I was just fooling around with some numbers, and realized that 13^2 (which gives you 169) is the reverse of 31^2 (which gives you 961 – which is the reverse of 169).
Is there any name for a number, the reverse of which, when squared, will also yield the reverse of the original number’s square?
Here’s another one:
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12^2=144
21^2=441
Do you know any others? Possibly with other powers?
Anyone know any use for it? Please leave a comment if you do.
I think what you have encountered is known as the rule of 9′s… this is a common reconciliation tool used by geeky accountants to identify a transposition of numbers! But it does seem to be at the base of your math… let me know ;-)
Professor Homunculus sez:
I don’t think that’s it. “The Rule of Nines” is a catch-all name for many of the very cool and useful things you can do with nines, one of them being a divisibility rule for 9 (which is the basis of the geeky accounting trick), all of them having to do with modular arithmetic in base 10.
One or more of those things may have something to do with this phenomenon, but that’s not the name of it. Would be interesting to see how Mod 9 fits in with it, though.
Thanks for the input. If you can figure out what the rule of nines has to do with the above phenomenon, please send it in. I’d be interested to see it.
Still looking for the name of this puppy, though.
Has anyone identified what this these numbers are called? I ran a few, results here http://pastebin.com/f2dd94ad6 and found many interesting patterns.
Professor Homunculus sez:
Not so far, but your results are pretty interesting. Thanks for doing that.
10^2 =100
0.1^2 =0.01 (without the decimals they are opposite)
20^2 =400
0.2^2 =0.04
22^2 =484 (which is the same way each way)
interestingly
33^2 =1089
99^2 =9801
haven’t found one exactly like yours though. I know that there is a name for this time of number but I don’t recall what it is lol.