On learning about the work of Dan Knopf

Prof. Dr. Dan Knopf, University of Texas, Austin
Associate Dean for Graduate Education; Professor, Department of Mathematics

ArXiv (24): A numerical stability analysis…, 2022; Convergence and stability… of Ricci flow, 2007
Books and Courses
Homepage(s): Dean’s Office
Publications: Gang, Zhou, Knopf, Dan, and Sigal, Israel M., Neckpinch Dynamics for Asymmetric Surfaces evolving by Mean Curvature Flow, 2013 and many, many others
Research and interests

Second email: 20 July 2022 at 1:08 PM

Dear Dean Dan Knopf:

Can we truly look at mathematics through the lens of mathematics? Is pure ever pure or is “applied/pure” just a different way of saying “finite/infinite”?  Is there a lens that looks both ways? Where do we place it (…at the Planck scale)? Are our dimensionless mathematical and physical constants on the cusp? …pi?

Just because I know you handle the abstractions of Ricci flows and the realities of getting students inspired to go on and achieve and contribute, possibly great things, I wrote my first note back on July 7. 

May I further correspond with you? Thank you very much.


PS. Today is my 75th birthday and I need memory aids to keep me on path. To that end, I have started a special page of just my correspondence and links to your work online believing you have the right chemistry, scholarship, and discipline to evaluate basic foundations. If there is a problem, please advise me. Thank you. -BEC
Bruce E. Camber

First email: Thursday, July 7, 10:28 AM

Dear Prof. Dr. Dan Knopf:

We have been working with the Platonic geometries in our high school and cannot find any references online to a very simple geometric figure of five octahedrons, all sharing a centerpoint, and three sharing two faces with another octahedron, and two sharing only one face. It is a very interesting image when the five-tetrahedrons are added on the top and bottom. That stack has 15 objects sharing the centerpoint. I took that picture just a few weeks ago but, to date, it appears that no scholar has written about it.

Have you seen any scholarly analysis of it?  Thank you.



PS The URL: https://81018.com/15-2/
Preliminary analysis: https://81018.com/geometries/
Thanks. -BEC

Five-tetrahedrons, five-octahedrons, five tetrahedrons and their gap

Bruce E. Camber