Is there a 3-dimensional pattern to Pi?

originally posted by: Deluxe
a reply to: TycoonBarnaby

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Question: Is there a 3-dimensional pattern to Pi?

Answer: Yes its called a sphere

originally posted by: FocusedWolf
Question: Is there a 3-dimensional pattern to Pi?

Answer: Yes its called a sphere

That was funny!

a reply to: FocusedWolf

I think you missed the point of the thread.
It appears you read the title and responded.
Unfortunately the title doesn't reflect the thread at all.

a reply to: DBCowboy

Well, don’t let them fool you.

The irrational number pi, does a very weird thing as you start calculating the digits. The same thing happens with prime numbers at ridiculous sizes...

Since both are representations of repeating patterns of numbers (not a sequence, just more digits) they both oscillate! Most of the time, primes stay above the curve of all primes. But at really large numbers it dips below that line. That is why the Riemann Hypothesis cannot be proven.

Pi also does the same thing. There are equations that are substituted for pi that also rise and fall above the actual value. In the end, it will mostly equal out (how many digits do you want to go?). I.e., it will give you useful results.

That is irrational numbers for you! And infinity! Which makes Euler’s Formula that much more amazing!!

ETA: Another dimension does not change much. But a relationship to other equations through another dimension might help (that was hoe Fermat’s Last Theorom was solved! Good question as to a geometric relationship might be there!)

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!

You don't extrude in 3 dimensions. Squares are a plane, in 3 dimensions, a set of 6 planes becomes a cube. A circle is a set of points a fixed distance from a center, the same is true of a sphere in 3 dimensions.

a reply to: DBCowboy

Do you mean like "we have any number of 10 possible different digits in Pi, so why do we not use that like directions in 3D-Space, so that 1 means straight up (+1 on the z-axis), 2 means straight forward (+1 on the x-axis), 3 means straight backwards (-1 on the x-axis), and so on?"

Well, that would be possible, I am just too lazy to put it into Mathematica. Another point - there are only 6 directions on x-y-z-axises (forward and backward), how about the other 4 digits? And which number should mean which direction? Okay, that is a finite number of alterations, nothing too troublesome.

I only fear that there will be a smear-blob of very short zick-zacking lines, which would not be very rewarding for coding this.. I am really very sure that there is no mystery to be lifted by this plotting.

a reply to: DBCowboy

Oh no, those "Scientists and mathematicians" have never looked for anything as complex as .. oh.. "3D"

Get some f*cking perspective.

originally posted by: ziplock9000
a reply to: DBCowboy

Oh no, those "Scientists and mathematicians" have never looked for anything as complex as .. oh.. "3D"

Get some f*cking perspective.

Yeah cursing people out over a question is how you contribute..

It is you who requires perspective.

a reply to: ManFromEurope

What you are talking about has been done and it's called a random walk.
Here is a random walk of pi with the first billion digits in a 2-d plane using base 4 and assigning a direction to each digit 0,1,2,3. It's very beautiful.
gigapan.com...

Here is another pi random walk assigning angles in a 2-d plane.
www.visualcinnamon.com...

There are people that have done random walks in 3-d space using base 6 assigning up, down, left, right, forward, back to the digits 0,1,2,3,4,5. Google "pi random walk base 6" to find some of the forums where this has been done.

All these random walks prove is that the digits of pi are random. They are great representations of the randomness however! Some very nice artwork. I'm considering downloading a software program to play with random walks for fun.

originally posted by: ziplock9000
a reply to: DBCowboy

Oh no, those "Scientists and mathematicians" have never looked for anything as complex as .. oh.. "3D"

Get some f*cking perspective.

Well aren't you a little ray of sunshine!

(Were the words too big for you to understand?)

originally posted by: JackKcaj
What about converting odd numbers in PI to zero and even ones to odd and seeing if it could be binary? I actually tried to do this before with mixed results, but it could be that there is data hidden in PI.

The issue with binary is that you still have to assign an arbitrary meaning to the numbers. For example, if you turned it all into 0's and 1's in the method you described, you still need to apply that string of binary to a specific set of machine instructions, ascii tables, or whatever else in order to translate it into some sort of meaning, and those conversions are totally arbitrary.

All you're really doing here is losing a whole bunch of data.

a reply to: Aazadan

Thinking along similar lines.

I would imagine, for instance, after converting to base 4 the process still uses that last digit value for values over 3.

If so, then 0 and 1 can appear an extra time due to the 8 and 9 decimal value. It makes the 1 to 4 and 5 to 8 values equal in response,plot, whatever and 1 - 2, 5 - 6 and 9 -10 position pairs equal. Not sure how meaningful the output is, other than interesting to view.

originally posted by: TycoonBarnaby
a reply to: projectvxn

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

My guess is that in order to make an irrational ball-bearing you'd also have to make flawless tools. But, like approaching the speed-of-light, or reaching absolute zero, we never really get there.

I'm not sure we're there yet. Everywhere we look there seems to be a limit to precision achievable vs. what is observable in a math problem.

a reply to: Deluxe

I'd like to add if pi is really a normal number (see link below) then the random walks will give no discernible pattern.
It would be equivalent to writing a computer program that simply creates random numbers (let us say truly random for the sake of argument) from 0 to 9 and then graphing them the same way. Obviously the graphs won't look the same but no patterns would emerge.

"In mathematics, a normal number is a real number whose infinite sequence of digits in every positive integer base b[1] is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b2 pairs of digits are equally likely with density b−2, all b3 triplets of digits equally likely with density b−3, etc."

en.wikipedia.org...

a reply to: projectvxn

Atoms are not points therefore we could never make a perfect sphere.

I think the pattern would look something like this

In the end all of our math is wrong - a number is a discrete reference. If we have a sequence, from zero to one - you can divide that space between those numbers into an infinite number of reference points, but its still an approximation because their are an infinite number of points between them. Pi in itself is a good example of this. Its a symbolic reference to a ratio - but its not a 'number' as its components can be extended to infinity.

a reply to: Speedtek

Actually, by definition, Pi is a number.

I think your problem is more with the foundations, or axioms, of modern mathematics whereby the irrational numbers naturally emerge from.

Pretty amazing the stuff that emerges from a few axioms and the Natural numbers.

Natural -> Integers -> Rationals -> Irrationals -> Reals (the rationals + irrationals) -> Complex numbers.

a reply to: TycoonBarnaby

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

More than a little assumptions on your part. Have you got any proof to back that up.