Is there a 3-dimensional pattern to Pi?

Sounds like it would be the opposite of fractals, but also closely related.

non repeating patterns that go on forever whereas fractals have aspects of repetitiveness that also go on forever.

a reply to: Harpua


I wonder if a pattern would emerge if we changed Pi from a base 10 to hexadecimal?

originally posted by: DBCowboy

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.

But numbers do have a pattern, re; Fibonacci.

You are referring to a sequence of numbers, which yes, can have a pattern (or not.)

Edit: I do understand what you are trying to get at with this thread, so I will leave you to it.

originally posted by: Bhadhidar


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

Instead of extruding a circle up in the Z direction (which would result in a cylinder), turn the circle through the Z dimension about an axis taken through the circle's diameter. That gives you a sphere.

a reply to: DBCowboy


The Fibonacci sequence, for those that don't know, is 1,1,2,3,5,8,... You take the sum of the two prior numbers to build the sequence in the next number.

If you go to PI to the millionth you will see that it doesn't follow that pattern at all, but you might be able to inter lock sets of numbers within a pair set to try and 3D a thing.

I am having difficulty understanding this.

Another way to state it would be "could you represent Pi differently to search for patterns?"

The use of 3d is throwing me off.

To answer your question....it might be an interesting idea to probe. Or a way to drive yourself insane.

Pi applies in all directions.

Radians are a more universal means of determining a circle(as well as angles in trig).

Converting rads to degrees, say 2r * 180/Pi will give you 59.32 degrees. The inverse also applies which means the equation can apply to any radii in any direction.

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

The coolest thing about Pi is that there are no real surprises.

a reply to: bigfatfurrytexan


Imagine a type of synesthesia where numbers are seen as shapes.

Linearly, there is no definable pattern, but twisting the numbers, circling the numbers, might define a pattern.

Does that make more sense?

a reply to: DBCowboy

Yeah. Im getting you.

Arranged into a nonlinear array.

It might help you look for relationships between number strings. That could be interesting, but maddeningly time consuming. Maybe a supercomputer could help.

a reply to: projectvxn


(4/3)* Pi * r^2

By the way, this will equal zero. Zero, in this case, is the equivalent to the total volume. Use your own numbers.

a reply to: bigfatfurrytexan


Or imagined another way, Pi is universal, but if you're using something other than a base-10 numbering identifier, would it change?

originally posted by: projectvxn
a reply to: projectvxn


(4/3)* Pi * r^2

By the way, this will equal zero. Zero, in this case, is the equivalent to the total volume. Use your own numbers.

I saw this. Infinite vs zero volumes.

It is interesting.

originally posted by: DBCowboy
a reply to: bigfatfurrytexan


Or imagined another way, Pi is universal, but if you're using something other than a base-10 numbering identifier, would it change?

It would still be just another circle in a different scale.

Pi is interesting because it works well with base 60(or any other base system), which is how Babylonians calculated pi, which was 3 * r^2 to them.

Which, interestingly, doesn't look much different from (4/3)* Pi * r^2 does it?



EDIT:
BOTH equations on their own describe a parabola on graph. in essentially the same way.

Therefore this same equation can be written like this to solve for r which will equal 0:

3 r^2 = 4/3 π r^2

a reply to: projectvxn

Volumes, thinking in 3-D has lead me down some strange paths.

Bees seem to like hexagons.
10 hexagons could be formed so that they have 16 shared seams.
Depending on the angle at the seams you might be able to make spheres with different volumes using some basic geometric building block.
Pi is more predictable in base 16.

a reply to: DBCowboy
According to Yulia Maximenko, Pi is not as constant as you think! Here's Sean Carroll to back her up.

Take your pick on how to calculte Pi

Hypersphere-4 Dimensional Sphere

What ever your current project is, be careful this time. Good luck.

a reply to: DBCowboy

Anytime you're working in 3D space you can always apply Pi.
Where it gets interesting in when you introduce the "t" variable.

3*r^2*t=(4/3)* Pi * r^2*t

That's time. It equals zero right now because we have not included a rate of change variable.

We can use this to calculate how much air a basketball will leak out over time. Seems silly but this has applications for inflatable habitats and other applications for space travel.

That equation looks like this:

3*r^2*Δ/t Base 60

(4/3)* Pi * r^2*Δ/t Base10

If you have a sphere...adjust accordingly for other structural shapes.

a reply to: TycoonBarnaby

I think he is asking if it's possible to create a geometric representation based on pi in two or more dimensions similar to the way the Fibonacci sequence gives rise to the Golden Ratio and then the Golden Spiral.

See en.wikipedia.org...

Perhaps he is thinking of a similar ratio based on pi where the infinity sum of the reciprocals of the digits of pi would converge. It would not. It is clearly a divergent series.

e.g.: 1/3 + 1/1 + 1/4 + 1/1 + 1/5 ..... (and on for all the digits of pi) = divergent

a reply to: Deluxe

Those are reciprocals.

1/n will always give you a number. But adding up those reciprocals won't give you a value equivalent to pi.

a reply to: projectvxn

Since you have the formulae down, let me explain (if I can) what I'm trying to do.


If we use the answer to the formulae, reconfigure the results, then work backwards, would the question still remain the same?

In stead of using an equals sign, imagine chemical formulae



Where it is reversable in direction.



Apologies if I'm confusing everyone. But I'm trying to think this in another way.

I'm trying to see if it is even possible.