Geometric construction of the square root

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Discussion Overview

The discussion revolves around geometric constructions for determining square roots, exploring various methods and their implications. Participants share their own work and interpretations related to the geometric representation of square roots, including connections to prime numbers and the Inverse Square Law.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant shares a link to a method for determining square roots geometrically and seeks feedback on their own related work.
  • Another participant provides a link to a graphical representation of square roots but does not elaborate further.
  • A participant describes their work involving a grid where whole number square roots intersect at specific points, while decimal square roots intersect according to their decimal values.
  • It is proposed that composite number square roots have multiple intersections, while prime number square roots have a single intersection, suggesting a relationship between primality and geometric representation.
  • A later reply discusses a graph showing that prime roots fall on a specific parabola, linking this observation to the Inverse Square Law and the Riemann zeta function, indicating a deeper connection to quantum systems.
  • One participant expresses frustration over the lack of comments or engagement on their contributions.

Areas of Agreement / Disagreement

Participants appear to have differing views on the implications of their geometric constructions and the connections to primality and quantum systems. The discussion remains unresolved with no consensus on the interpretations presented.

Contextual Notes

Some claims depend on specific definitions of primality and geometric intersections, and the mathematical connections to the Riemann zeta function are not fully explored or agreed upon.

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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).
 
Last edited:
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.
 
no comments?
 

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