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

- Tess the Tortoise’s shell demonstrates a heptagonal tiling of the Poincaré disk model of the hyperbolic plane.
- Tess is walking along Zeno’s Path, which alludes to Zeno’s dichotomy paradox. Zeno’s Path and the math behind it is also discussed in the to-do list that she holds.
- Tess is flying a Sierpiński tetrahedral kite (3rd iteration)
- The wall to Tess’ right is called the Riemann Wall, and alludes to Riemann integration.
- The Hilbert’s Hotel billboard on the Riemann Wall alludes to Hilbert’s paradox of the Grand Hotel.
- Tess is walking towards Integral Hill, which consists of two components: the Lebesgue terraces, alluding to Lebesgue integration, and the Riemann Cliffs, alluding to Riemann integration.
- Koch snowflakes are falling from the sky.

**Lighthouse**

**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.

Have you read our chronicles?