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Fun with math: Dividing one by 998001 yields a surprising result

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Re: Fun with math: Dividing one by 998001 yields a surprising result

#81

Post by toasterweasel »

bdg wrote: post #33
psykotic wrote: post #23

There's some sleight of hand here. Not all the digits are exactly right. Look how it skips from 997 to 999: http://www.futilitycloset.com/2012/01/08/math-notes-76/ Here's the math. Suppose you want a unit fraction 1/n with decimals that cycle through the 4-digit sequence abcd. Multiply by 10^4 to shift abcd into integer position, leaving repeating copies after the decimal point: 10^4/n = abcd + 1/n Solving for n give…

I just want to know I appreciate you posting this. Some people might be interested in "wow math sure can do some funky stuff", but others like myself really want to know why. I figure that's also covers a sizable group of us here on Hacker News.

It does indeed. I have a love/hate relationship with math. Love because it's fascinating and intergal to an understanding of our universe, hate because I had some horrible math teachers over the years...plus I do admit to being slightly lazy.

Re: Fun with math: Dividing one by 998001 yields a surprising result

#82

Post by donnawarellp »

dimitar wrote: post #77

Some fun that can fit on a poket calculator: 12345679 * 9 = 111111111 12345679 * 18 = 222222222 12345679 * 27 = 333333333 12345679 * 36 = 444444444 12345679 * 45 = 555555555 12345679 * 54 = 666666666 12345679 * 63 = 777777777 12345679 * 72 = 888888888 12345679 * 81 = 999999999 12345679 * 999999999 = 12345678987654321

this is my personal fav

Re: Fun with math: Dividing one by 998001 yields a surprising result

#83

Post by buddydvd »

dimitar wrote: post #77

Some fun that can fit on a poket calculator: 12345679 * 9 = 111111111 12345679 * 18 = 222222222 12345679 * 27 = 333333333 12345679 * 36 = 444444444 12345679 * 45 = 555555555 12345679 * 54 = 666666666 12345679 * 63 = 777777777 12345679 * 72 = 888888888 12345679 * 81 = 999999999 12345679 * 999999999 = 12345678987654321

And this too: 111111111111111111111111111 / 9 = 12345679012345679012345679

Re: Fun with math: Dividing one by 998001 yields a surprising result

#84

Post by jklp »

bdg wrote: post #33
psykotic wrote: post #23

There's some sleight of hand here. Not all the digits are exactly right. Look how it skips from 997 to 999: http://www.futilitycloset.com/2012/01/08/math-notes-76/ Here's the math. Suppose you want a unit fraction 1/n with decimals that cycle through the 4-digit sequence abcd. Multiply by 10^4 to shift abcd into integer position, leaving repeating copies after the decimal point: 10^4/n = abcd + 1/n Solving for n give…

I just want to know I appreciate you posting this. Some people might be interested in "wow math sure can do some funky stuff", but others like myself really want to know why. I figure that's also covers a sizable group of us here on Hacker News.

There is no why. It just is. This is the worst thing about being human :)

http://www.smbc-comics.com/index.php?db=comics&id=1914

Re: Fun with math: Dividing one by 998001 yields a surprising result

#85

Post by hashfold »

psykotic wrote: post #23

There's some sleight of hand here. Not all the digits are exactly right. Look how it skips from 997 to 999: http://www.futilitycloset.com/2012/01/08/math-notes-76/ Here's the math. Suppose you want a unit fraction 1/n with decimals that cycle through the 4-digit sequence abcd. Multiply by 10^4 to shift abcd into integer position, leaving repeating copies after the decimal point: 10^4/n = abcd + 1/n Solving for n give…

love the math. thanks for sharing.

Re: Fun with math: Dividing one by 998001 yields a surprising result

#86

Post by grusk »

dimitar wrote: post #77

Some fun that can fit on a poket calculator: 12345679 * 9 = 111111111 12345679 * 18 = 222222222 12345679 * 27 = 333333333 12345679 * 36 = 444444444 12345679 * 45 = 555555555 12345679 * 54 = 666666666 12345679 * 63 = 777777777 12345679 * 72 = 888888888 12345679 * 81 = 999999999 12345679 * 999999999 = 12345678987654321

The way I was introduced to this was as a math trick: Pick a number 1-9, multiply by 9, then 12345679, and you get a string of whatever number you picked.

Also, pick any three-digit number, multiply by 7, 11, and 13 (or 1001), and you get your three-digit number repeated twice.

Re: Fun with math: Dividing one by 998001 yields a surprising result

#87

Post by psykotic »

jklp wrote: post #84
bdg wrote: post #33

Earlier quoted context omitted.

I just want to know I appreciate you posting this. Some people might be interested in "wow math sure can do some funky stuff", but others like myself really want to know why. I figure that's also covers a sizable group of us here on Hacker News.

There is no why. It just is. This is the worst thing about being human :) http://www.smbc-comics.com/index.php?db=comics&id=1914

Nice trick. It works in any even base b:

    xy = b((x - b/2) + (y - b/2)) + (b - x)(b - y)
For b = 2 in particular, x - b/2 and x - b/2 are the negative 1's complements of x and y, and b - x and b - y are the 2's complements. More generally, they are the same kinds of complements generalized to base b.

Because of that symmetric relationship with complementation, I suspect there is a conceptual proof waiting to be found. By conceptual I mean something that isn't just blind formula crunching. That would get us much closer to "why".

Re: Fun with math: Dividing one by 998001 yields a surprising result

#88

Post by skeptical »

saraid216 wrote: post #65

I just want to repeat bdg's appreciation for the people who are explaining the actual theory, which is the interesting part. Funky results from arbitrary arithmetic is just a step short of numerology and while it's nifty in a stage magic kind of way, it's a little sad overall when you have no idea why that's the way it is.

Don't underestimate stupidity. Only a tiny percentage of people want to know why that's the way it is. The big majority will call you names if you attempt to discuss the maths. Stupidity is more popular and more appealing than reason. Want to be popular, be stupid and appeal to the stupid.

Re: Fun with math: Dividing one by 998001 yields a surprising result

#89

Post by masak »

akkartik wrote: post #57

What happens after 999? It wraps around back to 000! This is cool.

Well, being a rational number, it has to wrap around somewhere. And since 999 + 001 == 000 (with the caveats for carries that people have explained elsewhere), it makes sense for it to wrap around at that point.
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