Projects
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Math 124 Visual Projects
Each student began with a Math 124 problem, then asked new questions and built a visual model to make the story easier to see.
Sliding Ladder
What is actually changing when a ladder slides down a wall?
Marcus started with the classic Math 124 sliding-ladder related-rates problem, including the firefighter variation, and built visuals that reveal the hidden geometry.
Minimum Distance to a Curve
How do we find the closest point when the distance keeps changing?
Tessa started with a Math 124 optimization problem about minimum distance from a point to a curve, then generalized it with visual explorations.
Draining Cone
How does dripping water from a cone become a story about changing volume?
Aiden started with a Math 124 related-rates cone problem, then we turned it into a draining problem connected to differential equations.
Self-Similar Melting
How do different shapes melt if they shrink in the same self-similar way?
Celina started with a Math 124 related-rates melting problem, then expanded it into a broader visual comparison of shapes, volume, and surface area.
Cart and Pulley
How does one moving object force another distance to change?
Hannah started with the Math 124 cart-and-pulley related-rates problem and built visuals that connect motion, geometry, and changing lengths.
Rowing and Running
Where should you land if rowing and running have different speeds?
Arjav started with the Math 124 minimum-time problem about rowing across a river and running downstream, then built a strong optimization visual.
Lighthouse Along a Coast
How does a rotating light turn angular motion into motion along a coast?
Michael started with the Math 124 lighthouse related-rates problem, built fun visuals, and made Manim videos to help tell the story.
Fun Exploration Projects
Each student also pursued a broader curiosity project, starting with a question from nature, motion, sound, sports, waves, or visual art.
Shell Growth and Spiral Geometry
How do shells grow into spirals?
Celina’s second project explores shell growth using spirals, 3D curves, chamber walls, ribbing, and surface features.
Tangent Art / Curve Envelopes
How can straight lines draw a curve?
Marcus’s second project uses connected points, parametric curves, and envelopes to create 2D and 3D string-art-style visuals.
2D Wave Equation
What does a wave look like when it moves across a surface?
Aiden’s second project creates visual models of the 2D wave equation, including boundary behavior, initial conditions, and series solutions.
Guitar Bodies and Sound
How does a guitar body shape sound?
Tessa’s second project explores the math of guitar sound through the 1D wave equation and 3D cavity wave behavior.
Roller Coasters and Curvature
What makes a roller coaster curve feel smooth?
Hannah’s second project uses roller coasters to illustrate curvature, g-forces, torsion, and motion along curves.
Air Resistance and Magnus Effect
How do air resistance and spin change the path of an object?
Arjav’s second project builds motion animations incorporating air resistance and the Magnus effect, including bending soccer-ball trajectories.
Laplace Transform Geometry
What does a differential equation look like in another world?
Michael’s second project creates a collection of visualizations of the Laplace transform, connecting time-domain motion to s-domain geometry.