Help with Mathematical Concepts, Not Arithmetic (page 8)

talesin

It's not quite on topic, but .... I'm REALLY enjoying this thread.

I'm learning, and seeing that many have achieved the dream of education. And I now realize, that I no longer feel bitter that those opportunities were denied me.

:))

tal

Farkel

Not quite math, but number-related and one of my favorites:

"There are only 10 types of people in the world. Those that understand binary and those that don't."

Farkel

talesin

I love it! Day-yum, I remember typing what seemed like a million keycards for one teeny FORTRAN program ... OY!

memories

Hey, MUSIC is all about math, too. A lot of people don't realize that.

t

00DAD

Farkel, you told it wrong:

There are only three kinds of people in the world, those that understand math and those that don't!, or ...
There are only 11 kinds of people in the world, those that understand binary and those that don't!

Sheesh, don't blow the punch line dude!

kepler

Say, someone brought up Fermat...

Here's a variation on a theme.

3 x 3 + 4 x 4 = 5 x 5 And it's observable as a right triangle.

Was surprised to note one night while out for a jog that

3x3x3 + 4x4x4 + 5x5x5 = 6 x 6 x 6.

I was anxious to get home to check what would happen if I went to the next level.

It didn't work. But maybe it was telling something anyway.

Consider that A^2 + B^2 - 2AB cos theta = C^2. That's the general two dimensional formula formula for triangles. With right triangles (theta =90 degrees) the cosine expression vanishes. And then when you draw triangles on spheres, the angles do not always add up to 180 degrees. I can't visualize four dimensional space, but if I could, I think the rules for right angled geometry would be different from two and three dimensional objects.

Quendi

For all you people who are so interested in Fibonacci numbers I have only this to say:

x 2 = x + 1

Quendi

Razziel

Several experts have expressed the opinion that the way he proved it, however, was not what Fermat had in mind - so, in that sense, the solution is still lost.

I think very few believe fermat ever proved it.

I have been working the last couple of months with a friend on Fermat's Last Theorem in our spare time, and we think a solution with elementary arithmetic operations might indeed exist. And we've found an interesting way to reframe what the equation is fundamentally describing using the Fundamental Theorem of Arithmetic. Just by normalizing the equation and graphing it, it is apparent an integer solution is unlikely for n>2. If you graph the normalized equation, n=1 is linear, n=2 is the unit circle, and as n increases the graph quickly conveges towards a square. I've developed a spreadsheet that given a value for C and a value for n, I can tell you the finite domain where an integer solution would exist. We are now looking for ways to eliminate that finite domain.

That said, this is the most scrutinized mathematics problem of the last several hundred years, so the likelyhood we'll catch something that others did not is low. But it's still fun to try.

Help with Mathematical Concepts, Not Arithmetic

talesin

Farkel

talesin

00DAD

kepler

Quendi

Razziel

james_woods

Razziel

james_woods

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