Is there a 3-dimensional pattern to Pi?

Several members have been able to illustrate Pi in a visual representation.

Pi is the ratio of a circle's circumference to its diameter, so regardless of what numerical base it was, the representation shouldn't change.

But it does.

Doesn't it.

?

originally posted by: Bhadhidar
A point is a singular dimension “object”, which becomes a line when extended into a two dimensional space and a plane when extended into a three dimensional space.

A square becomes a cube in three dimensions.

How does a circle become a sphere, instead of a cylinder, in three dimensions?

Pi refers to a circle’s (two dimensional object) circumference; can Pi even be applicable in higher dimensions?

If the answer is yes, I’m sensing Aliens!

Many ways to define a sphere or circle

By parametric equation: x = r . sin( longitude ), y = r.cos( longitude )

By algebraic equation: x^2 + y^2 - r^2 = 0

Now to get a sphere, you have to add another dimension z and then you need an angle to get between the two

Parametric equation: x = r.sin(longitude) . cos(latitude)
y = r.sin(latitude)
z. r.cos(longitude) . cos(latitude)

PI is bounded by two limits ... the more precision you have the closer the two limits become.Eventually you get below the radius of an atom or an electron orbital, so it won't be measurable.
Algebraic equation: x^2 + y^2 + z^2 - r^2 = 0

You can have separate axii for each axis. Then you get ellipses and ellipsoids:

www.mathopenref.com...

The use of pi extends to any number of dimensions

en.wikipedia.org...

originally posted by: schuyler

originally posted by: TycoonBarnaby
Pi is an irrational number. Irrational numbers by definition have an infinite decimal expansion that does not repeat (no pattern.)

Also, a number has no dimension so your question is basically nonsense to a mathematician.

Think outside the box. Have you ever seen "Contact"?

I have seen Contact. I also have a PhD in mathematics, so this discussion so far has been quite hilarious.

Carry on.

originally posted by: TycoonBarnaby

originally posted by: schuyler

originally posted by: TycoonBarnaby
Pi is an irrational number. Irrational numbers by definition have an infinite decimal expansion that does not repeat (no pattern.)

Also, a number has no dimension so your question is basically nonsense to a mathematician.

Think outside the box. Have you ever seen "Contact"?

I have seen Contact. I also have a PhD in mathematics, so this discussion so far has been quite hilarious.

Carry on.

So, you have been indoctrinated into looking at math in a certain way. Any PhD will limit your understanding based on the course material.

This is limiting your ability to think outside of the material you were taught.

To cope with this limitation in yourself ... you find it hilarious.

I am glad all of the founders of math and science did not have limiting indoctrination ... otherwise we would never have progressed.

P

a reply to: pheonix358

I won't mock the fud.



I only have a Masters in another field. So I play with poo-poo and shouldn't ask questions.

originally posted by: TycoonBarnaby

originally posted by: schuyler

originally posted by: TycoonBarnaby
Pi is an irrational number. Irrational numbers by definition have an infinite decimal expansion that does not repeat (no pattern.)

Also, a number has no dimension so your question is basically nonsense to a mathematician.

Think outside the box. Have you ever seen "Contact"?

I have seen Contact. I also have a PhD in mathematics, so this discussion so far has been quite hilarious.

Carry on.

Cool, rather than looking your nose down at questions you don't get, try to internalize what the person asking the questions is visualizing.

It's more productive than condescention

originally posted by: pheonix358

originally posted by: TycoonBarnaby

originally posted by: schuyler

originally posted by: TycoonBarnaby
Pi is an irrational number. Irrational numbers by definition have an infinite decimal expansion that does not repeat (no pattern.)

Also, a number has no dimension so your question is basically nonsense to a mathematician.

Think outside the box. Have you ever seen "Contact"?

I have seen Contact. I also have a PhD in mathematics, so this discussion so far has been quite hilarious.

Carry on.

So, you have been indoctrinated into looking at math in a certain way. Any PhD will limit your understanding based on the course material.

This is limiting your ability to think outside of the material you were taught.

To cope with this limitation in yourself ... you find it hilarious.

I am glad all of the founders of math and science did not have limiting indoctrination ... otherwise we would never have progressed.

P

What I find hilarious is the amount of misinformation and word-twisting to try and fit this nonsense.

Also, that projectvxn consistently (as in every post in this thread) incorrectly references the formula for the volume of a sphere (radius is cubed not squared.)

I did try to enter into this conversation early on, and you will notice an edit on page 2 where I decided it was not worth my time to correct all of this misinformation.

originally posted by: projectvxn
The equation for measuring the volume of a sphere is (4/3)* Pi * r^2

Shouldn't that be (4/3)* Pi * r^3 ?
3 dimensions n all that

You should just do it...I think a good start would be Here

a reply to: TycoonBarnaby

Also, that projectvxn consistently (as in every post in this thread) incorrectly references the formula for the volume of a sphere (radius is cubed not squared.)

V=(4/3)πr^3

You're absolutely right. I fat fingered it and didn't notice my mistake.

I did try to enter into this conversation early on, and you will notice an edit on page 2 where I decided it was not worth my time to correct all of this misinformation.

You're just looking for an excuse to be an a-hole.

I transpose numbers and symbols. It would have been really cool of you to point out my mistake in order for the math to work.

The good news is, that if you square it you get a 2D representation of a sphere(guess what that is). Both representations are valid.

a reply to: projectvxn

No I am not looking to be an a-hole. I correctly explained why this whole question is nonsense on page 1: Pi is an irrational number. Period. QED.

Then on page 2 realized that this thread was not about getting an actual answer to the nonsense question asked, but it was for brainstorming ideas (that will all be wrong by the way, the proof of Pi being irrational is rather old, and there are a number of different ones,) and was going to just walk away.

Read through a couple of the different proofs for why pi is irrational and get back to me about changing bases or curving/bending numbers (whatever that means) having any effect on pi and it being irrational (or not... spoiler: it is.)

a reply to: TycoonBarnaby

Pi is an irrational number. Period. QED.

This is known. Not my point of contention.

I was trying to give the OP a visual representation of what he was talking about.

Not bending or twisting Pi(because that means nothing), but a circle or a sphere and what that would look like and how it could be done visually using math, pi in particular.

My 2D and 3D plot syntax is correct and the models show it.

My issue with you is your condescending attitude and your inability to understand what is being asked.

a reply to: projectvxn

Condescending attitude I will always own up to. Not one of my finer character traits.

I did, however, understand what was being asked.

The reason we can depict something like the Fibonacci sequence as a triangle, spiral, etc. is because the sequence was created from a defined rule/pattern. The reason we can't do that with pi is because pi is irrational (no pattern.)

A better question to consider is: Why can't we create a circle that has a rational circumference and a rational diameter?

a reply to: TycoonBarnaby

I think it's great the OP is asking these questions. I'm guessing at one time everyone with a real interest in Mathematics has asked similar questions, and probably asked them in an informal way due to lack of knowledge of Mathematics.

Anyhow your last post was spot on.

I'd really like to know if pi is a normal number or not. If it's truly random or not.

a reply to: TycoonBarnaby

Why can't we create a circle that has a rational circumference and a rational diameter

Which is why we use pi rational-approximations in robotics and other electronics calculations. CNC machines, Fanuc robots, and others work like this.

Calculating pi to infinite decimal places is a useless endeavor. it is better to approximate pi, especially in engineering where machine precision needs to be controlled.

It's good to use approximations(at least with Fanuc bots I've worked with) 3.1416(3.14159), 355/113(3.14159292035), 52163/16604(3.14159238738)*edit these are already well known and well identified ways of getting mathematical approximations for pi(there are many more)edit*, and so on as range estimators for how far you want the robot to turn for any given task(also setting time, speed and duration of spin). Simple decimal rounding like in the first example can be used to control a robot to a very fine degree in a 360-degree space.

Pi can certainly be approximated using rational numbers and you can define arbitrary conditions with it. Like how large of a circle you're gonna cut into a piece of metal.

originally posted by: projectvxn
a reply to: TycoonBarnaby

Why can't we create a circle that has a rational circumference and a rational diameter

Which is why we use pi rational-approximations in robotics and other electronics calculations. CNC machines, Fanuc robots, and others work like this.

Calculating pi to infinite decimal places is a useless endeavor. it is better to approximate pi, especially in engineering where machine precision needs to be controlled.

It's good to use approximations(at least with Fanuc bots I've worked with)

3.1416(3.14159), 355/113(3.14159292035), 52163/16604(3.14159238738)*edit these are already well known and well identified ways of getting mathematical approximations for pi(there are many more)edit*, and so on as range estimators for how far you want the robot to turn for any given task(also setting time, speed and duration of spin). Simple decimal rounding like in the first example can be used to control a robot to a very fine degree in a 360-degree space.

Pi can certainly be approximated using rational numbers and you can define arbitrary conditions with it. Like how large of a circle you're gonna cut into a piece of metal.

Now we are getting somewhere. Especially because if my memory serves me, the OP is an engineer.

If we could measure/create irrationally correct circles for our machining needs would it have a noticeable enough effect to care?

a reply to: TycoonBarnaby

The machine might care.

a reply to: projectvxn

I was thinking more along the lines of preventing breakdowns/malfunctions and reducing wear on the parts.

a reply to: TycoonBarnaby

I think that requires a bit of materials science that is beyond me.

We may also be getting into calculus and I've only just started picking up the pieces of the photon clock.

a reply to: TycoonBarnaby

www.acorn-ind.co.uk...

"The main challenge of creating a high quality bearing is ensuring that a near perfect spherical ball is created with a very smooth surface, resulting in fast movement with minimal friction."