When I was in my first grade I was trying to learn tables of 9 by heart.
9 X 1 = 9
9 X 2 = 18
9 X 3 = 27
9 X 4 = 36
9 X 5 = 45
9 X 6 = 54
9 X 7 = 63
9 X 8 = 72
9 X 9 = 81
9 X 10 = 90
is the tables. I was told multiplication is in fact nothing but addition. So, tables of two were very easy. Just keep adding two everytime. 2 x 1 = 2. For 2 x 2 just add 2 to previous number and so on. Learning tables this way was easy till the tables of 6. 7 was difficult but surprisingly I could memorize them. 8 was more difficult but my brain had more space. 9 was the most difficult of them all. I remember spending days together trying to learn the table of 9 by heart. It was impossible. My mom used to ask me what was 9 * 6 ... I couldn't answer. She asked for 6 * 9 ... I could answer.... It was then that I was introduced to commutative law. She asked me to remember all tables till 8. For table of 9, all I had to do was just recall all the table's 9th element. 9 * 10 was easy because all i had to do was just write 9 and append 0.
Now, I became a little better. But, as I had told you, 7 and 8 tables were pretty difficult for me. So, my mom told me another tricky method. She asked me to remember table of 9 till 5. i.e
9 X 1 = 09 (She added zero purposefully)
9 X 2 = 18
9 X 3 = 27
9 X 4 = 36
9 X 5 = 45
Then for the rest .. all I had to do was just reverse the number in the reverse direction ...
i.e
9 X 5 = 45 - 9 X 6 = 54 (Observe that the numbers are reversed .... )
9 X 4 = 36 - 9 X 7 = 63
9 X 3 = 27 - 9 X 8 = 72
9 X 2 = 18 - 9 X 9 = 81
9 X 1 = 09 - 9 X 10 = 90
It took more than a week to see and learn these things. I was amazed by this.
WOW !!!!!!! Was it same for other tables too ??? I tried ... but failed .. The tables of 9 instantly became my favorite. But, for the exam we were asked to learn only till tables of 8. ..... Murphy's law ??!!!!
As time passed, I still remembered my first encounter with table of 9. It was in my college that I actually learnt that this property of number reversal is actually due to a reason.
Try to prove ::: if 9 | (10x + y) then 9 | (10y + x) when x,y belong to set of integers.
Prime numbers exist and their properties are so very important. They are used in infinitely many places. I could get the essence of the very famous P vs NP problem from these prime numbers. These prime numbers have made the heads of greatest brains in the world spin.
I am reading a few scriptures on number theory and probability theory. The more I read , more I want to ...
This blog is a dedication to the beautiful world of mathematics and a small device which was originally created to make life of mathematicians easier and has now more takers than the subject of mathematics (Computers)....
Super one DOOOD.....
ReplyDeleteKeep it up....
:)
All the best..Keep posting some interesting articles and you will have a nice blog discussing the beauty of math..
ReplyDeletenice one da :) well written .
ReplyDeleteThank you all ...
ReplyDeleteThere are just too many things to post about the beauty of math ... Will keep posting..