Typically Desmos is used as a graphing calculator to plot functions from \( \mathbb{R}\) to \(\mathbb{R}\). It does, however, have lesser known features like lists, list comprehension, polygons, and the full scope of RGB colors, which allow us to do so much more. How much more?
A common exercise in introductory computer science courses will ask students to implement Conway's Game of Life. While to my knowledge no such course quite exists for Desmos, enthusiasts will take it upon themselves to give it a stab.
This example serves as a demonstration of how Desmos is quietly capable of so much more than it at first appears.
Lists in Desmos share some similarities with lists or arrays in many popular programming languages. Once a list is declared as a variable with some elements, its elements can be accessed with an index enclosed by square brackets.
The point-in-polygon problem asks whether a given point lies within some polygon. A simple technique is to shoot a ray from the point and count the number of intersections between the ray and the polygon's edges. If the point is within the polygon, the number of intersections should be odd; otherwise, the number of intersections should be even.
Thomae's function is a common function presented in introductory analysis courses which challenges students' intuition of what it means to be continuous.
Dynamical billiards generalizes the popular game of billards to a dynamical system modelling the motion of a particle within some boundary.