How would the universe be different if π = 3?

[Alan McDougall]

Q: How would the universe be different if π = 3?

 

There are sometimes questions about physical constants changing, and those questions make sense because there’s no real reason for the constants to be what they are. But π is mathematically derivable; it kinda needs to be what it is. You can’t, through the power of reason alone, figure out what the gravitational constant or the speed of light are, but you can figure out what π is.

 

But lets try think about it anyway, mathematics will be put on its head, planetary orbiting will alter etc?

[CaptainPanic]

The non serious answer: A circle would be 1.047197551*π ?

 

The attempt to give a serious answer: If the impossible would be possible, then it is a safe assumption that everything would change.

[Alan McDougall]

The non serious answer: A circle would be 1.047197551*π ?

 

The attempt to give a serious answer: If the impossible would be possible, then it is a safe assumption that everything would change.

 

Hi Captain,

 

Thanks for giving it a bash!

 

As an Engineer with Pi at exactly 3 would make calculating the points to drill holes on a pipe flange a peace of cake, just take the radius and mark of six places on the flange and drill immediately. It is sometimes a pain to get the exact equal distances between holes with Pi as it exists.

 

 

 

 

That circular physical objects, as you make them progressively closer to perfect circles, approach a circumference to diameter ratio of something other than 3.14159… If this were the case, it might indicate something about the geometry of spacetime. If space is not flat, that can change geometric relationships. For instance, imagine drawing a circle on the surface of an orange. If we allow distances to be measured only along the orange’s surface (disallowing paths that penetrate the orange or go into the empty space around it), then the ratio of the circle’s circumference to diameter is no longer going to be π. It will, in fact, depend on the size of the orange itself. If our universe is not flat, but a curved surface, that could distort the geometric relationships that we measure on physical objects resembling circles.

Edited July 17, 2012 by Alan McDougall

[ecoli]

Hi Captain,

 

Thanks for giving it a bash!

 

As an Engineer with Pi at exactly 3 would make calculating the points to drill holes on a pipe flange a peace of cake, just take the radius and mark of six places on the flange and drill immediately. It is sometimes a pain to get the exact equal distances between holes with Pi as it exists.

 

 

 

 

That circular physical objects, as you make them progressively closer to perfect circles, approach a circumference to diameter ratio of something other than 3.14159… If this were the case, it might indicate something about the geometry of spacetime. If space is not flat, that can change geometric relationships. For instance, imagine drawing a circle on the surface of an orange. If we allow distances to be measured only along the orange’s surface (disallowing paths that penetrate the orange or go into the empty space around it), then the ratio of the circle’s circumference to diameter is no longer going to be π. It will, in fact, depend on the size of the orange itself. If our universe is not flat, but a curved surface, that could distort the geometric relationships that we measure on physical objects resembling circles.

 

really? You need that level of precision for practical uses?

[Ben Banana]

Does anyone know how to make a manifold for this?

[ecoli]

!

Moderator Note

Are you sure you posted that in the right thread, Ben Bowen?

[Severian]

What do you mean by "n"? The number of spatial dimensions? If so, how is this derivable? We don't even know if it is 3, so surely we can't derive it!

[granpa]

not 'n'.

pi

[Severian]

Oh sorry - it looks like an n on my screen. What a strange font. Hang on... [math]\pi[/math] ... Edit: looks OK in a math font.

 

Edit 2: In order for [math]\pi[/math] to be different, we would have to be living on a curved space, since by definition [math]\pi[/math] is the ratio of circumference of a circle to its diameter. If the space is curved, than you can imagine going across the circle would take longer than you would expect from the circumference. Then you could have the laws of physics exactly as they are, but just have weird gravitational effects from the curved space.

Edited July 17, 2012 by Severian

[Alan McDougall]

Oh sorry - it looks like an n on my screen. What a strange font. Hang on... [math]\pi[/math] ... Edit: looks OK in a math font.

 

Edit 2: In order for [math]\pi[/math] to be different, we would have to be living on a curved space, since by definition [math]\pi[/math] is the ratio of circumference of a circle to its diameter. If the space is curved, than you can imagine going across the circle would take longer than you would expect from the circumference. Then you could have the laws of physics exactly as they are, but just have weird gravitational effects from the curved space.

 

http://www.askamathematician.com/2012/07/q-how-would-the-universe-be-different-if-%cf%80-3/

 

In fact, in that last two, Pi plays a pivotal role in the derivation of the uncertainty principle. In a very hand-wavy way, if Pi were bigger, then the universe would be more certain.

 

Aside from leading almost immediately to a whole mess of mathematical contradictions and paradoxes, if π were different it would change the results of a tremendous number of (one could argue: all) calculations, and the fundamental forces and constants of the universe would increase or decrease by varying amounts. π shows up in way too many places to make a meaningful statement about the impact on the universe, one way or another.

[granpa]

http://en.wikipedia.org/wiki/Lp_space

 

lp spaces are flat and each has a different value for pi

[D H]

I'm going to be quite contrarian here. Everyone is wrong. Well, almost everyone. Captain Panic's post #2 was correct.

 

 

lp spaces are flat and each has a different value for pi

No, they don't. They have a different value for the ratio of the circumference of a circle to it's diameter. That ratio is not [math]\pi[/math].

 

 

Edit 2: In order for [math]\pi[/math] to be different, we would have to be living on a curved space, since by definition [math]\pi[/math] is the ratio of circumference of a circle to its diameter.

Pi is a mathematical constant, not a physical constant. Mathematicians don't give a hoot whether the universe is Euclidean. By definition, [math]\pi[/math] is the ratio of the circumference of a circle to it's diameter in the Euclidean plane using the Euclidean norm. Alternatively, [math]\pi[/math] is the principal value of the inverse cosine of -1, or twice the principal value of the inverse sine of 1, or [math]4\int_0^1 \frac{dx}{1+x^2}[/math], or ... There are a bunch of different ways to express/calculate [math]\pi[/math]. Not a single one of these approaches involves the curvature of the physical universe.

 

 

Q: How would the universe be different if [math]\pi[/math] = 3?

This is a nonsense question. Pi is not a physical constant. Ask a nonsense question and you will get a nonsense answer. My answer is 42.

[John Cuthber]

It would be more difficult to draw hexagons.

[mathematic]

If you are looking for the ratio ® of the circumference of a circle to its diameter, try it on a sphere, then it would be a variable with 2 ≤ r < π, where 2 would be ratio for a great circle, while the upper limit is for circles getting very small.

[Alan McDougall]

It would be more difficult to draw hexagons.

 

Why?

 

I think the force of gravity would be higher because a planets mass would be compacted into a smaller area!

 

I'm going to be quite contrarian here. Everyone is wrong. Well, almost everyone. Captain Panic's post #2 was correct.

 

 

 

No, they don't. They have a different value for the ratio of the circumference of a circle to it's diameter. That ratio is not [math]\pi[/math].

 

 

 

Pi is a mathematical constant, not a physical constant. Mathematicians don't give a hoot whether the universe is Euclidean. By definition, [math]\pi[/math] is the ratio of the circumference of a circle to it's diameter in the Euclidean plane using the Euclidean norm. Alternatively, [math]\pi[/math] is the principal value of the inverse cosine of -1, or twice the principal value of the inverse sine of 1, or [math]4\int_0^1 \frac{dx}{1+x^2}[/math], or ... There are a bunch of different ways to express/calculate [math]\pi[/math]. Not a single one of these approaches involves the curvature of the physical universe.

 

 

 

This is a nonsense question. Pi is not a physical constant. Ask a nonsense question and you will get a nonsense answer. My answer is 42.

 

I know it is not a physical constant and said so in my posts, but it is not a nonsensical question and has been posed by many people many times? Is there a reason in a differnt universe that Pi could not be exactly=3?

[Ben Banana]

!

Moderator Note

Are you sure you posted that in the right thread, Ben Bowen?

Aren't we talking about the best waffle-baking irons to buy? Are you sure this topic doesn't belong in Mathematics? What else is there to talk about?

[Alan McDougall]

Aren't we talking about the best waffle-baking irons to buy? Are you sure this topic doesn't belong in Mathematics? What else is there to talk about?

 

I was not sure where to post this topic, it is more mathematical than astronomical , however, because it refered to how the "universe" would differ I put it under astronomy. Maybe it should be moved but I dont have the authority do do so!

[John Cuthber]

Why?

 

Because this wouldn't work

 

By analogy, a whole lot of "compass and straight edge " geometry wouldn't work.

[D H]

I know it is not a physical constant and said so in my posts, but it is not a nonsensical question and has been posed by many people many times?

Just because people who don't know what pi is / how pi is defined ask this question doesn't mean that the question isn't nonsense. It is.

 

Is there a reason in a differnt universe that Pi could not be exactly=3?

Yes. The value of pi has absolutely nothing to do with the physical universe.

 

I think what you are asking is "What if the circumference of a physical circle in our physical universe was 3*d rather than pi*d?"

This is still a nonsense question, but it is getting close to being a very good question. The reason it's still nonsense is because space-time is a pseudo-Riemannian manifold and space is a Riemannian manifold. Space locally appears to be Euclidean.

 

Here is the question you should be asking: "What if the circumference of a physical circle in our physical universe was not always pi*d?" or even better, "What is the shape of the universe?"

The evidence to date says that our universe is flat, or very, very close to it. Whether it must be flat, whether some other universe might be curved: Nobody knows. It's a very good question.