Desmos Projects
Some simulations I’ve worked on in high school and early college.
Physics
RC Circuit
- Models and simulates the flow of charge in an interactive resistance-capacitor circuit. Can modify variables such as the battery voltage or the dielectric constant and can switch between charging and discharging.
Physical Pendulum
- Models the simple harmonic motion of a physical pendulum (a rod). Also functions as a metronome using the period of rotation to determine the BPM. Changing the length and the axis of rotation will affect this period. Does not account for error that occurs when θ is approximated for sin(θ).
Large Angle Physical Pendulum
- Similar to the above, but is accurate to large angles. Uses an energy conservation approach (rather than simulating a nonlinear differential equation) to avoid error. Can also draw an approximated graph of the oscillatory motion.
Simple Harmonic Motion
- Models the simple harmonic motion of a point mass on a spring.
- See 3D version here
Math (Calculus and Statistics)
- Slope Fields
- Visualizes the slope field generated when the slope (dy/dx) is represented as a function of x and y.
3D Grapher
- This one was difficult
Curvature and Vector Functions in 2D
- Visualizes the multivariable concept of curvature and animates the velocity and acceleration vectors along the parametric graph.
Everything about Triangles
- Nearly everything about a triangle is found here: medians, altitudes, angle bisectors; the orthocenter, circumcenter, incenter, centroid, Euler’s line; the inscribed, circumscribed, and the secret 9-point circle, and more.
Linear Regression Visualized
- Visualizes how a linear regression is conducted by finding the minimum of the residuals squared (hence “least squares regression line”). A similar process is used when doing exponential regression as shown here.
Vector Projections
- Visualizes the projection of one vector onto another vector. Can help with understanding the dot product.
Riemann Sums
- Visualizes the process for how an integral is calculated and approximates the area under a curve.
Sierpinski’s Triangle Generated
- Choose a random point in an equilateral triangle. Find the midpoint between that point and a randomly chosen vertex of the triangle. Repeat this process using the new midpoint. 1000 repetitions later, a figure that looks like Sierpinski’s Triangle seems to magically appear.
Points Circle Illusion
- Based on an animation I found online, animates a series of points moving on line segments. When many points are simulated, the points appear to move in a circle.
Rotating Polyhedron
- Visualizes a 3D object rotating in a 2D space. Can adjust the number of sides and the point of view (angle). Try to see the figure rotate in 2 directions: counterclockwise (looking from above) and clockwise (looking from below).
Economics
Supply and Demand
- Models the various features of this fundamental graph in microeconomics, including the effects of elasticity, world trade and tariffs, taxes, and price floors and ceilings on consumers and producers.
Perfect Competition
- Models the cost and revenue curves (ATC, AVC, MC, MR, etc.) of a firm in a perfectly competitive market.
Imperfect Competition
- Models the cost and revenue curves and the resulting inefficiency that occurs in markets like monopolistic competition, oligopolies, and monopolies.
Comparative Advantage
- Models the production possibilities curve for two nations (with constant opportunity costs) and determines the terms of trade that are beneficial to both countries.
Consumption and Savings
- Based the marginal propensity to consume (tendency to spend), calculates the total money spent and saved for a given income.
Art
Drawing
- (Run the ticker before drawing) Creates a series of line segments as one drags the “cursor” across the screen. Can also modify the color.
Animated Sunset
- An animated sunset, make sure “t” is increasing
Rainbow Ripple
- A relatively basic creation that creates a “rainbow ripple” when running the ticker
Games
Graph Game
- Input a function and interval. Upon starting, drag the green point along the graph as evenly and accurately as possible. For an added challenge, try hiding the function to test your graphing knowledge.
Pong
- One of my more challenging projects, since there are numerous conditions required for the ball to bounce off the paddle, and Desmos does not allow two variables to be updated at the same time in the ticker. The ball speed increases by 10% per bounce.
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