# Educators, what resources have you built to better serve your students?

What resources (Desmos, Geogebra, math3d, etc.) have you built to help your students better understand or visualize topics in mathematics?

Riemann Sum visualization

Fundamental Theorem of Calculus Explanation

Error bound on integral for increasing function

• Some students of mine worked out what would happen if you find the unique circle passing through three nearby points on the graph of a function, and then take a limit as those points get close to each other. Similar idea to the tangent line development, but with circles. They ended up needing Taylor series to get the exact equations for the "tangent circle"!

1-form visualizer

• This visualizes the one form by looking at level sets of the covector in a small rectangle around each point. You integrate the 1-form along a curve by just counting how many level sets you cross (taking into account the spacing $$h$$ between level sets).
• Hah I like how we both have very distinctive styles with Desmos demos. These are great! Aug 4, 2022 at 19:15
• In my opinion, tangent circles make more sense in the more general context of plane curves (say, parametrized curves) rather than the particular case of the graphs of functions. The (reciprocal of the) radius of said circle is perhaps the most common definition of the curvature of a curve. Aug 5, 2022 at 6:38
• @Arthur I agree, but these were Calc 2 students who were "discovering" all of this on their own. Aug 5, 2022 at 11:46

Here are some physics-related ones... many not quite as polished as they could be.

update:

webvpython / glowscript (also supported on trinket.io)

• EMwave - EMwave on trinket.io - an interactive 3D animation that shows how the Faraday and Ampere-Maxwell laws propagate the electric and magnetic fields in a plane electromagnetic wave.

desmos

https://www.geogebra.org/u/robphy

• I love the spherical coordinates demo you have. I had a kind of crappy version that was not remotely as clean. Having the volume element represented is fantastic. Aug 6, 2022 at 1:18
• The special relativity Desmos demo is also great. Aug 6, 2022 at 1:19

## Automatic-Algebra.org

I built this website for the purpose of timed self-quizzes on topics that should (mostly) be prerequisite, "automatic" knowledge prior to a number of basic college courses. Available quizzes include:

• Times tables
• Negative numbers
• Order of operations
• Sets of numbers
• Special products
• Finding intercepts
• Special lines
• Graphing lines
• Decimal rounding
• Decimal relations
• Decimals to percent
• Sampling distributions
• Chained relations

I usually just use html/SVG combination and do it on a case by case basis. Examples include

https://www.math.kent.edu/~nazarov/switches/switchgame.html (Linear system in $$Z_2$$)

https://www.math.kent.edu/~nazarov/Hillcipher/hill.html (Linear cipher)

https://www.math.kent.edu/~nazarov/Buffon/buffon.html (Buffon's needle)

https://www.math.kent.edu/~nazarov/T-intersection/tint.html ("real life" linear equations problem (ill-posed without prohibiting left turn))

https://www.math.kent.edu/~nazarov/turmach (Turing machine emulation)

There is more stuff in that directory (mainly games made for Math. Club). It doesn't relate to the question directly, but you are welcome to take a look at it too just to see what can be done in two or three evenings with basic HTML skills (except Jeopardy: that one took a couple of weeks and was a work of several people). Some of these are not immediately obvious how to operate, but if you get interested in any of them, just let me know.

I've put together a number of online interactives in Javascript for College Algebra, Precalculus, Statistics, and Linear Algebra, available here: https://trkern.github.io/