## Tuesday, December 22, 2015

### Ramanujan's Birthday!

12/22/2015

12222015 is a composite, deficient, odd, odious, semiprime, square-free, and wasteful number.  It can be expressed as the sum of all of the integers from 45301 to 45569.

Today is Srinivasa Ramanujan’s Birthday, and a good day to talk about Brithdays and Magic Squares.

(Just a quick reminder - most of you have already decorated the house, bought presents and so forth - but if you haven't there are only 3 days left until Isaac Newton's Birthday!)

Ramanujan was a self-taught Indian mathematician, discovered by the British mathematician G. K. Hardy.  Hardy invited Ramanujan to return to London with him in order to study mathematics.

Ramanujan created his own Magic Square.

 22 12 18 87 88 17 9 25 10 24 89 16 19 86 23 11

Each row, each column and both major diagonal add up to 139.  You might also notice that the four corners add up to 139 also.

And, the two numbers between the top corners add with the two numbers between the bottom corners for a total of 139.

And, the two numbers between the left corners add with the two numbers from the right corners for a total of 139.

And, the four numbers above, below, to the right of, and to the left of the top left and bottom right corners add up to 139.

And, the four numbers above, below, to the right and to the left of the bottom left and the top right corners add up to 139.

And, the four numbers in the middle of the magic square add up to 139.

Are there more?  Oh yes!

The four numbers in the top left corner add up to 139.  The four numbers in the top right corner add up to 139.  The four numbers in the bottom left corner add up to 139.  AND, the four numbers in the bottom right corner add up to 139.

I’m glad were through ... we are through aren’t we?  Not yet!

The square containing the 88, 17, 10, and 24 (2nd and 3rd rows, 1st and 2nd columns), and the square containing the 9, 16, 25 and 89 (2nd and 3rd rows, 3rd and 4th columns) also add up to 139.

Finally we are at the end.  You may not have noticed, but the icing on the top is that the top row is Ramanujan’s birthday (22/12/1887 – written in the British format (Day/Month/Year) with the year split into two two-digit numbers).

Of course, I could go on about the mathematical mysteries of 139.

Or I could start into a lecture on how to create your own birthday.  (Or, even better, create one for your sweetheart’s birthday.)

Maybe out save those topics for another day.

Email me if you want me to cover either of those topics.

MOC TOD LIAMG TA UDE TOD MOIBM

(backwards)

And Arthur Benjamin has a really nerdy paper on how to make birthday magic squares at: https://www.math.hmc.edu/~benjamin/papers/DBMS.pdf .  (But what makes it really nerdy is the picture of him in a nerdy math shirt.)

David