ------- Equation 2
Now subtract equation 1 from equation 2, then:
10n - n = 9.999... - 0.999...
9n = 9
n = 1 ------Proved!
You can also understand it differently. As we add further 9s at the end of 0.999..., it will come closer and closer to 1.
Let us first understand what is the factorial of a number.
For any whole number n, its factorial will be:
n! = n x (n-1) x (n-2) x ..... x 3 x 2 x 1
Factorial of a number is denoted by excalimation mark(!). For example lets take factorial of 6:
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720
Now, How to find out 0!. The way we find factorial of 0 is by completing the pattern. So lets complete the pattern:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Now 5! can be written as:
5! = 6!/6 = 720/6 = 120
4! = 5!/5 = 120/5 = 24
3! = 4!/4 = 24/4 = 6
2! = 3!/3 = 6/3 = 2
1! = 2!/2 = 2/2 = 1
Here's the main part:
0! = 1!/1 = 1/1 = 1
So by completing the pattern we finf out that 0 factorial is equals to 1.
You can also understand it in a different way. 3! means that there are total 6 unique ways to arrange 3 objects, 2! means there are 2 ways to arrange two objects and 1! means there are only one way to arrange 1 object.
Now, If I ask you what are the total number of ways in which you can arrange 0 objects? then the answer must be 1. For an illustration see below:
Arrangement of 3 objects - 😄 😍 💗 | 😄 💗 😍 | 😍 💗 😄 | 😍 😄 💗 | 💗 😍 😄 | 💗 😄 😍 - 6 ways
Arrangement of 2 objects - 😄 😍 | 😍 😄 - 2 ways
Arrangement of 1 object - 😄 - 1 way
Arrangement of 0 objects - ________ - 1 ways
I hope you understand now!
There are so many fun facts of maths that can be included in this article but I did'nt wanted it to be too long. But you can include your favorite fun facts about maths in the comment section. Finally I would like to wrap up this article with a question: Which one is your favorite maths fact of the above? Comment it in comment section below. Share these interesting facts of maths to your friends and family and help us reach more audience. Thanks a lot for going through a long article like this. See you in the next one.