**Julia Collins,** School of Science, Edith Cowan University, Joondalup, Australia

**Articles****Homepage**(s) Australian Academy of Science, ECU – Maths Crafts Australia (founder)**Publications**: Get Smart: Maths, 2018, Numbers in Minutes, 2019**Twitter**: @haggismaths, UOW Library**YouTube**

Fourth email: 1 December 2022 @ 12:06 PM

Dear Dr. Julia Collins:

Your doctoral dissertation may not be directly relevant to expand our understanding of pi but given that knots are an important part of the dynamics of geometric unification theory (and I believe pi plays a much more substantial role between the Planck units [such as Planck Length and Planck Time] and particle physics than currently appreciated), it’s an important read.

Have you ever seen a five-octahedral gap? https://81018.com/2022/05/19/five/#Gap Do you think it could be significant?

Thanks.

Warmly,

Bruce

Third email: July 6, 2022, 9:59 AM

Dear Dr. Julia Collins:

Surely you are among the geometers, chemists, and physicists who know that five tetrahedrons sharing a common edge create a gap: https://81018.com/gap/ Most do not know that five octahedrons create the same gap; and that stacked, that gap is a beautiful thing to see: https://81018.com/15-2/ *

My initial study of the gap is here: https://81018.com/geometries/

I have unsuccessfully searched for studies that explore the very nature of it. Could it be associated with quantum fluctuations? Might this be the beginning of a geometry for quantum fluctuations?

Do you have any insights that could help me grasp these realities more profoundly? Thank you.

Most sincerely,

Bruce

*PS. Those are models we created and photographed. The face-to-face vertical alignment from tetrahedron-to-octahedron-to-tetrahedron would necessarily create a horizontal alignment much like that pictured. -BEC

Second email: Wednesday, March 16, 9:46 AM

Dear Dr. Julia Collins:

I hope my note below to JPL-NASA is OK with you!

I think a collaboration between you and Marc would be great!

Thanks.

-Bruce

____________________________________________

https://www.jpl.nasa.gov/contact-jpl

RE: How many decimals do we need? Marc Ryman comments on pi and “*How far off would your odometer be if you used the limited version of pi above? It would be off by the size of a molecule.*“

Your article about Marc Rayman’s calculation and conclusion is similar to Julia Collins’ more recent article, “Why bother calculating pi to 62.8 trillion digits?” It was in The Conversation, August 2021. It would be great to have Marc and Julia write an article actually showing us all the mathematical steps involved and reflecting on the logic of it all. Or, I could try writing it up with extensive quotes, but I think it’d be better coming from the two. I’ll send Julia a copy of this note.

I have quotes from both here: https://81018.com/pi-day-march-14/#References

Thanks.

First email: Monday, March 14, 11:51 AM

“With 32 decimal places, we could calculate

the circumference of our Milky Way galaxy

to the precision of the width of a hydrogen atom.

And with only 65 decimal places, we would know

the size of the observable universe to within a Planck length….“

Dear Dr. Julia Collins:

Thank you for your article. Fascinating.

I’ll be quoting you. Is there a better primary source than “The Conversation”?

Pi turns the universe on its head by giving us access to facets of infinity:

continuity, symmetry and harmony.

Here’s my Pi Day page: https://81018.com/pi-day-march-14/

Best wishes,

Bruce