Upon studying the work of Eric Wolfgang Weisstein

TO: Eric Wolfgang Weisstein, MathWorld, Eric Weisstein’s World of Science,
Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237
FM: Bruce E. Camber
RE: Naming conventions, basic geometries, simple math, and your online presence especially what I have learned from your website, CV, MathWorld, and Wikipedia

This page: https://81018.com/weisstein/ Also, see the references to Steve Wolfram.

Fourth email: 15 April 2025

Dear Dr. Eric Weisstein:

I would like to discuss two homepages with you. I need your wide-deep view of mathematics to get some assurances that, though I’m idiosyncratic, there is a possibility that the work might eventually have something to do with our understanding of reality.

Thank you.

Most sincerely,

Bruce

Third email: 22 September 2023 (On naming the Aristotle Gap)

Dear Dr. Eric Weisstein:

The five-tetrahedral figure that Aristotle missed became an 1800-year mistake. Lagarias-Zong highlighted it in their 2012 AMS article, Mysteries in Packing Regular Tetrahedra (PDF). In 2003 Jonathan P. K. Doye (Cambridge, Oxford) did an analysis that was helpful.* The earliest reference to that gap, I believe, is the Frank & Kasper’s 1958 article,  Complex alloy structures regarded as sphere packings (PDF). ** 

1. Do you know if that 7.36+ degree gap has a formal name?  It’s a five-tetrahedral cluster. Are you aware that most geometric construction kits like Zometool cannot recreate it? I am not sure if the programming tools compensate for it. Do you know if Mathematica automatically displays that gap if five tetrahedrons are mapped together?

2. Are you aware that the same gap is created with five octahedrons? Do you have a discussion about that figure? Does that five-octahedral cluster have a name? Thank you so very much.

Warmly,

Bruce

 PS. These are the few other references that I have: “A model metal potential exhibiting poly tetrahedral clusters” by Jonathan P. K. Doye, University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom, J. Chem. Phys. 119, 1136 (2003) Compete article, ArXiv.org as a PDF: http://arxiv.org/pdf/cond-mat/0301374‎
** Definitions and basic principles” (PDF), Acta Crystall. 11. and Frank, F. C.; Kasper, J. S. (1959) and “Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures”, Acta Crystall. 12.

Results: On Mon, Sep 25, 2023 at 10:13 AM Eric reported, “Not that I know of. Though I will add the n-cluster to MathWorld and PolyhedronData as ‘tetrahedral ring.’ As far as the gap goes, calling it something like the ‘Aristotle gap’ seems appropriate.”

Because of his stature in the mathematical world, I believe Weisstein’s article on the Aristotle Gap was the first time the gap was formally named and prominently referenced. -BEC

Second email: 9 January 2020

RE: Planck Scale to the current Age of the Universe in 202 base-2 notations

Dear Dr. Eric Weisstein:

In December 2011, three teachers and about 90 students unwittingly opened a rather idiosyncratic door by naively following the embedded geometries of the tetrahedron and octahedron. We divided the edges by 2, connected the new vertices, and kept going further and further inside (on paper). Our initial model is on the web —  http://81018.com/tot/ — and is quite straightforward. On paper in 45 steps within, we were in the range of elementary particles. In another 67 within, we were in the range of the Planck scale. It seemed like the beginning of a nice STEM tool. We then began multiplying the edges of our desktop model by 2. In about 90 steps going out, we were in the range of the size and age of the universe. We began writing it up but quickly realized it was entirely idiosyncratic, no matter how logical or simple or mathematical.

It is very similar to the base-10 work that Kees Boeke did back in 1957. The difference is that we have an inherent geometry and a continuum from the smallest possible unit of time, Planck Time, to the current time, the Age of the Universe. If Planck Length and Planck Time are logically taken to be first moment of time, the progression becomes a natural inflation (with Planck Charge, Planck Mass and the speed of light within all the equations) and there is a natural homogeneity and isotropy.

Can you help us? What’s wrong with our chart?  What have we failed to understand?

Thank you.

Most sincerely,

Bruce

 First email: Apr 22, 2017, 11:01 AM

Re: http://scienceworld.wolfram.com/physics/CoulombForce.html

Dear Dr. Eric Weisstein:

In a New Orleans high school we have been working with base-2 notation and simple geometries to tile and tessellate the universe. A fun exercise, we applied base-2 notation from the Planck Units and discovered many numbers that are difficult to grasp. The coulombs progression is particularly difficult for me to help interpret meaningfully for the students.

I hope you don’t mind a few naive questions. I’ll try to be succinct:
1. Is there a coulombs output rating of the sun? Does that make sense?
2. Is there a coulombs rating of the solar system? Does that make sense?
3. Is there a coulombs “guesstimate” for the galaxy? Does that make sense?

Thank you.

Most sincerely,

Bruce

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