This page is a collection (and brief explanation) of applets made with GeoGebra and Mathematica. These applets are designed to give a flexible, illustrative, and elementary explanation of various mathematical concepts using graphics and animations.
GeoGebra applets
Volume of a Sphere as Cross Sections shows how the volume of a sphere can be described as the integral of the cross sections of the sphere.
Solids of Revolution – Between Two Curves shows how to calculus the volume of a solid of revolution which is defined as the area between two curves/functions.
Partial Derivatives and Tangent Planes shows what partial derivative mean geometrically and how tangent planes are defined using those partial derivatives.
Defining the Derivative sequence
The applets in this sequence all show visual/geometric proofs of the different derivative rules. Most of these were created during my time as Teacher’s Assistant for my AP Calculus instructor.
Defining the Derivative for Sines uses the definition of sin(θ) and cos(θ) in the unit circle to define the derivative for each of those functions.
Defining the Derivative for Tangent uses the definition of tan(θ) in the unit circle to define the derivative for that function. The math can be carried out two different ways; one which uses two equations for the area of a triangle to find the length of d(tan(θ)), and another which uses light projection (as if there were a point light source at the origin, a vertical wall at x=1, and an object which can cast a shadow at dθ; this would make d(tan(θ)) the shadow of dθ on x=1). I have not yet figured out how to use the second projection method.
Defining the Derivative for Secant uses the definition of sec(θ) in the unit circle in an attempt to define the derivative for that function. I have not found a way to actually define the derivative for secant using this method, but the interactive might still be helpful.
Defining the Product Rule uses the change in area of a rectangle to define the product rule. The rectangle is defined as having side lengths dependent on two different functions — f(x) and g(x) — which makes the area of the rectangle f(x)*g(x).
Mathematica Applets
Modeling Electron, Molecular, and Hybridized Orbitals: In a molecule, the individual electron orbitals can add together to create molecular and hybridized orbitals. The shape of these orbitals is determined by how the constituent electron orbitals are oriented. NOTICE: This link is currently broken. I am currently looking for ways to include it here, but have not yet found any reasonable solutions.