(a+b)^2=a^2+2ab+b^2 But why?

So Lets prove it :
Consider a line 

Take any arbitrary point 

So now we can say that length of line is a+b
Now we have to square a+b
that will be

lets add all the squares and rectangles

This will be  a² 

Now it is a²+b²

Here there are two rectangle in the above diagram

As we know that Area of rectangle is Length X Width

So it will be a x b

Now lets add every square and rectangle

a² + b² + a x b + a x bi.e., a² + b² + 2ab

Thus 

(a+b)²=a² + 2ab+b² 

Read more »

Factorial of a Number

Definition : It just means to multiply a series of descending natural numbers. (symbol :-    ! )

For Example :  1) 3! = 3 x 2 x 1 = 6

                         2) 5! = 5 x 4 x 3 x 2 x 1 = 120 

Note : 1! is 1 and 0! is also 1

Factorials are use in many fields of Mathematics but particularly in Permutation and Combination.

Note : We can have factorial for negative numbers as well as decimal numbers but we need to get into a subject called the "Gamma Function"

Program to Calculate Factorial of a Number

Read more »

Calculate Area of Square, Area of Parallelogram, Area of Trapezoid, Area of Circle and Area of Ellipse

Here are some formulas to calculate Area of Square, Area of Parallelogram, Area of Trapezoid, Area of Circle and Area of Ellipse...

Note :-  a =  Side of a square.
             b =  Breadth.
             h =  Height.
             r =  Radius

Formulas

Square = a 2
Parallelogram = b*h
Trapezoid = 1/2* (b1 + b2)*h
Circle = π r 2
Ellipse = π r1 r2

Click on the Buttons to find Area of Square, Area of Parallelogram, Area of Trapezoid, Area of Circle and Area of Ellipse.


1) Click on the button to find the


2) Click on the button to find the


3) Click on the button to find the



4) Click on the button to find the



5) Click on the button to find the







Note : I have considered the value of π upto 3.14159265 in the above programs.

Read more »

Kaprekar Number

D.R.Kaprekar

Kaprekar Number 6174

Rules :

•  Select any four digit number, but do not select the numbers like 1111, 2222, 3333,...



•  Arrange the digits in decreasing order.



•  Now arrange the digits in ascending order.



•  Subtract the smaller number from the larger number.



•  Repeat the steps until you get 6174 in repetition.

For Example :- Lets take a number 1234


Step 1:-  Arranging the digits in descending order we get 4321.

Step 2:-  Arranging the digits in ascending order we get 1234.

Step 3:-  Subtract 1234 from 4321 = 4321 - 1234 =  3087.

Step 4:-  Arranging the digits in descending order we get 8730.

Step 5:-  Arranging the digits in ascending order we get 0378.

Step 6:-  Subtract 0378 from 8730 = 8730 - 0378 = 8352.

Step 7:-  Arranging the digits in descending order we get 8532.

Step 8:-  Arranging the digits in ascending order we get 2358.

Step 9:-  Subtract 2358 from 8532 = 8532 - 2358 =6174

Step 10:- Arranging the digits in descending order we get 7641.

Step 11:-  Arranging the digits in ascending order we get 1467.

Step 12:-  Subtract 1467 from 7641 =  7641 - 1467 = 6174.

 

.

.

.

.

.

.

You will find that all four digit number using kaprekar rule will reach the number 6174

Read more »

Birthday Date Calculation

   Birthday Date Calculation Trick

Step  1: Add 18 to your birth month.



Step  2: Multiply by 25.



Step  3: Subtract 333.



Step  4: Multiply by 8.


Step  5: Subtract 554.


Step  6: Divide by 2.


Step  7: Add your birth date.


Step  8: Multiply by 5.


Step  9: Add 692.


Step  10: Multiply by 20.



Step  11: Add only the last two digits of your birth year.



Step  12: Subtract 32940 to get your Birthday.

Read more »

Angel Number

Angel Number 421

Step 1 :- Select any whole number 


Step 2 :- Suppose a whole number is even then divide it by 2.
               If it is odd then multiply by 3 and add 1.


Step 3 :- Repeat the step 2 till you get the loop value 4,2,1 in repetition.

For Example :- Let us consider a whole number 15.

 As 15 is an odd number so (15 × 3) + 1 = 46.


Now 46 is an even number so (46 / 2) = 23.


Again 23 is an odd number so (23 × 3) + 1 = 70.


70 is an even number so (70 / 2) = 35.


35 is an  odd number so (35 × 3)  + 1 = 106.


106 is an even number so (106 / 2) = 53.


53 is an odd number so (53 × 3) + 1 = 160.


160 is an even number so (160 / 2) = 80.


80 is an even number so ( 80 / 2 ) =40.


40 is an even number so ( 40 / 2 ) = 20.


20 is an even number so ( 20 / 2 ) = 10.


10 is an even number so ( 10 / 2 ) = 5.


5 is an odd number so ( 5 × 3 ) + 1 = 16.


16 is an even number so (16 / 2) = 8.


8  is an even number so ( 8 / 2) = 4.




4 is an even number so ( 4 / 2 ) = 2.




2 is an even number so ( 2 / 2 ) = 1.




1 is an odd number so (1 × 3 ) + 1 = 4.


4 is an even number so ( 4 / 2 ) = 2.




2 is an even number so ( 2 / 2 ) = 1.

                     .
                       .
                     .
                       .
                     .
                       .
                     .
                       .

so the number 4 , 2 , 1 goes on............


Note :- The angel number 421 is the smallest prime formed by the two powers in logical order from right to left.

Read more »

Multiply Using Line Method

Multiply two numbers using line :

Lets take an example 45 X 23 :



Step1 : Draw  4 lines shown in the Diagram.

Step 2 : Now again draw 5 lines as shown in the Diagram..

Step 3 : Now draw 2 lines which intersects both 4 and 5 lines...

Step 4 : Follow the Diagram....

Step 5 : Make two partition As shown below  ..

Step 6 : Now count the red dots on  left side, Middle (top + bottom) and right side...

  

Step 7 : Now add all the numbers in the following manner

                                               8                ......{Left side}
                                               2   2           .......{Top + Bottom}
                                                    1   5      .......{Right Side} 
                                    _______________
                                         1   0    3    5     ........{Answer}


So our answer is 1035......

Read more »

Adding Time

Here is a nice simple way to add hours and minutes together:

Let's add 1 hr and 35 mins and 3 hr 55 mins together.


What you do is this:
make the 1 hr 35 mins into one number, which will give us 135 and do the same for the other number giving us 355

Now you want to add these two numbers together:

 

135
355
____
490

 

So we now have a sub total of 490. What you need to do to this and all sub totals is add the time constant of 40.

No matter what the hours and mins are, just add the 40 time constant to the sub total.
490 + 40 = 530

So we can now see our answer is 5 hrs and 30 mins! 


NOTE: Works only when the tens places are 6 to 9

Read more »