Radical Edward
January 10th, 2004, 1:56 PM
does anyone here know anything about clock mathematics? I have come across it a few times, and it seems simple enough;
rather than the numbers being on a line, they are on a ring, like a clock is 1-2-3-4-5-6-7-8-9-10-11-12
so when we are at 10 on a 12 hour clock, and we add 4 (hours), then the time we get is not 14, but 2, and so on. I believe this is used in encryption, and for solutions to elliptic equations (and probably other things now that wiles solved fermat's theorem)
however I was wondering about this, has anyone done this before:
instead of numbering from 0 or 1 to n, how about numbering from -n to 0 or -1 (depending on if you want a zero or not. the neat Idea I had about doing this would be for roots, since the root of a negative number gives an imaginary number we would need another axis. so rather than a clock, you could have a tube and do maths on that. or, if you wanted to be really neat, you could convert the i-axis into a clock too, and get a torus out of it.
what would the mathematical implications be of trying to perform maths on this construct? are there other possible topologies, other than tubes and toruses? how about a twist in the torus, so that say we have our i-clock starting at i=0 on the real number n, and it ends on n+1?
I just thought this would be fun to play with anyway if anyone wants to think about it.
rather than the numbers being on a line, they are on a ring, like a clock is 1-2-3-4-5-6-7-8-9-10-11-12
so when we are at 10 on a 12 hour clock, and we add 4 (hours), then the time we get is not 14, but 2, and so on. I believe this is used in encryption, and for solutions to elliptic equations (and probably other things now that wiles solved fermat's theorem)
however I was wondering about this, has anyone done this before:
instead of numbering from 0 or 1 to n, how about numbering from -n to 0 or -1 (depending on if you want a zero or not. the neat Idea I had about doing this would be for roots, since the root of a negative number gives an imaginary number we would need another axis. so rather than a clock, you could have a tube and do maths on that. or, if you wanted to be really neat, you could convert the i-axis into a clock too, and get a torus out of it.
what would the mathematical implications be of trying to perform maths on this construct? are there other possible topologies, other than tubes and toruses? how about a twist in the torus, so that say we have our i-clock starting at i=0 on the real number n, and it ends on n+1?
I just thought this would be fun to play with anyway if anyone wants to think about it.