You mean no one's noticed in the last 2500 years?
EDIT: Well, yes, someone *has* noticed, and a slightly more thorough search of the (online) literature shows that my discovery had already been discovered; I've emailed the professor to let him know I've found it. Science demands no less, of course! Heck, I don't mind independently rediscovering things, at least it means I'm doing something right... but it was fun while it lasted!
This is where I lose just about everyone, but bear with me, I'm kinda excited about this in an übergeeky way.
I love numbers. I do math puzzles for fun. I dallied with Fermat (for all n>2 there are no integer solutions for an+bn=cn) for a while, proving for my own satisfaction the cases for n=3, n=4 and n=5, even after Wiles ended the game once and for all. I independently (re)discovered Newton's method for extracting roots.
Mainly, I've always had an odd fascination with integer solutions to the Pythagorean Theorem, to wit: a2+b2=c2
Anyway, the family of solutions I got interested in are of the form b = a + 1, as in: 32+42=52;
202+212=292;
1192+1202=1692;
.
.
.
I happened to notice a fairly simple ratio between the successive solutions, and forgot mostly about it until this morning when I happened to be talking about math geekery with a friend online. He mentioned Dr. Ron Knott's Pythagorean Triples site, and I looked into the section on consecutive legs (which is the part I was playing with -- a2+(a+1)2=c2 -- and much to my surprise, there's no mention of the ratio, although there are several methods for constructing numbers that will solve the equation. Hmm! says I to myself, and email my findings off to Dr. Knott, fully expecting an email in a week or so saying that yes, this ratio was first noticed by (so and so) in (seventeen fifty-something) or some other thing like that.
I got a response in a little more than an hour that my discovery appears to be new.
*blinkblink*
He offered to submit it to the Online Encyclopedia of Interesting Sequences under my name with his comments (he makes it sound more like math than I do), and I asked him to please go right ahead because I haven't the faintest idea how to so do.
I guess that says something about The Theorem, if it still has secrets to reveal two and a half millennia after Pythagoras ... I have no idea what it says about me, other than that I have a certain gift for numbers, or I probably have too much time on my hands... or both. :)
This is where I lose just about everyone, but bear with me, I'm kinda excited about this in an übergeeky way.
I love numbers. I do math puzzles for fun. I dallied with Fermat (for all n>2 there are no integer solutions for an+bn=cn) for a while, proving for my own satisfaction the cases for n=3, n=4 and n=5, even after Wiles ended the game once and for all. I independently (re)discovered Newton's method for extracting roots.
Mainly, I've always had an odd fascination with integer solutions to the Pythagorean Theorem, to wit: a2+b2=c2
Anyway, the family of solutions I got interested in are of the form b = a + 1, as in: 32+42=52;
202+212=292;
1192+1202=1692;
.
.
.
I happened to notice a fairly simple ratio between the successive solutions, and forgot mostly about it until this morning when I happened to be talking about math geekery with a friend online. He mentioned Dr. Ron Knott's Pythagorean Triples site, and I looked into the section on consecutive legs (which is the part I was playing with -- a2+(a+1)2=c2 -- and much to my surprise, there's no mention of the ratio, although there are several methods for constructing numbers that will solve the equation. Hmm! says I to myself, and email my findings off to Dr. Knott, fully expecting an email in a week or so saying that yes, this ratio was first noticed by (so and so) in (seventeen fifty-something) or some other thing like that.
I got a response in a little more than an hour that my discovery appears to be new.
*blinkblink*
He offered to submit it to the Online Encyclopedia of Interesting Sequences under my name with his comments (he makes it sound more like math than I do), and I asked him to please go right ahead because I haven't the faintest idea how to so do.
I guess that says something about The Theorem, if it still has secrets to reveal two and a half millennia after Pythagoras ... I have no idea what it says about me, other than that I have a certain gift for numbers, or I probably have too much time on my hands... or both. :)