# Geometric construction of the square root

• JeremyEbert
In summary, the conversation discusses a method of determining square roots using geometric constructions, along with a graph showing the divisibility of numbers and the relationship between a number's primality and its square root. The graph is based on the Inverse Square Law and has connections to the Riemann zeta function and quantum systems. The individual is seeking feedback on their work.
anyone?

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

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).

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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.