Mathematical Web Applications

Last Change: October 5, 2022

Diversions

• Pirouette. A Spirograph clone for drawing and printing hypocycloids.
• Phosphene. Create patterns using identical square tiles.
• Holy Cross Hometowns. (H. Tucceri and C. Cao.)
• Non-Attacking Queens. Place $n$ queens on an $n \times n$ chess board so that no two attack each other.
• The Fifteen Puzzle. Unscramble numbered tiles.
• Draw on the surface of a torus. (Inspired by a question at math.stackexchange.com.)
• Hypercube. Explore the geometry of a cube in four-space.

Teaching Tools

• Precalculus:
  • Exponential growth.
• Calculus and Analysis:
  • Riemann sums. (C. Cao and H. Tucceri)
  • Taylor polynomials. (C. Cao and H. Tucceri)
  • Taylor approximation.
  • Series convergence. (C. Cao and H. Tucceri)
  • Guess the supremum. (C. Cao and H. Tucceri)
• Complex Analysis and Differential Geometry:
  • Draw on the surface of a torus.
  • Shadows of surfaces in higher dimensions.
  • Möbius transformations.
  • Riemann surfaces.
  • Surface gallery.
  • Plane curves.
  • Frenet frames.
  • Lissajous figures.
• Group Theory:
  • Subgroups of $(\mathbf{Z}_{m} \times \mathbf{Z}_{n}, +)$.
  • Cosets in $(\mathbf{Z}_{m} \times \mathbf{Z}_{n}, +)$.
  • $D_{3}$ Explorer and Navigator.
  • $D_{4}$ Explorer and Navigator.
  • $D_{6}$ Explorer.
  • Draw on the surface of a torus.
• Linear Algebra:
  • Geometry of linear transformations.
  • Matrix Multiplcation.
  • Gaussian Elimination.
  • Matrix inversion.