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The number PI


jarjarbinks

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I always wondered about that number PI, 3,1416...

So many things can be involved with that number that it's kinda strange. Also, why wouldn't we use 3,1416cm as 1 instead of 1cm as 1. wouldn't be easier ?

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I always wondered about that number PI, 3,1416...

So many things can be involved with that number that it's kinda strange. Also, why wouldn't we use 3,1416cm as 1 instead of 1cm as 1. wouldn't be easier ?

Misunderstanding. No worries.

Ok, so you want to make the centimeter "pi". "Pi" what? And then, if you made a circle with the diameter (or radius, take your pick) value of "Pi", what is the circumference?

:)

It is not an artifact or error of our system of measurement or some problem with numbers or the decimal/base ten system. It's a fundamental relationship that pervades all number systems.

Edited by onefourfour
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Misunderstanding. No worries.

Ok, so you want to make the centimeter "pi". "Pi" what? And then, if you made a circle with the diameter (or radius, take your pick) value of "Pi", what is the circumference?

:)

It is not an artifact or error of our system of measurement or some problem with numbers or the decimal/base ten system. It's a fundamental relationship that pervades all number systems.

maybe not pi = 1cm , but just that 1 would be pi.

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maybe not pi = 1cm , but just that 1 would be pi.

If the radius of a circle is Pi, what is the circumference?

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If the radius of a circle is Pi, what is the circumference?

It's the crust to hold the Pi filling. :w00t:

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Misunderstanding. No worries.

Ok, so you want to make the centimeter "pi". "Pi" what? And then, if you made a circle with the diameter (or radius, take your pick) value of "Pi", what is the circumference?

If pi is the diameter, then the circumference is pi2.

If pi is the radius, then the circumference is 2pi2.

I wonder, why would you wonder about such a basic, easily calculated quantity?

Actually, I don't really wonder. What really makes me wonder is how people live with such an ignorance of even the most basic mathematical facts.

Harte

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Here's one I made earlier

math-cake-pi-305125_zpse1eb064b.jpg

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If pi is the diameter, then the circumference is pi2.

If pi is the radius, then the circumference is 2pi2.

I wonder, why would you wonder about such a basic, easily calculated quantity?

Actually, I don't really wonder. What really makes me wonder is how people live with such an ignorance of even the most basic mathematical facts.

Harte

Perhaps you should wonder a little more. The purpose of the exercise was to demonstrate to the OP that Pi is a function of geometry and not a number you can rub out by making the units this or that.

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If pi is the diameter, then the circumference is pi2.

If pi is the radius, then the circumference is 2pi2.

I wonder, why would you wonder about such a basic, easily calculated quantity?

Actually, I don't really wonder. What really makes me wonder is how people live with such an ignorance of even the most basic mathematical facts.

Harte

Therefore the circumference will be 9.86960440109. This is only an approximate circle of course ;)

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I always wondered about that number PI, 3,1416...

So many things can be involved with that number that it's kinda strange.

Not to me. It's simply a number which falls out naturally from the relationship between a circle's diameter and its circumference.

Also, why wouldn't we use 3,1416cm as 1 instead of 1cm as 1. wouldn't be easier ?

How exactly would this work? If I reach up and pluck a pair of apples from a tree, according to your concept how many apples do I have? Two? 6.2832...? 2/3.1416...?

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Pi is only one representative of the set of irrational numbers.

The set of irrational numbers is larger than the set of rational numbers - the numbers we use everyday.

IOW, there are more irrational numbers between zero and one than there are rational numbers on the entire number line.

Pi happens to be the first such number discovered (no the Greeks didn't know this.) There are infinitely many more - the second cardinal infinity - which is infinitely larger than the first (which corresponds to the "counting" numbers and fractions.)

Harte

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I also always thought pi is a strange number as it's used in so many unrelated equations.

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Pi is only one representative of the set of irrational numbers.

The set of irrational numbers is larger than the set of rational numbers - the numbers we use everyday.

IOW, there are more irrational numbers between zero and one than there are rational numbers on the entire number line.

Pi happens to be the first such number discovered (no the Greeks didn't know this.) There are infinitely many more - the second cardinal infinity - which is infinitely larger than the first (which corresponds to the "counting" numbers and fractions.)

Harte

A genuine question for you Harte:

We can draw a circle with infinite precision - but we cannot calculate the circumference with infinite precision - there is always a discontinuity in the calculated length.

Is this indicative of a fundamental gap in our knowledge, is there an as yet undiscovered value that WILL actually give a finite answer?

Just curious to have your take on this.

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>

I always wondered about that number PI, 3,1416...

So many things can be involved with that number that it's kinda strange. Also, why wouldn't we use 3,1416cm as 1 instead of 1cm as 1. wouldn't be easier ?

Pi is the ratio of the diameter to the circumference. Basically, you can lay the diameter around the circumference 3.14159 times. Or its takes 3.14159 of the diameter (the distance straight across a circle.) to go around the outside of the circle. It has no real numerical value, it is just the ratio between those two.

It is useful in a lot of geometry and above because angle's can be figured as a slice of a circle.I'm sure there are more uses for it, I just don't remember anything else about it. High school was over 20 years ago, and I haven't done any of that since, really.

So I guess to answer your use it as one question, you can't because 1 is an actual value and a real number while Pi is not only an irrational number, but does not represent an actual value, it is just the comparison of one thing to another explained mathematically.

Edited by D.B.Cooper
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A genuine question for you Harte:

We can draw a circle with infinite precision - but we cannot calculate the circumference with infinite precision - there is always a discontinuity in the calculated length.

Is this indicative of a fundamental gap in our knowledge, is there an as yet undiscovered value that WILL actually give a finite answer?

Just curious to have your take on this.

Had to respond, I believe the extent to which we can get the precision of the circle, no matter which method or device or program you use, is actually directly related to how precisely we can calculate its circumference. basically, the discontinuity you speak of exists in the drawing of the circle as well because the same formula is used in the calculation.

Any machine has to have the formula for circumference programed in to set the parameters of it's circle. how else will it draw it? even if you use a manual compass, the ratio exists in the compass itself, in the design and building of it. Your circle does not exist without Pi. well, there is just free hand, but i think it would still apply if you drew a precise circle. it would figure into your hand/arm/pencil movement somewhere, or your circle would not be.

And not a gap in our knowledge, but a sign of our intelligence that we can find such a numbers, and it brethren. It is possibly a side effect of where we are in relation to the rest of the universe, meaning how we are experiencing this universe. To find a number that is so essential to this linear, physical experience, and yet is seemingly unending and incalculable is like witnessing a miracle. a "shadow" of the infinite reflected here in the finite.

I sometimes wonder how there can be so many of these reflections or shadows of the infinite can exist right in front of our faces, and yet no one bats and eyelid or even questions or wonders if that is or could be such a thing, proof right here that the infinite universe is infinite and the infinite casts a shadow onto our finite line here.

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As I said before, pi shows up in many equations. Why? For instance, here is Einstein's field equations of general relativity:

post-50472-0-21648200-1417453111_thumb.j

Edited by StarMountainKid
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A genuine question for you Harte:

We can draw a circle with infinite precision - but we cannot calculate the circumference with infinite precision - there is always a discontinuity in the calculated length.

Is this indicative of a fundamental gap in our knowledge, is there an as yet undiscovered value that WILL actually give a finite answer?

No, it is the nature of irrational numbers to be imprecise in our engineering problems.

You cannot arrive at a precise numerical answer for a circumference or area of a circle because for both you have to multiply by pi. The decimals in pi continue to infinity without repeating (as they do for every irrational) so it is impossible to arrive at an absolutely precise answer.

It's just the way irrational numbers work.

However, I'd like to point out that it is impossible to measure anything absolutely as well. We cannot, therefore, "draw a circle with infinite precision" either. Even with the absolute best measuring stick imaginable - which has yet to be invented - you can't measure down past the Planck length, leaving some unknowns waaay out in the line of decimals.

Harte

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Pi is only one representative of the set of irrational numbers.

The set of irrational numbers is larger than the set of rational numbers - the numbers we use everyday.

IOW, there are more irrational numbers between zero and one than there are rational numbers on the entire number line.

Pi happens to be the first such number discovered (no the Greeks didn't know this.) There are infinitely many more - the second cardinal infinity - which is infinitely larger than the first (which corresponds to the "counting" numbers and fractions.)

Harte

It's a transcendental number, a little different than the irrationals... There may not be an infinite many transcendentals. Yeah, way more irrationals than rational numbers though. (Infinitely) :)

Edited by onefourfour
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As I said before, pi shows up in many equations. Why? For instance, here is Einstein's field equations of general relativity:

post-50472-0-21648200-1417453111_thumb.j

I think it means the force spreads out from a center in all directions equally.

Edited by onefourfour
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As I said before, pi shows up in many equations. Why? For instance, here is Einstein's field equations of general relativity:

post-50472-0-21648200-1417453111_thumb.j

I think it means the force spreads out from a center in all directions equally.

Alex,

I'll take curvature of space/time for 1000. :whistle::innocent::tsu:

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It's a transcendental number, a little different than the irrationals... There may not be an infinite many transcendentals. Yeah, way more irrationals than rational numbers though. (Infinitely) :)

From wiki:

All real transcendental numbers are irrational, since all rational numbers are algebraic.

Didn't want to get that far into it in an explanation concerning circumference here.

Harte

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Alex,

I'll take curvature of space/time for 1000. :whistle::innocent::tsu:

Does gravity curve spacetime in a perfect sphere from origin? If you understand exactly what is being described and can put it in english, please... do

The curve shape itself is a square function... right? lol

Can YOU help us? :)

Edited by onefourfour
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