Mathematical Concepts

Now that the construction of the Mathemalchemy installation is mostly done, we can work on the next phase of our project: documenting all the different mathematical concepts illustrated or evoked in the installation. Over the next few months, more material and links will be added. Here is a start.

Bakery

Tortoise Story

Garden and Reef

Lighthouse

OctoPi Mural

Mandelbrot Bakery

  • Symmetry groups (wallpaper groups on wallpaper, action of reflection on pretzels)
  • Tessellations (pi-cookies, Marjorie Rice tiling by pentagons on floor)
  • Topology on manifolds (train tracks on picture on wall, mirrored by cake mold and little train on shelves)
  • Optimization: traveling salesman algorithms (TSP art on Bob Bosch’s furnace grill)
  • Geometry: inversion of the plane w.r.t. circles (Indra’s pearls-inspired construction on oven door); hyperbolic disk (tessellated by pentagons on cartwheel)
  • Fractals: apollonian gasket (on cartwheel), roof of oven, Mandelbrot set (wall decoration and doorknob)
  • Dynamical systems: periodic orbit of pentagonal billiard in cutout above door, Mandelbrot set (those c for which the orbit of z=0 remains bounded under repeated iteration of the z to z^2+c map)
  • PDE: time-dependent Schroedinger equation on rim of bowls

Tortoise Story


Lighthouse

  • Glass dodecahedron (beacon in lighthouse) a straight-line trajectory on the dodecahedron from a vertex to itself that does not pass through any other vertex (one example of an infinite number of such trajectories, proved by J. Athreya, D. Aulicino and P. Hooper)
  • Stereographic projection – LED light at the base of a patterned 3D printed sphere creates a 2D shadow of the sphere pattern on the ceiling
  • Helicoid lighthouse

OctoPi Mural

  • Fano plane octonion mnemonic
  • Wave equation, with waves created from a dripping fluid
  • Navier-Stokes equation, with a vortex created by a gas streaming around and past an obstacle
  • Ingrid Daubechies’ plot of a wavelet (painted as a graffiti ferocious ocean wave) 

Garden and Reef

  • The Sieve of Eratosthenes
  • Prime/Composite number play
  • Fractal Flowers and ground cover
  • Alexander Horned Sphere
  • Hyperbolic Flowers – represent hyperbolic plane, a surface with constant negative curvature on which hyperbolic geometry holds.