New Math Formula

Tormod · 10-06-2002

In the meantime (for those of us who don't quite get the gist of this conversation), here is a couple of links:

A History of Pi

How to compute 1 billion digits of Pi

...and then we can probably fly through this one:
Pi Trivia Game

Eugene · 10-06-2002

And a great deal more, Tormod - going back some 4 millenia. Correlating the line and arc to a common point of origin is probably one of the most intriguing problems ever encountered by mathematics.
Thanks for the links....

Eugene · 10-06-2002

Capt. Obvious, I'd have to see the fraction 3.1416 derives from to show that it is a rational number.

If you are referring to the quadrature formula, sqrt pi (radius), it most certainly does give the side of a square with the same precise area as that of the given circle - and whether the pi ratio be rational or irrational.

Is this what you're referring to?

Captain Obvious · 10-07-2002

umm... sure... 3.1416 = 31416/10000

I suggest you try ridiculous numbers in your equation.

Pi r^2 = (sqrt(Pi) r)^2

Pi = 4, r = 1
4 * 1 = (2 * 1)^2 = 4

Pi = 25 r = 3
25 * 9 = (5 * 3) ^2 = 225

in fact for all positive values of x and all values of y
x * y^2 = (sqrt(x) * y)^2

And no, it does not work for arbitrary Pi, as your error is described by (x - Pi)/Pi where x is your arbitrary value of Pi.

There IS an exact value of Pi, we just don't use it, as we are willing to accept error. For instance 3.14 mostly correct, it only has error of around .05%.

Am I making any sense at all?

Eugene · 10-08-2002

Captain Obvious,

Yes, I think you make a great deal of sense, but for the most part confirming that pi is arbitrary, even by the use of ridiculous pi ratios. More rationally (if you'll excuse the expression) the ratio given above, 355/113, shows more succinctly that it is arbitrary by reason that we cannot discern empirically between it and the traditionally accepted irrational pi ratio.

The rub of the whole thing is IMHO that we have no documented proof for curvature of what we assume to be the straight line. And surely, just as there can be no such thing as the perfect circle, neither can there be the absolutely straight line. It's more than a philosophical question, for we do also have a finite pi ratio, 256/81, that derives from a finite mathematic progression, a discrete and irrefutable algorithm with finite upper and lower bounds. Though considerably wide of the irrational pi, it cannot be disregarded for so long as pi is shown to be arbitrary.

Thanks for showing the 3.1416 fraction. I find that to be extraordinarily interesting. Let's keep in touch - though I'm not always able to respond as readily as I may wish.

Robust · 12-09-2004

Eugene, t6he tringlature formula you give is actually a 2-part formulae:

r*sqrt2 *pi/4*sqrt2 is the complete formulae, where the 1st part gives chord distance to the quadrant. The 2nd part is a conversion factor giving distance on the arc. A most useful formulae I use extensively.

"All things number and harmony." - Pythagoras

Robust · 12-10-2004

Eugene, hello again! You mention that the trianglature formulae has created quite a stir in science quarters the world over. The only place I've heard it mentioned is on a somewhat remote science forum, and which is really more of a chat room than science. However, I too find the formulae most intriguing and applicable as well in that it correlates distance on the circle quadrant by both its arc and chord length - thus area of the closed continuum analyzed in such manner as to be defined by a whole number or ending decimal.

It's all a very intriguing prospect indeed and frought with much controversy, as one might expect. Any source info you or others might give on this subject would be greatly appreciated. I'll give a followup as I can.

"All things number and harmony." - Pythagoras