# Thomas C. Hales

University of Pittsburgh

Pittsburgh, Pennsylvania

**Articles**: Computer related *A proof of the Kepler conjecture *(PDF)

**ArXiv** (27): The Kepler conjecture

B**ooks**: *Dense Sphere Packings: A Blueprint for Formal Proofs *Review

**Homepage** Another

**Wikipedia**

**YouTube**

`Second email: Thursday, July 7, 2016 @ 10:53 AM`

Dear Prof. Dr. Thomas Hales,

Bruce Camber

Second email: Thursday,July 7, 2016, 10:53 AM

References: https://en.wikipedia.org/wiki/Kepler_conjecture

Dear Prof. Dr. Thomas C. Hales,

In 2011 we divided the edges of the tetrahedron, connected the new vertices to find the half-sized tetrahedrons in each of the four corners and the octahedron in the middle. We did the same with the octahedron and found the half-sized octahedrons in each of the six corners and the eight tetrahedrons, one in each face, all sharing the common center point.

We continued dividing by 2 and in forty steps we were down in range of the proton and fermion. In another 67 steps we were in the range of the Planck base units. To normalize the process we used the base-2 exponential notation from the Planck base units and went out to the Age of the Universe and the Observable Universe in just over 201 notations. Kees Boeke’s base-10 work is interesting; this simple model was fascinating.

Just high school people, we thought we had a great STEM tool. As we studied it, it became more. The first 67 notations challenged us to see this very small universe in new ways. In time, we began to think it could be a possible paradigm shift in the way we look at our universe. Our working model is here: https://81018.com/chart/

We have done a little work with your proof of Kepler’s conjecture.

The first reference is here: https://81018.com/number/#5

Might you give us a little feedback? We would be most grateful.

Most sincerely,

Bruce

First email: 17 January 2016 @ 9:56 PM

References: https://en.wikipedia.org/wiki/Kepler_conjecture

A proof of the Kepler conjecture – Annals of Mathematics

Dear Prof. Dr. Thomas Hales,

We are high school folks wrestling with issues that are way beyond our training. I need a really good mathematician to help with what we consider to be a possible paradigm shift in the way we look at our universe.

In my very rough-draft paper, working title, “On Building The Universe From Scratch,” I have made several references to your proof of Kepler’s conjecture. It is my second-most important number (after pi).

The first reference is here: https://81018.com/number/#3

“The Feigenbaum constants, Buckingham Pi theorem, the fine-structure constant, dimensionless quantities and physical constants were cited less often. We have added two numbers not cited at all: mathematician Thomas Hales‘ number from his proof of the Kepler Conjecture and what we call the Pentastar 7.38 degree gap.”

The primary reference is here: https://81018.com/number/#Kepler

I know you are a busy person with the highest credentials; I humbly ask if you could you take a look and give us a little feedback? We would be most grateful.

Most sincerely,

Bruce

******************

Bruce Camber