What do you think about pi - should it exist?

[Patashu]

I've thought about it some more - pi - and I've come to the conclusion that the problem is something of a paradox. Let me explain. When you measure the circumference, you intersect a straightline with the circumference twice. But when you divide the circumference by the diameter, the instances of the diameter around the circumference do not intersect. To me that means the problem is like saying "a circle intersected by its diameter leaves an infinite remainder when its diameter is unable to intersect as it bends around the circumference". The reason this leads me to think of the problem as a paradox is that you can't measure a circle using the diameter without destroying the relationship of the diameter to the circle that makes the circle the circle (I am not that confident in this idea but I will state it as I have).

What I am saying is that the width of the circle is relevant to the final calculation of the problem and that you must calculate the diameter in identical ways to get a meaningful solution (if the diameter intersected with itself as it moved around the circle, your answer would change by at least 2 x value of the line you are using).

Yes, we cannot calculate pi perfectly. That does not mean we cannot derive formulae or methods to approximate or even approach it, as can be seen here: http://en.wikipedia.org/wiki/Calculating_pi
Did you have a point?

 

[MoonlessNight]

What I am saying is that the width of the circle is relevant to the final calculation of the problem and that you must calculate the diameter in identical ways to get a meaningful solution (if the diameter intersected with itself as it moved around the circle, your answer would change by at least 2 x value of the line you are using).

I don't understand what you are saying here? But it seems to be somewhat related to the "problem" that the diameter intersects the circumference in two places and thus should somehow count for "double" when determining circumference.

This really isn't a problem, if I am close to what you are driving at. What I mean is this:

Take a circle of radius 2 and a circle of radius 1 centered at the same point. Draw a line from the center of both circles to a point on the bigger circle. Note that the line intersects with exactly one point from each circle. As you rotate the line around the circle you can draw a bijective (that is to say you touch every point from both circles and never touch more than one point from either circle at any given time) correspondence between the points in the two circles. So the circles have the same cardinality, in some sense have the same "size" of points, thought the bigger one clearly has a larger circumference. Cardinality doesn't correspond to length.

As for pi, it really depends on how you look at numbers to determine whether it should be there or not. Algebraically speaking, it's kind of irrelevant. You can have a closed number system and be able to solve any polynomial you want starting with the integers and adding everything you need without ever hitting pi. Of course you'll still need numbers like the square root of two, but you don't need transcendental numbers like pi.

But geometrically speaking, pi has a very good reason to exist. And once you get into things like Complex Analysis, or multi-dimensional real analysis circles and higher dimensional analogues of circles become very important and so pi becomes very relevant.

As for the number itself and its expansion, that isn't really problematic. Well, I suppose it really screws up the notion of numbers being a (finite) vector space over the rationals, but algebraic closure does that too. As for the "infiniteness" of the expansion, that is only problematic by trying to fit everything into rational terms. Looking at where pi is on the number line, there is no question.

 

[anonymous1515]

Hahaha. What a silly thread. But I love it!

 

[Quintessence]

Why should'nt Pi exist?

 

[anonymous1515]

Why should'nt Pi exist?

Oof. Thats a toughy.

 

[monkeypsycho62]

How could we make it not exist?

"GWAAAH!!! Curse you, vile number! I banish you from existence!"

*stabs a circle*

 

[Patashu]

"Imagine...a universe with no pi."

'So what does (gamma(1/2))^2 equal?'

"..."

 

[Gottservant]

You are laughing but I think pi must be the result of sin.

Like it is a sin to divide 22 by 7.

 

[Jebediah]

You are laughing but I think pi must be the result of sin.

Like it is a sin to divide 22 by 7.

This is your mind on Christianity...

 

[Morcova]

LOL

Ouch... I think i hurt something.

 

[Morcova]

You are laughing but I think pi must be the result of sin.

Like it is a sin to divide 22 by 7.

LOL

What is your highest level of education?

 

[Patashu]

You are laughing but I think pi must be the result of sin.

Like it is a sin to divide 22 by 7.

 

[Washington]

As for the infinite points on a circle, in the theoretical sense this is quite true, but in our physical world this is not true, or at least need not be.

If one assumes a point cannot be any larger than a single atom, then it would be simple to calculate the number of such points on the circumference of any circle. Take the carbon atom--it's Van der Waals radius (half the distance two carbon atoms can get to one another) is 170 picometers. So if one were to draw a circle one meter in circumference with a carbon pencil there would be 2,941,176,470.6 such points. But, if one could fit the carbon atoms right up next to each other---not really possible--- (C has an atomic radius of 70 pm) there would be 14,285,714,285.7 points.

(a picometer is equal to one trillionth (1/1,000,000,000,000) of a meter)

My question is, why would a god construct a world where one of the most basic geometrical relationships is irrational.

 

[Nathan Poe]

You are laughing but I think pi must be the result of sin.

Like it is a sin to divide 22 by 7.

OK -- why would it be a sin to divide 22 by 7? Is there a sinful math prohibition in the Bible?

 

[Patashu]

As for the infinite points on a circle, in the theoretical sense this is quite true, but in our physical world this is not true, or at least need not be.

If one assumes a point cannot be any larger than a single atom, then it would be simple to calculate the number of such points on the circumference of any circle. Take the carbon atom--it's Van der Walls radius (half the distance two carbon atoms can get to one another) is 170 picometers. So if one were to draw a circle one meter in circumference with a carbon pencil there would be 2,941,176,470.6 such points. But, if one could fit the carbon atoms right up next to each other---not really possible--- (C has an atomic radius of 70 pm) there would be 14,285,714,285.7 points.

(a picometer is equal to one trillionth (1/1,000,000,000,000) of a meter)

My question is, why would a god construct a world where one of the most basic geometrical relationships is irrational.

My answer would be that you can't have it any other way. You can't make a circle without using pi; similarly, you can't have euclidean geometry without allowing for circles to be made. In fact, given that pi shows up in other equations and places, not just circles, it's inescapable. You'd have to ditch math, geometry, the works entirely to escape pi.

 

[Gottservant]

LOL

What is your highest level of education?

You think my highest level of education is relevant?

I know better.

 

[Gottservant]

"Let your yes be yes and your no be no for whatever is more than these is of the evil one" - Jesus

Is pi infinite? Yes or No? Yes, in principle... but no because in reality you can't calculate it? That contradicts the above and is therefore sin.

Therefore it is a sin to divide 22 by 7.

God does not create confusing relationships. It is written "God is not the author of confusion but of peace" 1Co 14:33 . I therefore am justified in saying that just because you have a sign like "divide" doesn't mean you can always use it.

Let's see how you handle my scriptures...

 

[quatona]

You are laughing but I think pi must be the result of sin.

Like it is a sin to divide 22 by 7.

This may easily become post of the year at FSTDT.

 

[anonymous1515]

"Let your yes be yes and your no be no for whatever is more than these is of the evil one" - Jesus

Is pi infinite? Yes or No? Yes, in principle... but no because in reality you can't calculate it? That contradicts the above and is therefore sin.

Therefore it is a sin to divide 22 by 7.

God does not create confusing relationships. It is written "God is not the author of confusion but of peace" 1Co 14:33 . I therefore am justified in saying that just because you have a sign like "divide" doesn't mean you can always use it.

Let's see how you handle my scriptures...

This is a joke. It has to be, right? Just because something confuses you it's a sin? Wow...that's an excellent message for young kids. "Kids, don't bother trying to figure things out for yourselves. If you get confused, you're gonna go to hell. It's safer to be ignorant."

 

[Jebediah]

"Let your yes be yes and your no be no for whatever is more than these is of the evil one" - Jesus

Is pi infinite? Yes or No? Yes, in principle... but no because in reality you can't calculate it? That contradicts the above and is therefore sin.

Therefore it is a sin to divide 22 by 7.

God does not create confusing relationships. It is written "God is not the author of confusion but of peace" 1Co 14:33 . I therefore am justified in saying that just because you have a sign like "divide" doesn't mean you can always use it.

Let's see how you handle my scriptures...

Usually with a bic lighter.