On learning from number theorist, Shabnam Akhtari

Shabnam Akhtari, Eberly College of Science,
Pennsylvania State University
, University Park, PA 16802

Homepage(s): BanffBlog, Penn State, Oregon, Wikipedia
Lecture: Proofs-number-theory-and-sequences, [Video], MASSOLIT, August 2022

First email: Fri, May 5 @10:17 AM

Dear Prof. Dr. Shabnam Akhtari:

When does a number first become a geometry?

In a high school geometry class, studying pi (pi) and assuming* that pi defines the first moment in time, we said something like, “At the finite-infinite definition of pi is continuity-symmetry-harmony.”

Pages to unpack that statement are here:

With your extraordinary depth of field, do any of these pages make any sense to you? 

Thank you.

Most sincerely,


PS. What we were assuming is that (1) the sphere with its two vertices is the most simple physical object and (2) that the Planck base units are the first definition of natural units.


We found a tutorial online by Prof. Dr. Shabnam Akhtari which opened new insights on the relation between Fibonacci sequences (linear) and exponential sequences. In her course overview it says, “…we consider: (i) the definition of arithmetic sequences; (ii) the direct proof showing that each term in an arithmetic sequence is the arithmetic mean of its neighbours; (iii) the definition of geometric sequences; and (iv) the direct proof showing that each term in a geometric sequence is the geometric mean of its neighbours. Akhtari, S. (2022, August 30). Proofs: Number Theory and Sequences – Direct Proofs Using Arithmetic and Geometric Sequences [Video]. MASSOLIT.