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Exhibit Plans

The Math Factory Working Group is developing a wide array of exciting exhibit plans. This section of the website serves as a brainstorming area for exhibit ideas — members, please feel free to add in any and all thoughts you may have. No idea is too outlandish or too ambitious to be worth considering. (This is, after all, the fun part!) Our goal is to produce the most engaging, exciting, and mathematically diverse collection of exhibits possible.

Ideas for the overall structure, layout, or organization of the museum should be added on this page, below. Ideas for individual exhibits should be organized into thematic collections. Members, please add new collections as you're inspired to, or add ideas to existing collections. We've also included a place for exhibits that don't yet fit into an identified collection. Depending on the size and location of the eventual museum, the collections might roughly correspond to galleries, walls, or just clusters within the museum.

Some of the websites featured on the Featured Links page would surely be rich inspirations for possible exhibits.


Overall structure of the Museum


Entryway

  • The entry to the museum ought to have an attractive portal connected with the theme or name of the museum. For example, "Math Factory" might lead to a decoration with gears, chutes, etc. arranged/combined in mathematical forms or with mathematical symbols. Perhaps a design contest for the entrance sent to design schools/firms would work?
  • We should have a large-scale, interactive exhibit outside the museum itself in a place where it will attract attention. Possible ideas for this would be: a kinetic sculpture based on mathematical ideas which can be manipulated in some way by passers-by; a set of very large, soft, space-filling polyhedra which can be rearranged and possibly climbed on by kids; please any other ideas if you have them.
  • Just inside the entryway we should have a large, eye-catching mathematical sculpture, to whet the appetites of visitors for what is in store.
  • Another option is to have artwork of Bob Bosch of Oberlin College. For examples of his work see: http://www.dominoartwork.com/ and http://www.oberlin.edu/math/faculty/bosch/tspart-page.html The TSP art could be something for visitor's to follow the TSP path until they complete the circuit.

Visitor experience

  • We want to collect feedback on the interest level generated by different exhibits. Potentially we could automate this process to some extent: visitors could receive reusable e-paper name badges as their tickets. These badges could contain RFID chips so that we can track who is visiting each exhibit and how much time they are spending there. If we ask each visitor about their mathematical level, it would also allow us to understand the difficulty level of each activity, and potentially offer tailored hints/suggestions at the exhibits. Of course, the badges would be returned on exit, and no name or other personally identifying information would be stored — just statistics on the visitors to be used in research and development.
  • To increase the visual attraction of exhibits and engage more visitors than the one or two currently actively using the exhibit, we could have the materials of the exhibit be able to be sensed by the computer systems underlying the exhibits, and images based on the acitivities displayed on large screens above the exhibits. For example, a basic exhibit on circles where the visitor draws a circle with her finger by putting a loop on a post and pulling it taut and going around the post could gain a great deal of impact by recording the track of the finger and adding it in a new color to an accumulating display of circles. If we had a similar one for ellipses, the visual contrast would be attractive, and would help illustrate the mathematical differences and similarities between these curves.
  • Museum Shop: To support the mission of the museum and to distribute materials of mathematical interest and educational value, we should have a Museum Shop, both physically at the museum and on-line.
  • The NY Hall of Science has the capability to track the paths of individual visitors through the museum, it seems to me that could be put to good use. Perhaps to deal with speed issues in Ken's traveling salesman exhibit (see the Miscellaneous Exhibits.) We could think of developing a base technology platform, including the "smart tables" or "smart trays" of the previous item plus information about visitors and their positions which could be used as the infrastructure of many exhibits.
  • To reach as broad an audience as possible, we should replicate as many exhibits virtually in our on-line museum as we can.
  • We could also create a series of kiosks with both a virtual and a physical element to be placed in a variety of allied museums around the country, allowing some collaborative, math-based activities that would create opportunities for real-time collaboration by visitors at very geographically diverse sites. [Idea suggested by Dr. Duane Adams]
  • Visitors will hopefully generate a lot of materials that is "theirs" over the course of their visit — cool curves from the chaotic pendulum, maybe a pretty tiling pattern, etc. The store could potentially self hard copies of some of these items to their creators. Or it could sell "soft copies" — for a nominal fee, all your displays are saved and put on a personal subpage of the museum website (which you could open to the public or not as you see fit.) Or we could give away some of these things, or include them in the membership package, etc.
  • We should have exhibits that tie in with the eventual name of the museum. For example, if we do go with Math Factory, we have to have some highlighted exhibits about factoring ( see the Mathematics of Numbers.)

Physical environment

We can use various aspects of the finishes of the space we are in to illustrate or display mathematical concepts. Some examples:
  • It might be nice to use floor tilings (or mosaic installations!)that illustrate some important mathematics. For example, one room could be tiled with black and white tiles in the pattern of the Gaussian primes. [or the spiral arrangement of the natural number primes.] Another could show a tiling that reflects cells in the affine Weyl group of type G_2. Another could show Pascal's triangle modulo some integer (replacing numbers with colors). In the Mathematics of Shape Collection, we might simply want to have the floor include regular triangle, square, hexagon tilings, Cairo tiles, and/or semiregular tesselations.
  • We could have a window or windows with reproductions of rose windows and highlight the mathematical/numerological structure of the windows. Or we could have other mathematical stained glass window patterns.
  • If there is a staircase(maybe a helix or archimedean spiral?), the handrail could be integrated with the number line exhibit proposal
  • To what use might we put the ceiling? The Mathematikum has a few mathematical sculptures hanging from its ceilings.
  • In some rooms, particularly in the Curves Collection room, the ceiling itself could be built down to make a quadric surface, such as an ellipsoid or paraboloid. For examples see John Kostick's Quadric Designs webpage.
  • If we create a traveling exhibit, and if the quadric-surface framework can be created to be easily installed/un-installed/stored/transported, we could include a quadric surface framework canopy over (portions of) the traveling exhibit, which would serve both as an eye-catching portion of the exhibit itself, and potentially a place from which to hang math-related objects such as various polyhedron models, or models of various other curved surfaces, etc.

Room Arrangements:
The most current animated cartoons are able to reach out to youngsters and adults at the same time. They are able to achieve this status by carefully choosing their material on a variety of levels. I hope that at the Math Factory, we will be able to attain this same result. I recommend that this will be possible if each of the rooms in the museum has projects that can be understood and appreciated by all ages and all math backgrounds. As an example of this, consider a room where Counting is the key concept. There can be a section assigned to the History of Counting (counting systems of the Babylonians, Egyptian fractions, Roman numerals, the abacus etc.). Other subdivisions in the Counting room could be summarized by:
Basic counting skills - enumeration - 1 to 1 correspondence (pre K-2)
Counting by grouping (2-5)
Counting with multiplication (4-6)
Counting through patterns (all ages) - fence posts, coins/bills, dominoes, points-lines-regions
Fundamental counting principle - telephone numbers (HS)
Pigeonhole principle (HS)
Sequences - (HS)
arithmetic - theater seat problem
geometric - money-money-money, bouncing ball problem
Fibonacci - hare-raising problem, staircase problem, great train problem
Harmonic – connections to music, sum is infinite etc.
Combinatorics and binomial distribution (HS - college)
Probability (HS - college)
Assorted problems - locker problem, checker problem, spaghetti problem, desert problem (HS - college)
Counting by approximation – German Tanks, Fish in thee sea, leaves on a tree, grains of sand, electrons in the universe
Counting to infinity and beyond - (HS - college)
Sometimes the parts are equal to the whole!
Additional room suggestions:
Arithmetic Room:
Four basic operations - hands on manipulations (K-6)
Operations with fractions and decimals - hands on manipulations (4-12)
Operations with variables - hands on manipulations (7-12)
Understanding the connection between integers and polynomials
Understanding the connection between rational numbers and rational expressions
Working in bases other than base 10
Modular Arithmetic
Operations with matrices
Arithmetic of complex numbers
Generating prime numbers
Sums and products that result in transcendental numbers (π, e, ϕ)
Summing up infinitesimals

Function Room:
Sets (K-12)
Basic functions
Transformations
Making the algebraic/geometric connection
Arithmetic of functions

Geometry Room:
2D and 3D shapes (preK-6)
Polyominoes
Tessellations
Perspective drawings
Sphere packing

Art Gallery:
Here you could curate a few exhibits per year, inviting artists in any media to submit mathematically relevant work on a particular theme. Unlike the permanent collections, this would change and be a source of interest for repeat visitors and a way to get more people involved. Examples: an exhibit on the mobius strip, or the use of polygons, tesselations in quilts, mosaics, etc. This might encourage artists to stretch themselves mathematically, creating more math awareness all around.

Created by whitney. Last Modification: Sunday 15 of August, 2010 23:19:14 EDT by fried.