Beauty of Maths

5 Comments:

1. 

   Nimit

   June 21, 2006 at 10:55 pm

   Here is one more series I like. The sum of consecutive odd numbers adds up to perfect squares, like this:
   1 = 1×1
   1+3 = 2×2
   1+3+5 = 3×3
   1+3+5+7 = 4×4
   1+3+5+7+9 = 5×5
   1+3+5+7+9+11 = 6×6
   1+3+5+7+9+11+13 = 7×7
   1+3+5+7+9+11+13+15 = 8×8
   and so on 🙂
2. 

   OneManArmy

   June 22, 2006 at 9:18 pm

   If you know the square of a number, you can find the square of the next number by this method.

   Say for E.g. you know the Square of 5 and you need to find the square of 6

   5 square = 25
   6 * 2 = 12 (Double the number whose square is required)
   -1 = -1
   ————-
   6 Square = 36
   ————-

   I found out this method when i was in School.
3. 

   Rashmi

   June 23, 2006 at 9:24 am

   Other way you can do it is – for example

   13 Square=

   Step 1- 3 square= 9

   Step 2- 1*3*2 = 6

   Step 3- 1 Square = 1

   you get 169

   It helps as you go higher number
4. 

   Rashmi

   June 23, 2006 at 9:28 am

   In Nine’s table when you add to the answer you always get nine.

   For example- 9*2= 18 = 1+8
   9*3= 27 = 2+7
   9*4= 36 = 3+6
5. 

   Nilesh

   June 23, 2006 at 3:09 pm

   The Beauty of Numbers

   12345679 * 9 = 111,111,111
   12345679 * 18 = 222,222,222
   12345679 * 27 = 333,333,333
   12345679 * 36 = 444,444,444
   12345679 * 45 = 555,555,555
   12345679 * 54 = 666,666,666
   and so on….

   The Amazing Number 1089:
   1. Choose a 3 digit number (where the units and hundred digits are not the same)

   I will do it with you here by arbitarily selecting 825

   2. Reverse the digits of the number you have selected.

   The reverse of the number is 528

   3. Subtract the 2 numbers (the larger minus the smaller)
   Our calculated difference is 825 – 528 = 297

   4. Once again, reverse the digits of the difference.
   Reversing the digits of 297 we get the number 792

   5. Now add the last 2 numbers
   We add the last 2 numbers 297 + 792 = 1,089.

   The result will always be 1089

   Now lets look at multiples of 1,089
   1,089 * 1 = 1,089
   1,089 * 2 = 2,178
   1,089 * 3 = 3,267
   1,089 * 4 = 4,356
   1,089 * 5 = 5,445
   1,089 * 6 = 6,534
   1,089 * 7 = 7,623
   1,089 * 8 = 8,712
   1,089 * 9 = 9,801

   Do you see a pattern? Look at the first and ninth products. They are reverses of one another. The second and the eighth are also reverses of each other and so on.

   Another feature of 1089

   We will consider 1 and 89…..Take any number and the sum of the square of its digits and continue the same way…
   Each time you will reach 1 or 89

   Take a look at the number 30
   n = 30:

   3(2) denotes square of 3

   3(2) + 0(2) = 9 –> 9(2) = 81 –> 8(2) + 1(2) = 65 –> 6(2) + 5(2) = 61 –>
   6(2) + 1(2) = 37 –> 3(2) + 7(9) = 58 –>5(2) + 8(2) = 89 –> 8(2) + 9(2) = 145 –> 1(2) + 4(2) + 5(2) = 42 –> 4(2) + 2(2) = 20 –> 2(2) + 0(2) = 4 –> 4(2) = 16 –> 1(2) + 6(2) = 37 –> 3(2) + 7(2) = 58 –> 5(2) + 8(2) = 89

   You see 89 is repeating and this will continue in a loop…

   Similarly n = 31

   3(2) + 1(2) = 10 –> 1(2) + 0(2) = 1 –> 1(2) = 1

   Last but not the least
   Formula for Salvation = 108 * 9 Navkar Mantra 🙂