Below you will find some of the applets that I wrote. Some of them have an associated blog post. Enjoy

Calculus and Real Analysis

• A continuous, nowhere differentiable function: the Blancmange function (blog post)
• Epsilon-delta definition of limit of a function (blog post)
• The limit of a sequence (blog post)
• Cantor set (blog post)
• Using a race car to approximate instantaneous velocity
• Using a draining water tank to approximate instantaneous rates of change
• Dot product discovery applet (blog post)
• Cross product discovery applet (blog post)
• Basic vector operations (blog post)
• Parametric function grapher (blog post)—created by Marc Renault
• Pittsburgh Steelers logo using parametric curves (blog post)

Geometry

• Carnot’s Theorem (blog post)
• The Japanese theorem for quadrilaterals (blog post)
• The Japanese theorem for cyclic polygons (blog post)
• The Euler line (blog post)
• The Pascal line (blog post)
• Morley’s theorem (blog post)
• What shape are the golden arches—parabolas vs. catenary curves (blog post)

Linear Algebra

• Dot product discovery applet (blog post)
• Cross product discovery applet (blog post)
• Basic vector operations (blog post)

Dynamical systems

• The Discrete Logistic Equation (blog post)
• Discrete Dynamical Systems (blog posts)
• Cobweb plot of the logistic map (blog post)
• Families of dynamical systems (blog post)
• Three Gap Theorem/Steinhaus Conjecture (blog post)

Physics

• Parallel rays striking a parabolic mirror (blog post)
• The envelope of rays reflected by a parabola: the Tschirnhausen cubic (blog post)

Water waves: written with Tom Edgar (Dickinson ’02) in the summer of 2001 (see the Water Waves website that goes along with the applets)

• Shallow water waves
• Deep water waves
• Waves over a varying sea floor
• Wave trains
• Beach waves

Miscellaneous

• Sam Loyd’s “P. T. Barnum’s Trick Mules” Puzzle (blog post)