National Mathematics Day (in India)

[khansaheb]

National Mathematics Day
( i.e. Birth Day of Srinivasa Ramanujam )

See This Absolutely Amazing Mathematics Noted By Great Mathematician *रामानुजम*
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

And Look At This Symmetry :

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

 

[Agent Smith]

Srinivasan was an autodidact, with very little formal training in math. It's not an exaggeration to say that, to him, numbers were as natural as breathing. I wonder which of his numerous mathematical discoveries ... well ... takes the cake?

 

[Steven G]

Anyone who can do math in his sleep I vote for. Ramanujam was just an amazing mathematician!

 

[Steven G]

Srinivasan was an autodidact, with very little formal training in math. It's not an exaggeration to say that, to him, numbers were as natural as breathing. I wonder which of his numerous mathematical discoveries ... well ... takes the cake?

Even if he had formal training it wouldn't have helped as he was brighter than any teacher that he would have had in any school anywhere in the world. You just can't teach someone like him, unless you bring in the big people in mathematics--and in the end he would teach them a thing or two.

 

[Agent Smith]

Even if he had formal training it wouldn't have helped as he was brighter than any teacher that he would have had in any school anywhere in the world. You just can't teach someone like him, unless you bring in the big people in mathematics--and in the end he would teach them a thing or two.

I did a superficial scan of his Wiki page. Interesting stuff. I'm not a magi (that's what mathemtician-astrologer-astronomers were call, back in the bronze age), but I'm especially intrigued, it kinda catches me eyes, by his use of $\sqrt$ in his "calculations". I briefly recall coming across an algorithm for finding the square root, but the teachers used to skip it, perhaps anticipating the computer age (I'm an old timer). What, in your opinion, is Sri Ramanujan's greatest contribution to math? Are (some of) his works subjects in their own right? I believe there are some ... "note books" which are still awaiting ... decipherment.

 

[Agent Smith]

What about [imath]1729[/imath], the smallest number that can be expressed as the sum of 2 cubes in 2 different ways, [imath]1^3 + 12^3 = 10^3 + 9^3 = 1729 = 1^3 + (3 + 9)^3 = (1 + 9)^3 + 9^3[/imath]?

And ...

[imath]1^3 + 3^3 + 9^3 + 3(3^2)(9) + 3(3)(9^2) = 1^3 + 9^3 + 3(1^2)(9) + 3(1)(9^2) + 9^3 = 1729[/imath]

In other words ...

[imath]\left(3^{3 - 3}\right)^3 + 3^3 + 3^{3 + 3} + 3^{3 + 3} + 3^{\frac{3 + 3 + 3 + 3 + 3}{3}} = 1729[/imath]

"Au contraire, Mr. Hardy, it is a very interesting number." ~ Ramanujan.