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May 10, 2006

Pi = 3

3.14159...add infinitum.

Where does it all end and who in their right mind would want to find out?
Even the best computers haven't calculated Pi to the last decimal so why should we mere mortals even try?

But if you must, there are essentially 3 methods to calculate Pi to many, many decimals.


1. One of the oldest is to use the power series expansion of atan(x)
= x - x^3/3 + x^5/5 - ... together with formulas like pi =
16*atan(1/5) - 4*atan(1/239) . This gives about 1.4 decimals per term.


2. A second is to use formulas coming from Arithmetic-Geometric mean computations.
They have the advantage of converging quadratically, i.e. you double the number of decimals per
iteration.
For instance, to obtain 1 000 000 decimals, around 20 iterations are sufficient. The disadvantage is
that you need FFT type multiplication to get a reasonable speed, and this is not easy to
program.


3. The third, and perhaps the most elegant in its simplicity, arises from the construction of
large circle with known radius. The length of the circumference is then divided by twice the radius
and pi is evaluated to the required accuracy.

It sure seems like a lot of work for such little (real) return. At least that's what the good folks of the Indiana Legislature thought in 1897 when House Bill No. 246 was introduced.

HB 246 was introduced as an easier, more efficient way to square a circle and it basically amounted to,

Pi = 3.

On January 15, 1897 Edwin J. Goodman of Solitude, Indiana introduced bill #246 to the Indiana House of Representatives that not only legislated \pi =16/sqrt(3) > 9, but also squared the circle and trisected an arbitrary angle.
The bill was passed back to the general assembly by the Committee of Education with the recommendation that it be passed. It was passed on February 5, 1897 with a vote of 67 to 0.

Then, it went to the Indiana Senate. By accident, a mathematics professor from Purdue, C. A. Waldo, happened to be attending the debates on the day the bill was read to the Senate. Needless to say, the professor quickly re-educated the members of the senate on the value of Pi.

Why would they try something like that? Simple.

An ex-teacher from the eastern part of the state was saying: 'The
case is perfectly simple. If we pass this bill which establishes a
new and correct value for pi , the author offers to our state
without cost the use of his discovery and its free publication in
our school text books, while everyone else must pay him a royalty.'"

But that only works if the calculation is correct. As Waldo pointed out.


The roll was then called and the bill passed its third and final
reading in the lower house. A member then showed the writer [i.e.
Waldo] a copy of the bill just passed and asked him if he would like
an introduction to the learned doctor, its author. He declined the
courtesy with thanks remarking that he was acquainted with as many
crazy people as he cared to know.


Here's how Pi = 3

x = (Pi+3)/2

2x = Pi+3

2x(Pi-3) = (Pi+3)(Pi-3)

2Pix-6x = Pi^2-9

9-6x = Pi^2-2Pix

9-6x+x^2 = Pi^2-2Pix+x^2

(3-x)^2 = (Pi-x)^2

3-x = Pi-x

Pi = 3


By that logic, Pi does in fact equal 3...if you're a state legislator.

( From Sci.Math )


- Joatmoaf -





May 10, 2006 at 09:03 PM | Permalink

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Comments

What's Pi in binary?

Posted by: libmeister at May 11, 2006 5:56:29 PM

libmeister,

I believe that if Pi were 3 then the value can be represented (0-2)

Posted by: Joatmoaf at May 11, 2006 7:39:55 PM

Joatmoaf,

Huh??

*Returns to eating a banana and learning sign language from Koko, the Gorilla*

Posted by: Kiki B. at May 11, 2006 11:45:31 PM

I call bullshit on the legislature thing. Show me proof. It's more likely akin to this: http://www.snopes.com/religion/pi.htm

As in, an urban legend.

Posted by: Silent Ounce at Apr 6, 2007 3:42:45 PM