According to Adam Spencer on Triple J, today is "International Π Approximation Day".

So here's my approximation:

About three.

So here's my approximation:

About three.

6 comments | Leave a comment

International Pi Approximation Day - Sum Res Cogitans

Using Occam's Razor to shave Schrödinger's Cat

22 July 2004 @ 07:47 am

International Pi Approximation Day

According to Adam Spencer on Triple J, today is "International Π Approximation Day".

So here's my approximation:

About three.

So here's my approximation:

About three.

6 comments | Leave a comment

6 comments —

I disagree. I think it's three and a bit. If you just say 'about three', you could also be referring to the number e.

Well, I was only being *approximate*.

In most applications in my day-to-day life in which I use numbers, rounding to the nearest integer is usually good enough. And lets just assume that, with money, I work in the unit "cents" not "dollars".

I have never found a practical use for knowing the value of Pi.

And I suspect that's the case for the vast majority of people.

However, I am appreciative of the minority of people that work with these kinds of numbers every day, like engineers.

In most applications in my day-to-day life in which I use numbers, rounding to the nearest integer is usually good enough. And lets just assume that, with money, I work in the unit "cents" not "dollars".

I have never found a practical use for knowing the value of Pi.

And I suspect that's the case for the vast majority of people.

However, I am appreciative of the minority of people that work with these kinds of numbers every day, like engineers.

I spent altogether too much time working with Pi at uni determining axial rotations of molecules. Especially since I was more interested in bacteria than metal complexes.

355/113 = 3.14159292

The Chinese had the best approximation. The next best approximation is 103993/33102 which is just a bitch to remember.

The first set of numbers can be generated by remembering the sequence 3,7,15,1 (which is the denominators of the continued fraction of π. Similar sequences can be fairly trivially generated for any number) which is basically 2n+1 where n is taken modulo 4 (i.e. consisting of the numbers 0-3, so 1,2,3,0).

From that sequence of numbers you generate the following table:

where each entry is equal to the top number multiplied by the previous column and added to the column before that.

The Chinese had the best approximation. The next best approximation is 103993/33102 which is just a bitch to remember.

The first set of numbers can be generated by remembering the sequence 3,7,15,1 (which is the denominators of the continued fraction of π. Similar sequences can be fairly trivially generated for any number) which is basically 2n+1 where n is taken modulo 4 (i.e. consisting of the numbers 0-3, so 1,2,3,0).

From that sequence of numbers you generate the following table:

3 | 7 | 15 | 1 | ||
---|---|---|---|---|---|

0 | 1 | 3 | 22 | 333 | 355 |

1 | 0 | 1 | 7 | 106 | 113 |

where each entry is equal to the top number multiplied by the previous column and added to the column before that.