A hypothetical value of pi

[Freethinker]

Well Tim, you are close. I am messing with heads here. Being the Devil's (god's?) Advocate, just for kicks.

 

However WebFeet, some people actually believe in the inerancy of the bible. That although men may have done the physical writing, it is perfect as from god him/her/it's self. Thus it can not be a mis-quote.

 

But quite simply, as with many other parts of the bible, it is just plain WRONG.

 

As to my own thoughts on pi, I like it with ice cream.

 

Or... the Japanese researches have calculated 50 billion decimal digits of Pi, that's about 8 digits for every person in the world today.

 

ftp://www.cc.u-tokyo.ac.jp/README.our_latest_record

 

But I prefer to use the pi buttom on my calculator lol.

[Wannabe Genius]

But quite simply, as with many other parts of the bible, it is just plain WRONG.

My apologies freethinker, for a moment there I thought you were being serious about the bible.

 

Personally I have serious problems with god, religion and the bible, especially others forcing their religion onto me. I have my own religion, created from 12 or more years studying music and 4 years studying the philosophical history of it. God has no place in it other than to provide me with material for "proving" it wrong. well, offering a choice anyway... Unlike other religions, I have no desire to force my beliefs onto others. If asked, I tell them what I believe. if they show an interest I explain. after that, it's up to them.

 

Ok. ramble over and back to pi. hmm, I had no idea that the current value of pi was so hi. I carry 33.55 million digits on my linux desktop. But I do require that level of precision for some calculations. Although using such a length takes up a hell of a lot of time. There is a reason for it, but that is for when my work is published some time down the line.

 

As to my own thoughts on pi, I like it with ice cream.

I was wondering when someone was going to say that. I've never had a discussion without it. (BTW I like mine with custard or fresh cream. Fresh mind, straight from the farm. non of your 6 day old supermarket poison)

 

going back to an earlier post, I stated this:

a) It is a "circular" number, as is Pi

B) It is a number of infinite length, as is Pi

c) It has musical significance, As does Pi

d) Whilst being imperfect itself, it forms geometric perfection

e) -->

Nobody has yet commented on this so I would like to ask the following.

 

How accurate would be the possibility of such "circular" numbers be to offering an alternate value of pi? and what other cumbers exist that have this circular reference and fit the above specification? Do people agree with this possibility?

 

Martin

[Cleroth]

We still can't determine the value of pi since:

a curve is composed by atoms, we would need to calculate the atom's mesure to know how much is pi. since we dont know the exactly mesure of an atom.................we cant find pi.

 

'answer' for the big question:

of course pi would be diferent in other dimensions, if atoms had a diferent size. even in our world there are diferent size of atoms, there fore there are many 'pis'. ex: there would be a pi for paper,metal...etc....

 

if there is really such another dimension then atoms dimension would be equal though...

 

another thing...if you want to know if other dimensions really exist then i will try to explain has better has possible:

 

| <---- imagine this is 1 mm of paper in first dimension

<---- this is 1 mm of metal in second dimension

- <----- this is the 2th mm of the paper in the first dimension

~ <------- this is the 2th mm of the metal in the second dimension

 

then it will be like:

|-~

 

in other words:u cant see the other dimension since its between the 2 mm of the paper, same for the second dimension

[Freethinker]

pi is the ratio between the circumference and the radius/ diameter for a given circle on a single Cartesian planar surface. When you add a 3rd dimension, it is no longer a Cartesian planar surface and I would think, pi is no longer relevant. I do not think that pi itself would then change.

[Freethinker]

Originally posted by: Cleroth

We still can't determine the value of pi since:

a curve is composed by atoms, we would need to calculate the atom's mesure to know how much is pi. since we dont know the exactly mesure of an atom.................we cant find pi.

 

'answer' for the big question:

 

of course pi would be diferent in other dimensions, if atoms had a diferent size. even in our world there are diferent size of atoms, there fore there are many 'pis'. ex: there would be a pi for paper,metal...etc....

 

pi is not dependant upon the "depth" of the boundary (atoms). It is based on singular reference location. e.g. the extreme outside of an object, regardless of what materials/ atoms it is compossed of. It functions in pure mathematics, which has no atom width to deal with.

[Wannabe Genius]

Hi

 

Its been a while since I last posted, but in the meantime, I have spent a bit of time considering this question and, from a musical perspective at least I believe I have an answer.

 

Within music, there exists two equations attributed to the author Charles E.H. Lucy, the very man who asked me this particular question. Although they are attributed to Lucy, they relate to the natural scale of music and were first discovered by John Harrison in the 17th century. These equations, known as the arger and lesser notes are as follows:

 

Larger = 2^(1/(2*pi))

Lesser = 2/( ( larger )^5 )^( 1/2 )

 

now, seeing as the lesser note is built from the larger, we can essentially ignore this value for now.

 

If we wish to have an "Alternate" value for pi, the larger note ( 1.116633 ) would change considerably and would render the entire scale useless. In order for any other value to create a useable scale, a working range would have to be created.

 

In order to create the equations, I decided on a range of 1.1 to 1.14. This would essentially gaurantee that a workable solution "would" always be found.

 

When I initially began calculating the equations I came up with the following:

 

x = pi^y where y = 1/(pi/a)

 

In this equation, pi can have any value required.

 

a is a positive integer greater than 2 and less than 1,000.

 

this is inserted into the larger ratio as follows:

 

Larger = 2^(1/(2*x))

 

In order to test this equation I constructed a small c++ based program which calculated a range of values.

 

This told me two things.

1. pi would always have to be greater than 1
   
2. not every value worked

In this lay a probem. I was looking for one simple equation which would cover all values. Unfortunetly this equation is as elusive as the unified theory of everything. Instead, I had to compromise in that rather than having one equation, there actually exists 3 seperate equations where if the first doesn't work, the second or third invariably does.

 

the second and third equations are:

 

2) x = ( ( pi^2 )^n )^y

3) x = ( ( pi/2 )^n )^y

 

y is the same as in equation 1.

 

n is an integer less than or equal to 100. If a number does not work prior to n reaching 100, it probably never will.

 

Again I tested this equation using a small c++ program similar to the one I wrote for the first equation.

Out of the 9,999,001 values I tested between 1 and 10,000, only four values would not evaluate true.

 

To test these, I worked in incremental steps of 0.001

 

The only values to fail all attempts are:

 

[*]1

[*]133.865

[*]1348.9

[*]1661.77

 

Interestingly, although I initially ran this under Linux, I also tested it under windows. Windows did not recognise these values as being unsolveable.

 

This program is available via email to anyone wishing to have a look at the code which is ansi compliant and compiles ok on both windows and linux. I am assuming that it will compile ok under Mac as well but as I've never used one, I cannot be certain.

 

I've not even considered any use for this outside of music but if anyone can think of one, I would be interested to hear them.

 

Still pretending to be clever!

Martin.