Thank you for those topics, they are interesting. Graphics programming has been something I've avoided because it's always felt too intimidating, but this feels

Thank you for those topics, they are interesting. Graphics programming has been something I've avoided because it's always felt too intimidating, but this feels like a nice place to start. Dynamic detail rendering built on octrees feels like a good way to handle the demands VR. I am not sure what benefits of ordering it as (2^N)^3 rather than (2^3)^N or just thinking of it as 8 all the time. Intuitively the inverse function will use log_8. I haven't come across Viete's formula before, I love these kinds of graphical solutions. The use of calculators depends on two things, the kind of test and how accelerated a curriculum is. Standardized tests like the SAT have specific calculator and non-calculator sections. As of this year AP Chemistry will allow them during both the MC and FRQ, but that wasn't always the case. Macro and Micro both only allow a four fucntion calculator. Whether calculators are allowed in classes depends on the teacher, but generally advanced/honors/ap classes emphasize learning to solve problems without one. Advanced classes focus on encouraging a more bottom up approach to learning how to solve problems, but in a class like Calculus, the CAS system in mainstream calculators make assessments trivial. On the AP and SAT exam, the NumWorks calculator is allowed and that's capable of running MicroPython 1.12. For my finals in AP Physics C, AP Chem, multi-var calc (in high school), I wasn't allowed a calculator. Similarly for all of my college math and cs courses, I wasn't allowed anything more than a four function calculator, despite taking the Matlab section of linear algebra and numerical analysis. I feel frustrated that most schools fail at teaching students how to use calculators effectively. I get genuinely annoyed when students tell me they prefer a Ti-84 over a Ti-89, because it's "less confusing". Some teachers in my school district even encourage a Ti-84 for 90% of Calc BC and only talk about the Ti-89 for those handful of topics that require it. Very few teachers, let alone students, use the CAS system. I tutor in those classes every year, it hasn't changed. I remeber I was asked by a teacher I had a good rapport with to give a presentation/demo for a handful of the other teachers during lunch. Having students graduate not knowing the "solve( f(x) = 0, x)" or how the calculator can do both symbolic and numerical integration is a failure of the education system. The TI Nspire II CAS not only has python, it has a color screen and can display animations, like turtle. If you jailbreak the Nspire with Ndless, you can even get micropython and there's an sdk that supports c and assembly to make apps. The newest Nspire OS doesn't allow the jailbreak though, and there's no way to downgrade. The only thing we used excel for in HS was making a graph or chart. I make sure my students leave with some profiency in excel, function nesting, cross sheet references, conditionals, and sorting at a minimum. There's a difference in knowing how to use a calculator and being able to use the calculator to do what ever you want. It's the same as students knowing the steps to solve a specific math problem but not knowing why.