Pi cant just be an arbitrary form of number.

This is in Skunk works because its speculative thought experiment to understand the meaning of Pi. I cant believe its just an arbitrary form of number. Heres a theory im thinking of

r , a straight line
The next spatial dimension is curvature. A mathematical expression for circumference of circle 2pi*r ,
The next spatial dimension is area. A mathematical expression , is area of sphere 4 pi*r squared
The next spatial dimension is volume. A mathematical expression for volume is 4/3pi*r cubed,
The next spatial dimension is solid, and which is density, the mathematic expression for density is mass/volume.


A things I notice is that pi is a constant term that appears in dimension order shifts. Could this be because Pi is an expression for space, implying space is a ethereal form of constant that permeates all dimensional levels?

Could it be possible to develop an mathematical expression that eliminates mass from the Density = mass/volume mathematical; expression so the mathematical expression contains r quaded (r x r x r xr)

a reply to: AthlonSavage

well I've had my fair share of nights thinking about Pi. I was always telling my self that if there is a Planck Unit, then the number of dots on a given line is not infinite but very much finite, then by calculating the numbers of Planck unit in a circle of a 1 meter circumference, we should know how many digits are required for it to be rational, I have calculated it with a 1 meter circle but realized that we have already went way beyond the number of digits given by the Planck units in a 1 meter circle. Should we stop Pi at the number of digits given by the number of planck units in the circle? I realized we can't since mathematics are just an abstraction of reality.

a reply to: AthlonSavage

Could this be because Pi is an expression for space, implying space is a ethereal form of constant that permeates all dimensional levels? - See more at: www.abovetopsecret.com...

It's because pi (an irrational number) is the ratio between the diameter of a circle and its circumference. That's why it's so handy when dealing with calculations involving circles and spheres.

Pi is not an arbitrary value.

a reply to: AthlonSavage

Pi is a number representing a ratio.

It is very specific.

While a plane curve requires at least two dimensions to be defined in, a curve is not a dimension.

Curves can be higher dimensional than just two dimensions too. One example of this would be a helix, which is a type of curve.

I'm also baffled why you would see significance in quantitizing a circle (an abstract mathematical concept) by Planck Lengths? One can quantitize a 1 meter circle by widths of a penny but would that be any less significant than one quantitized by Planck Lengths?

a reply to: Phage

I realise the relationship it has with an circle and radius. What im am postulating with interest is how its constant expression is maintained as the geometrical expression; for a perception of space is increased in complexity, curve, area, volume etc. That constant in my mind must should also be found with expressions for density and probably even energy to allow consideration of if its possible to represent E = MCsquared, as E = to a geometric term that eliminates M. I had this thought today after seeing a thread on Quantum waves not existing in physical. That the solid we see is an summation of the quantum makes me consider this could be possible.

a reply to: AthlonSavage

What im am postulating with interest is how its constant expression is maintained as the geometrical expression; for a perception of space is increased in complexity, curve, area, volume etc.

Right. As long as the curve and area are circular and the volume spherical.

You are correct though, pi is not an arbitrary number. Its value is quite specific to the ratio between the diameter and circumference of a circle.

a reply to: chr0naut

While a plane curve requires at least two dimensions to be defined in, a curve is not a dimension.

I was trying to convey the abstract idea of area is higher order than curve, and volume high order than area. I don't really like the description dimension, as Dimensions is used too much as a new agey term.

a reply to: AthlonSavage

Have you also given consideration to other Transendental Numbers (of which Pi is only one of an infinite number). Consider 'e' (the base of the natural logarithms), too.

originally posted by: AthlonSavage
a reply to: chr0naut

While a plane curve requires at least two dimensions to be defined in, a curve is not a dimension.

I was trying to convey the abstract idea of area is higher order than curve, and volume high order than area. I don't really like the description dimension, as Dimensions is used too much as a new agey term.

I agree that the nomenclature has been hijacked with a non-mathematical definition!

But since you are heading into that 'space' (metaphorically), here's something to think about:

Science has proofs of the existence of higher dimensions beyond the three (and a half) that we now "see". The half dimension i'm speaking about is the time dimension which we can only see unidirectionally in. This is often referred to as the "arrow of time". We also don't seem to be able to see dimensions higher than the fourth at all, by normal means.

My gut feeling is that there is some simple mathematical reason that allows us to see three and a half dimensions and no more. I also feel that the 'half visibility' of time is the key to the discovery of this mathematical reason.

a reply to: Phage

Right. As long as the curve and area are circular and the volume spherical.

So I continue with my thought experiment considering your comment. If a mathematical expression could be developed to show a circle or sphere is a integration summation of symetrical geometries like triangle, pentagons, then it should be possible via that expression to work backwards to derive expressions for those individual geometries in terms of Pi. Im not a mathematician, so of course im speculating but it seems reasonable idea.

The analogy is like considering how a electronic square wave is an integration summation a range of Sinwaves at different frequencies, and where for each individual Sin wave its rate of propagation is determined by the relationship of Pi to Frequency. Interesting to this I have seen threads on how frequency can produce different crystalline shapes within water. (and crystalline shapes are essentially symmetrical geometric shapes.

Considering that analogy im wondering if be possible to find a mathematical expression for a sphere in terms of integrations of symmetrical shapes, where each shape has a unique frequency. Therefore essentially instead of integrating a range of sine waves at different frequencies to produce the square wave, integrate a range of geometric shapes at different frequencies to produce the sphere.

Depending on what combination of geometric forms used and there associated base frequencies used to sum the representation of the sphere, the calculation output would also end up having its own unique frequency for the sphere. This is the interesting part because change the base geometries used to sum the sphere would allow changing the frequency calculated for the sphere.

a reply to: AthlonSavage

what you have described here sounds a lot like the Taylor expansion series for sine cosine and exponential functions. these functions operating on vectors, integrated over 3-space will produce a sphere. additionally, there are many fascinating series convergent on PI.

if you haven't taken at least two semesters of calculus, id say you're a natural.