Mathematical Connections in the Terrace

Terrace of Mathemalchemy

Terrace

Mathematical Connections

Baker’s Map

The top of the buffet table rests on two supports that illustrate the Baker’s map, well-known as a standard example of a mixing system in dynamical systems theory.

Wikipedia Repeated application of the baker’s map to points colored red and blue, initially separated. The “stretching” and “joining” is shown as two distinct steps, although they are often considered a single iteration. After several iterations, the red and blue points seem to be completely mixed. Inspired by a similar animation by Craig Zirbel.
By Eviatar Bach – CC BY-SA 4.0

The folding map evoked in the table supports is closer to the operation
carried out by true bakers than the version more standardly used in
mathematics (illustrated in the little animation), which cuts the
elongated dough into two pieces to stack them on top of each other. The
folding version has similar mixing properties, as bakers have known for
a long time.

Traveling wave

The “traveling wave” design of the balustrade of the Terrace is inspired by its nearness to the Bay.

WikipediaGif of a traveling wave made with “desmos graphing calculator” by Abhinav P BCC BY-SA 4.0

Wallpaper groups

The designs on the two little mats show the two wallpaper groups that were not illustrated in either the Bakery or the Curio Shop;  together with the mat at the entrance to the shop downstairs, they show the 3 patterns that have 90 degree rotation symmetry and therefore lend themselves well to cross-stitching. The 2 designs here, with the 9 designs shown in the Bakery and 5+1=6 designs in the Curio Shop, give us the complete set of 17 wallpaper groups.

  • Mats on the Terrace
  • Mat mice with marked symmetries
Johnson solids

The purple frames of the poufs are three different polyhedra of the full collection of Johnson solids, all present in the installation. (Try to find them all! Hint: they are all realized as solids of which only the edges are indicated. You can also find all the archimedean solids if you wish – these have some but not all of their facets filled-in, and also the 5 platonic solids – with all their faces filled-in.)

Celestial dynamics

The small telescope alludes to the importance played in mathematics by the challenge of understanding celestial dynamics, throughout the ages. In particular, the mathematical study of celestial dynamics by Henri Poincaré gave rise to the whole mathematical subfield of Dynamical Systems.

Telescope in the corner of the Terrace

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