Geometric construction of the square root

[JeremyEbert]

Is anyone familiar with this method of determining square roots?

http://www.cs.cas.cz/portal/AlgoMat...onstructions/SquareSquareRootConstruction.htm

I have an equation that I'm working on that expands on this a bit and I'd love some feedback.

 

[JeremyEbert]

anyone?

http://www.uwgb.edu/dutchs/Graphics-Other/PSCI/sqroot.gif

 

[JeremyEbert]

Well, here is some of what I've been working on.
https://www.physicsforums.com/attachment.php?attachmentid=31636&d=1296068205

On the grid, whole number square roots are where the (x),(y) and a (circle) all intersect at once.

All other square roots (decimal numbers) intersect on a (circle) and the (x) according to their decimal value (y).

A composite number square root has more than one (circle),(x) intersection at its value (y).

A prime number square root only has one (circle),(x) intersection at its value (y).

 

[JeremyEbert]

This graph is just showing the divisibility of numbers and the fact that primes have no factor larger than one. Nothing surprising there. What I find surprising is that a numbers primality shows up at its square root. These prime roots only fall on the parabola in my graph that has a vertex of 1/2. All other numbers roots fall on multiple parabolas that have a vertex greater than 1/2 according to their factors. This graph is based on the Inverse Square Law which generally applies when some force, energy, or other conserved quantity is radiated outward radially from a point source. Its been shown that the non-trivial zeros of the Riemann zeta function have a real part equal to 1/2 and have a deep connection to the allowable energy levels in quantum systems that classically would be chaotic. I think this graph shows more of that connection.

 

[JeremyEbert]

no comments?