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Mathematical Topics

  1. Topology and Geometry
    • Regular Polyhedrons. Set of the five perfect solids, each a half meter across. (m) (T+)
    • Buckyball. Truncate an icosohedron to produce a Buckminister Fullerene...this is accompanied by a soccer ball and a C60 model. (m) (T)
    • Minimal Surfaces. Soap films on wire frames. (s) (T+)
    • Conic Sections. Cone which can be sectioned to show circle, ellipse, parabola and hyperbola. (m) (T)
    • Saddle Shape Three-dimensional model of non-Euclidean surface; can also be produced by a square soap frame (s). (m) (T) *
    • Inner Tube. Toroidal surface to show or cut up. (m) (T)
    • Spherical Blackboard 1m diameter black spherical surface to draw on. (m) (T) ***
    • Ellipse Drawing Board. Drawing stencil for blackboard use. (m) (T)
  2. Chaos and Catastrophe
    • Chaotic Pendulum Coupled, double, physical pendulum executes chaotic motion when non-linear initial conditions are imposed. (m) (T) ***
    • Fold Catastrophe. One variable with no return: air pressure as the essential factor controlling the inflation and, ultimately, the catastrophic rupturing of a balloon. (m) (T)
    • Cusp Catastrophe. One variable with recovery from catastrophic change as demonstrated by toy metal "clickers" or frogs. (s) (T)
    • Zeeman Catastrophe Machine. Too complicated to describe in a sentence, this model nicely demonstrates a butterfly catastrophe involving two planes of stability separated by catastrophe. (m) (T)
    • Lorenzian Waterwheel. The rotation direction and speed of this water wheel is completly unpredictable. (m)
    • Spontaneous Symmetry Breaking. A symmetric rod that buckles in a random direction under a load: an asymmetrical solution to a symmetrical equation. (m) (T)
  3. Statistics and Algorithms
    • Binomial Distribution. Marbles fall through array of pegs into slots to form a distribution curve. (m) (T+)
    • Boltzmann Distribution. Mechanical analog of energy level populations which models a gas at essentially any temperature. [TP4.6/AA1.4] (m) (T+)
    • Towers of Hanoi Move the stack of four disks, two pegs to the right, in the minimum number of moves while keeping larger disks under smaller ones. (m) (T)
    • Random Walk Model Two-dimensional array of corks; the throw of a die determines which cork is removed to show a path across the board. (m) (T) *