What is Mr. H working on?

If you want to know a little bit about Group Theory in particular, here is a link to a website that attempts to introduce the concepts.

https://www.cantorsparadise.com/an-invitation-to-group-theory-c81e21ab739a

Here is a Wikiversity page that you can peruse if you would like a little more of a technical introduction.

https://en.wikiversity.org/wiki/Introduction_to_group_theory

Aside from my academic work, as a result of an article that Mr. Nell sent me over a summer, I am attempting to create my own user-friendly, 3D representation of the quaternions.  If you would like, you can read more about them here:

https://en.wikipedia.org/wiki/Quaternion

and here is a (pretty technical) article that describes their application in computer graphics programming:

https://www.3dgep.com/understanding-quaternions/

1/12/26: I have lately been very interested in building fairly comprehensive physical models of a few scenarios that have either piqued my interest recently, have been something that I have had students work on to a lesser degree, or that have haunted me from my undergraduate coursework.  A few of them are below...

Desmos 3D Model of a Baseball Hit in Fenway Park (extension of a student project...the goal is to eventually include a wind component and air resistance on the ball)

Desmos Model of a Ball's Path with Air Resistance (2D)

Balloon Tethered to the Ground (Buoyance Model with Trigonometric Component) (a haunt from my undergraduate modeling course...the goal is to eventually include a weight attached to the balloon which further affects the air resistance on the balloon, as well as increasing its mass, and allowing for user adjustments of the balloon's size)

Arc Length of a Projectile's Flight (Air Resistance Ignored) This started as a question from Ms. Graber and turned into a rabbit hole of amalgamated concepts from calculus for me. You can find two usable formulas at the very end of the PDF.