## Wednesday, 4 April 2012

### Three Times the Symmetry

Just saw a post at Futility Closet that makes me wonder, yet again, where does he find these things... O. K. so this one was from Scripta Mathematica (1955..what, you don't browse old math mags on a daily basis???)

If you haven't discovered his blog yet, just go there and ramble around... there is no particular theme other than, in the words of an old song, "things that make you go, Hmmm!"

First, there was this palindrome... if you don't know the word, it means it reads the same front to back and back to front, like "Madam I am Adam." only numerical. (Long after I first wrote this, I learned that the Catalan term for a numeric palindrome is "capicua", which I am told means "heads and tails.")

0264 + 4125 + 5610 = 0165 + 5214 + 4620

Ok, admit it, that's cute... not mind bending cute, but cute... but then he adds,

If you put multiplication signs in the middle of each of the terms... it is STILL true (do check please)

02 × 64 + 41 × 25 + 56 × 10 = 01 × 65 + 52 × 14 + 46 × 20

Ok, that elevates it to damn near mind bending cute... if you doubt it, go find a second example. Do it with just two four digit numbers to make it easy, or do it with five if you think that is easy...and if you manage, just to torque your brain, see if it also works if you replace the multiplication sign with a Plus sign... Yeah...

02 + 64 + 41 + 25 + 56 + 10 = 01 + 65 + 52 + 14 + 46 + 20

Nah, that's it, there couldn't be anymore... I mean what else could you do ?
No, don't even imagine that if you squared each term it would still work... don't check, that couldn't possibly be true...

No really, that would just be impossible...

Stop looking down here...you know it couldn't be true...

Stop I say

Well, I warned you... now you have only yourself to blame...