November 17, 2019

Similarities between Mathematics and Life


Similarities between Mathematics and Life
 
“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”  ~S. Gudder
Same way our motto should be to make things as simple as possible.

Rule of Maths: If it seems easy, you are doing it wrong.
Vivekanandji told, “If in a day you do not come across any problem/trouble means you are going on wrong direction”.

“Maths may not teach us how to add love or subtract hate but it gives the hope that every problem has a solution.”
We should believe in Nothing is impossible in life and be optimistic in life.
“No one makes a lock without a key. That’s why God won’t give you problems without solutions.”

“Problems in life are like finding X in Maths, it doesn’t matter how many times find the solution for it. It is still unknown in the next question.”
We should be dynamic in our life. According to situations we need to adapt ourselves.

“It is magic until you understand it, and it is Mathematics thereafter.”
We are amazed at many occasions in life until we do not understand or we are not aware of it.

“Good Mathematics is not about how many answers you know. It’s how do you approach when you don’t know.”
Good life is not about how many people you know….but it’s how do you behave when you don’t know about them.

Maths is not only for solving numbers. It’s also for dividing sorrow, subtracting sadness, adding happiness and multiplying love and forgiveness.

“As far as the laws of Mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”  ~Albert Einstein
In our life also many things which seem real but do not exist and vice versa.

October 18, 2019

To find all the numbers which gets reverse when multiplied by 4



To find all the numbers which gets reverse when multiplied by 4
2178 is the smallest number which gets reverse when it is multiplied by 4.
Some other numbers are:
2178 × 4 = 8712
21978 × 4 = 87912
219978 × 4 = 879912
2199978 × 4 = 8799912
21999978 × 4 = 87999912
21782178 × 4 = 87128712  
2199….(n-4)times… 78 x4=87 99….(n-4)times…21
But if number of digits(n) is multiple of 4 then 1 more number is possible and which is
21782178…..2178 × 4 = 87128712……8712
Where n is number of digits in the number

Note: There are no such numbers which gets reverse when they are multiplied by 2,3,5,6,7,8,10,11,12..... and so on.

October 3, 2019

To find all the natural numbers which gets reverse when multiplied by 9


To find all the natural numbers which gets reverse when multiplied by 9
1089 = 33×33
1089 ×9 = 9801 = 99×99
1089 is the smallest natural number which gets reverse when multiplied by 9.
There is interesting pattern for all the numbers.
 



1089 × 9 = 9801
10989 ×9 = 98901
109989 × 9 = 989901
1099989×9 = 9899901
10999989×9 = 98999901 
10891089×9 = 98019801
 ..............  
If number of digits in number is not  multiple of 4 then only one number is possible.
10999…(n-4) times 89 ×9 =98999…..(n-4) times 01
 Where n is number of digits.

If number of digits in the number  is multiple of 4 then 1 more number is possible.
10891089 × 9 = 98019801
10891089…….1089 × 9 = 98019801……….9801