# Irrational Pi Defrocked

### #1

Posted 11 March 2005 - 08:00 PM

FORMULA: sqrt area/ sqrt pi ^ = radius; thus, radius * pi = area.

Please note change in formula from that originally given.

The formula gives the radius to any circle of a prescribed area - regardless of any and all known pi values as might be applied. What do you think?

"All things number and harmony." - Pythagoras

### #2

Posted 11 March 2005 - 08:16 PM

___the asterisk(presumably indicating multiplication) following the caret (presumably indicating exponentiation) relates pi (presumably a multilicand) to no multiplier. Something seems missing.

___I add, that if you use 22/7 as the approximation for pi & re-write it in base twelve as 1A/7 then do the division, you arrive at a repeating base twelve decimal & not a transcendental base ten decimal.

___Very interesting.

### #3

Posted 12 March 2005 - 01:33 AM

"All things number and harmony." - Pythagoras

### #4

Posted 14 March 2005 - 05:19 AM

As far as I know it wasn't Euler that proved pi is irrational, Pythagoras had realized it must be but he didn't exactly like to admit there could be such a thing as an irrational number.

### #5

Posted 14 March 2005 - 07:15 AM

it seems to contradict the traditional, and by definition right, A=pir^2...

Bo

### #6

Posted 14 March 2005 - 08:38 AM

The square of pir?A=pir^2

I think a part of the trouble is that it's tricky to write formulae in ASCII.

### #7

Posted 14 March 2005 - 09:06 AM

The square of pir?

I think a part of the trouble is that it's tricky to write formulae in ASCII.

It looks to me like they trying to say:

radius = sqrt(area) / sqrt(pi^2) or IOW

The radius is equal to the square root of the area over the square root of pi squared.

Of course the square root of any number squared is just the absolute value of that number so I don't see how that's supposed to reduce pi to a rational entity, the square of pi squared is still pi. Then again, sinc this makes no sense at all maybe they're trying to say something else.

### #8

Posted 14 March 2005 - 09:10 AM

I add, that if you use 22/7 as the approximation for pi & re-write it in base twelve as 1A/7 then do the division, you arrive at a repeating base twelve decimal & not a transcendental base ten decimal.

base twelve decimal: I would suggest to call that a twelfthal...

One can certainly find rational values, arbitrarily near pi and periodic, in whichever base one chooses.

edit: try for example 3490/1111

### #9

Posted 14 March 2005 - 09:15 AM

Strictly, the square root of a number squared can be either + or - the same number but this is a detail.Of course the square root of any number squared is just the absolute value of that number so I don't see how...

According to my interpretation the formula would be equivalent to the usual one. Your interpretation would give the radius as pi times the normal one apart from sign.

### #10

Posted 14 March 2005 - 09:23 AM

Strictly, the square root of a number squared can be either + or - the same number but this is a detail.

According to my interpretation the formula would be equivalent to the usual one. Your interpretation would give the radius as pi times the normal one apart from sign.

How can the square root of any number squared be negative? Isn't the square of any number always positive? Isn't the square root of any positive number positive itself? I was taught that this was exactly what the absolute value function meant. Does the absolute value function actually mean something else?

### #11

Posted 14 March 2005 - 09:36 AM

YesIsn't the square of any number always positive?

Yes and no:Isn't the square root of any positive number positive itself?

Any number has two square roots, and three cubic roots, and four fourth roots etc...

It's not a good definition of absolute value, which means what you mean by it.I was taught that this was exactly what the absolute value function meant. Does the absolute value function actually mean something else?

### #12

Posted 14 March 2005 - 09:48 AM

edit: it was a moment of delirium, while typing I switched thinking of a positive square to a real one. Pure imaginary has a real and negative square.

### #13

Posted 20 March 2005 - 05:30 PM

The problem originally stated on the Australian forum considered the turning of a circular metal disc to give an area of precisely 16 units. What radius would the mechanical engineer give to his machinist?

"All things number and harmony." - Pythagoras

### #14

Posted 20 March 2005 - 06:02 PM

The formula gives the correct area to any circular plane regardless of the pi value employed.

No it won't. Are you really trying to say that someone could use 4, 10 or 100 as the value of pi?

### #15

Posted 21 March 2005 - 02:18 AM

Show us how. Like St. Thomas, I shall believe when I shall have passed my fingers through the holes in his hands.The formula gives the correct area to any circular plane regardless of the pi value employed.

We haven't even been totally sure of what the formula is exactly.

### #16

Posted 24 March 2005 - 12:27 AM

Show us how. Like St. Thomas, I shall believe when I shall have passed my fingers through the holes in his hands.

We haven't even been totally sure of what the formula is exactly.

OK....employing the given formula requiring the radius for an area of 16 units to the circular plane. I'll employ several different pi values, starting with the irrational pi and followed by that of 355/113 and that followed by the rational value of 256/81. I myself use the finite pi value of 3.1640625.

sqrt area/sqrt 3.14159265359 pi = 2.25675833419 radius; r^ pi = 16 area;

sqrt area/sqrt 3.14159292035 pi = 2.25675823838 radius; r^ pi = 16 area;

sqrt area/sqrt 3.16049382716 pi = 2.25 radius; r^ pi = 16 area;

sqrt area/sqrt 3.1640625 pi = 2.24873078056 radius; r^ pi = 16 area.

"All things number and harmony." - Pythagoras

### #17

Posted 24 March 2005 - 06:06 AM

But what's that got do do with the radius and the circumference of a circle? It will work with any rational value of a, even if a-square is quite different from pi. How about 0.0723?

pi = 0.0000006103515625, area = 16, radius = 5120

How's that, for a perfect circle? Almost worthy of Giotto!!!