Saturday, August 27, 2011

Sevenths are awesome

Is it common knowledge that sevenths are awesome?  In my experience, no.

If your 6th grade math teacher didn't drill it into your brain, you may not know off the top of your head that 1/7th is .142857 repeating.  The cool thing is that if you did know that off the top of your head, you could also know the decimal equivalents of 2/7, 3/7, ... , 6/7 without any additional memorization.

2/7=.285714 repeating
3/7=.428571 repeating

hey...those are the same string of 6 numbers just shifted over by a few places! It continues:

4/7=.571428 repeating
5/7=.714285 repeating
6/7=.857142 repeating

And there you have it.  Somehow they're all just the same infinite string of numbers starting at slightly different positions.  Like many math facts, if you carry this around your whole life, you will find many excuses to use it, and you will at some point even have a great nerd moment where someone else actually wants to know 3000/7 and you can tell them 428.571428 repeating before they have even located their calculator.  Mathemagical.

Perhaps The Answer to the Ultimate Question of Life, The Universe, and Everything is more like 6/7 than 6*7.  In any case, why do sevenths work like this and what deeper math is at play here?  Feel free to offer any thoughts you may have.

Added 8/30: Apparently these are called cyclic numbers!  Thank you, internet.

1 comment:

  1. data mining (for things that are "cool") in an infinite set