The Desmos Visual Code Atlas is a book, website, and workshop project, in progress, on using Desmos as a visual mathematical laboratory.
The project grows out of years of teaching precalculus, calculus, differential equations, and multivariable calculus with interactive graphs, animations, 3D models, and visual explanations.
Desmos is often introduced as a graphing calculator. Used deeply, it becomes something larger: a place where formulas move, parameters become experiments, geometric ideas become visible, and students can test mathematical claims for themselves.
This atlas is meant to show the visual and the code side by side. Each page would connect a finished Desmos visual to the formulas, sliders, lists, restrictions, colors, animation choices, teaching use, and student questions that make the visual work.
During pandemic-era online teaching, especially in 3D calculus, visual examples became a promise I made to students: every lecture would include something new to see. Desmos, Desmos 3D, screenshots, animations, and 3D-printable models became part of how I kept large online lectures alive and mathematically grounded.
Over time, that work grew into a large visual archive. Some examples are quick classroom demonstrations. Some are polished interactive models. Some are seeds for student projects, undergraduate research, public math pages, or future papers. The common thread is that the mathematics becomes easier to discuss when the object is visible and editable.
A first Desmos visual can be very small. One useful starting pattern is a point moving along a curve as a time slider changes:
"Time slider"
T = 0
"Curve coordinates"
x(t) = t
y(t) = sin(t)
"Moving point"
(x(T), y(T))This tiny pattern already contains the heart of the atlas: define a mathematical object, give it a parameter, animate the parameter, and ask what the motion reveals.
Open Desmos Graphing Calculator and try the pattern by adding a slider for T.
Substantial draft material already exists for this project, including an atlas outline, a Desmos syntax and code-style guide, and several prototype chapter sections. Two sample directions are especially strong:
This opening chapter teaches a reusable pattern: a time slider, coordinate functions, and a moving point. From that one idea, students can build projectile paths, cycloids, car motion, bouncing balls, and trails.
The point is not only to learn syntax. The point is to see how static formulas become motion, and how motion creates new mathematical questions.
Another draft chapter builds an interactive integration tool with left, right, midpoint, trapezoid, and Simpson methods. The visualizer is designed to show the rectangles, trapezoids, Simpson parabolas, subdivision slider, numerical approximation, and comparison with the true integral.
This is the kind of page that could become a teaching tool, a student project, a workshop activity, and a polished atlas entry at the same time.
A longer draft also reworks volume-by-slicing lecture notes around student-facing visuals. Each example is paired with a Desmos visual prompt, a slice slider, and a clear description of what students should see as the region becomes a stack of cross sections.
This work also connects to a broader visual mathematics class and project ecosystem. The goal is to help students move from a question to a model, from a model to a visual, and from a visual to a mathematical explanation they can share.
I proposed a Math 380 topics course built around this kind of visual mathematical work. The department did not have a good spot for it at the time, so I am teaching a smaller version through the College Edge early fall start program. I would still like to turn the idea into a full course, possibly in another home such as computer science or applied mathematics, where students could build mathematical tools, visual explanations, and interactive models.
I also think this could become a fun online course for teachers: a place where instructors learn Desmos, build their own visual tools, and leave with usable classroom materials.