Random Question: Pi

[Zionoxis]

I Googled a bit and could not find it, so I am borrowing your brains for my mindless curiosity. Is there a mathematical formula to replicate pi exactly? I was curious about this as I was thinking about my calculator and how they programmed it to utilize pi as an infinite digit number (or if they cheated and just memorized the first 20 digits or something similar)

 

[pjoa09]

hanh? 22/7?

edit: I am wrong!

 

[Awaken]

http://www.csgnetwork.com/picalc.html

http://www.devhardware.com/forums/t...-to-calculate-pi-need-more-digits-165634.html

 

[Meer]

So, really high precision meter sticks?

 

[Dapper Dan]

Pretty sure they've just programmed pi into your calculator. Calculators are only accurate up to a certain number of digits, anyways.

 

[A22]

I've once read that pi digits are completely random.

 

[Moocow]

Well, you could perfectly measure the circumference of a perfect circle and divide by the circle's diameter.

Or this:
http://en.wikipedia.org/wiki/Pi#Estimating_the_value

 

[Zionoxis]

Is it bad that the simple fact that wiki stated it was impossible to reproduce made me all the more interested?

 

[WhatTheFunction]

Since pi is irrational there will be nothing to represent it exactly. That's the point of it being irrational. It's also infinite.

*Edit: By 'nothing' I mean that the definition of an irrational number is that it can't be expressed by an exact quotient. Obviously values like the sqrt(2) are irrational but as you can see you can express it just not in a fraction. So, no, pi won't ever be expressed exactly. There are still scientists discovering digits of pi as we speak.

 

[Jah]

Here's a nice page for mathematics :

http://mathworld.wolfram.com/PiFormulas.html

 

[BigApplePi]

I've once read that pi digits are completely random.

I'm not sure the answer to that is known, but I didn't google.

How is "random" to be defined? The expansion can't be totally random if something determines it. It is determined by a relationship between the circumference of any circle to its diameter.

 

[whatstheMATTER?]

Pi definitely provides a springboard for philosophical musings on the mathematics of nature, I guess like most constants. To answer your question though, no there isn't, given that it is a ratio for a specific geometric phenomenon, and nothing more. A more interestingly ubiquitous ratio is the Golden Ratio.

btw, I love number theory.

 

[Otherside]

There is an exact mathematical solution for Pi. It involves an infinite series, but it exists.

 

[Otherside]

This guy solves it in less than 30 seconds.

http://youtu.be/eaiF1RExTUw

 

[Otherside]

There is an exact mathematical solution for Pi. It involves an infinite series, but it exists.

Not joking about this though.

 

[Otherside]

The problem with Pi is that if it is an irrational number (which is still the prevailing theory), then it is saying that a perfect sphere cannot exist in the world of quantum physics.

Alternatively, it could be the problem with quantum physics.

 

[whatstheMATTER?]

I was going to say that trying to understand the nature of Pi has returned some interesting mathematics, like Leibniz's formula, its modifications, infinite series, leading to cantor's work and a subsequent plateau. But now that we know its nature, we see that it is unremarkable in its transcendental properties, except for the fact that it is that specific ratio, which has relations to any explorations affected by it, macro to micro.. orbits always have imperfections or wobbles, particles tend towards a sphere but measurements both physical and theoretical are still far from ideal. Yea... dunno what else to say.

 

[BigApplePi]

There is an exact mathematical solution for Pi. It involves an infinite series, but it exists.

One has to be careful about the word, "infinity." Does is really exist?

 

[BigApplePi]

Pi definitely provides a springboard for philosophical musings on the mathematics of nature, I guess like most constants. To answer your question though, no there isn't, given that it is a ratio for a specific geometric phenomenon, and nothing more. A more interestingly ubiquitous ratio is the Golden Ratio.

btw, I love number theory.

Can we define, "The Golden Ratio"?

Yep to number theory. We can define the natural numbers, 1,2,3,4,...,
but their relationships in such strange ways seem to defy any randomness among them. Are we to expect this or not to expect this?

 

[Otherside]

Can we define, "The Golden Ratio"?

Yep to number theory. We can define the natural numbers, 1,2,3,4,...,
but their relationships in such strange ways seem to defy any randomness among them. Are we to expect this or not to expect this?

Isn't the "golden ratio" just the ratio of a rectangle's short side/long side dimensions? As I remember, there isn't anything scientifically or mathematically important about it. Not really similar to Pi because Pi is constant for all spheres.

 

[Otherside]

One has to be careful about the word, "infinity." Does is really exist?

Well, there are a lot of real phenomena that are defined by infinite series functions, and that brings in the aspect between what we can measure and what can exist. A complex tone will mathematically have an infinite number of harmonics, but at some point their amplitude will fall below the noise floor of the equipment we use to analyze them.

I've crossed the line from particles to waves and there's nothing original about that, but the example isn't totally abstract.

 

[DragonsAreForever]

You lot can have your pi with numbers but mines will have whipped cream.

 

[Vrecknidj]

One has to be careful about the word, "infinity." Does is really exist?

There is an exact mathematical solution for Pi. It involves an infinite series, but it exists.

This is basically correct. There are some problems with interpretations of the word "infinity," but, it's still basically correct.

There are formulas (hundreds of them, actually--see the above post from Wolfram about that) that will generate pi. But, as pi is an irrational number, is is expressed as a non-repeating, non-terminating decimal. Among other things, this just means that there is no final, finitely-numbered decimal position to the number. This doesn't mean that pi isn't exact. Pi is exact. But, if by "exact" you demand a rational number, then your demand is inappropriate.

Many people have trouble wrapping their minds around what irrational numbers mean, but, they're every bit as important, real, functional (pardon all the unintended equivocations on those terms and their math definitions) as rational numbers.

So, in part because pi has "infinitely many" decimal places, the formulas that can be used to calculate it can only provide you with more and more accurate approximations. If you cannot carry out all of the infinite iterations of the formula, then you cannot get to the "last" decimal place. (How handy that there is no last decimal place, right?)

I think the most fun idea here is the juxtaposition that 1) pi has a "definite" value, and that 2) pi has an "indefinite" number of decimal places.

Dave

 

[BigApplePi]

I think the most fun idea here is the juxtaposition that 1) pi has a "definite" value, and that 2) pi has an "indefinite" number of decimal places.Dave

I'd go for "indefinite" over "infinite." What we are talking about is we can always add one more decimal place. That decimal place is accurate and meaningful and real. Yet if the universe is finite, there comes a point where we CAN'T add any more places because the finite universe won't allow it. I don't think any of us will be there when that happens.

 

[Felan]

e < pi but e has more heart and wears cooler shades. Both pi and e are transcendant numbers. Together they are pie, which is yummy in any form. I like e better because e to the x is it's own derivative, that just makes me giddy!

 

[BigApplePi]

e < pi but e has more heart and wears cooler shades. Both pi and e are transcendant numbers. Together they are pie, which is yummy in any form. I like e better because e to the x is it's own derivative, that just makes me giddy!

Pi & e = Pie? That's sacrilege! You think they are transcendental but they are irrational. Your statements need a work around. Pi has rounder connotations. e to the x has to be derived. What's so brave about that?

 

[Paintzee]

Imagine a length, any length approaching zero to approaching infinity. This is the x axis. Now imagine a second length, its only criteria be that it be equal in length to the first length. This is the y axis. These two lengths represent any length in space. If the length is defined as one unit, using Pythagoras theorem the hypotenuse is an irrational number, the square root of two. This length in space must also exist if the other two lengths are absolute, therefore none of the lengths can be absolute. An absolute point cannot exist, only a distribution around a point.

This same argument works for pi.

 

[Vrecknidj]

 

[Vrecknidj]

The various posts here which make connections between numbers and space are themselves potentially suspect.

I'm not convinced that the finitiude of the universe (should the universe turn out to be finite) has anything to do with infinity as a mathematical concept, or indefinitely long decimals, or anything else.

The ability to convert mathematical ideas into spacial representations is a nifty feat for us humans, but it doesn't necessarily represent any facts about the world.

 

[BigApplePi]

The various posts here which make connections between numbers and space are themselves potentially suspect.

I'm not convinced that the finitiude of the universe (should the universe turn out to be finite) has anything to do with infinity as a mathematical concept, or indefinitely long decimals, or anything else.

The ability to convert mathematical ideas into spacial representations is a nifty feat for us humans, but it doesn't necessarily represent any facts about the world.

Agreed. But what was that definition of infinity as a mathematical concept again? I don't recall seeing it.