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What would you like to see at MoMath?






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94 Answers 94

An exhibit - with both individual workstations and one whose results are projected (to draw people in) - where users use parallelograms to specify affine transformations which in turn define Iterated Function Systems and their associated fractals. See here for background. With a few moves/ clicks a user can start making fractal ferns, clouds, spirals and starfish as well as classical objects such as the Sierpinski gasket. It is great because you don't have to know anything to start making pretty pictures, but you immediately get a sense that there is something significant going on. For those who want to see beyond the pretty pictures, one could explain the contraction mapping theorem (terrific fun in its own right) and develop affine-linear transformations starting with rotations, scalings and translations. Trying to find the transformations which define a particular fractal by "finding enough smaller copies of the fractal to cover the fractal" is also great fun, which is compelling even for children.

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Stereographic projection lamps, please!


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@kjetilbhalvorsen, if you get it working, I'd love to see pictures! – Vectornaut Mar 21 at 21:52

Klein bottle (with a description containing at least 15 characters)

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  1. what kind of problems mathematics deals with, and
  2. how it deals with them.




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I'm a Mathematics & Theoretical Physics undergrad, so I though I'd share what got me hooked on Maths. As a teenager it first dawned on me that Maths wasn't the "dry", boring subject taught at school when, on my own at home, I first started playing around with nD geometry and generalised Euler's Theorem to nD by noticing the patterns. The thing that really made me fall for Maths though was reading about the Riemann Hypothesis in New Scientist when I was 16. [It's hard to believe, but none of the Maths teachers I'd had had even mentioned primes, and I was hooked.

The thing I'd put in MoMath is the Mandelbrot set across a HUGE wall using a projector that gradually zoomed in and in. After a set time it could start again but zoom in on a different area. You could include higher-order Mandelbrot sets and other infinite fractals. The beauty of fractals is their beauty appeals to everyone [Importantly including NON-Mathematicians!] and gets an important point across: "MATHS IS BEAUTIFUL!"; in the blink of an eye. It would show clearly & quickly both the richness & beauty that lies within Mathematics and that it's NOT the dead, dull, dry subject many people think.

I would suggest screening a range of pre-recorded maths "lectures", catering for the diverse spectrum of Mathematical-understanding of the visitors.

MoMath, if done right, seems like a brilliant idea. Good luck with the project, and I wish you every success! :-)

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Downvoted because it's a rant; also, Dick Palais has already suggested fractals. – Daniel Moskovich Dec 30 '10 at 20:53


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A huge fountain that doesn't work.













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Indeed, it is somewhat out of control. Rather than flag and state my objections or alert the moderators or start a meta thread listing objections, I will wait and see if you bring it back under control. Your unedited opinions may be OK for your blog; I think your posting (at this writing) needs pants. Gerhard "Ask Me About System Design" Paseman, 2011.10.21 – Gerhard Paseman Oct 22 '11 at 3:53

Look at the 'surfer video' which among other things shows how visualizations of algebraic geometry can be presented in real-time in an exhibition.

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Something from Erik Demaine on linkages would have wide appeal.

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I'd love to see a wall sized picture of the matrix of a random element of the monster group acting in a faithful representation.

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S. Carnahan---I think that's a really good argument in favor of the proposal! When I read your comment, my first thought was, "Come on... 196882 can't be that big." Then I multiplied it by a millimeter, and---WHOA. I would love to see an auditorium-sized wall filled with a corner of one of the monster matrices, with the entries in 4-millimeter type, and a little plaque saying that two write out the whole matrix, you'd need a wall two Empire State Buildings high! – Vectornaut Oct 26 '11 at 6:25


On January 12th, at 9:30pm ET, follow this link to join the live session using Elluminate:

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Instead of an answer, I think this should be edited into the original question. Otherwise it will be lost in the long list of suggestions. – Douglas Zare Jan 3 '11 at 16:19


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A book scanner.

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Please elaborate? – Kevin H. Lin Dec 25 '10 at 23:41
It is full of mathematical technology and, out of all proposals in this thread, gave the most positive feedback to mathematics. – darij grinberg Dec 26 '10 at 14:15

Maybe it will be good to place in such a museum some of the famous original papers or copies (like the Poincare's article on topology or homology or the Grothendieck's papers on schemes or maybe the famous page where Fermat had declared his Great Theorem).

Also it will be good to place here some of the drawings of (for example) mobile telephones with mathematical calculations.

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I honestly can't imagine that the general public would get anything out of this. – Qiaochu Yuan Dec 31 '10 at 16:54


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Finding Tumors with Linear Algebra (and a lending hand by logarithms):

Example of the use of linear algebra (and with less emphasis, logarithms) in a toy example of computerized tomography (CT scana).

Computer (Bob) chooses a transparent plexiglass box among four such boxes in a horizontal square grid in which to place an opaque box/tumor. The top of the grid must be covered so the investigator (Alice) can't see where the opaque box is. She can, however, rotate a laser penlight to shine a laser beam horizontally through the boxes and observe any shadow on the opposing side (complete attenuation). Bob displays a diagram of the four empty boxes and asks where the tumor/opaque box is. After Alice figures out how to locate the box, Bob asks what the minimum number of positions for the penlight for effectively locating the opaque box is. Next a second opaque box is placed randomly in the grid and the process iterated.

Placement of a third opaque box results in failure, but now a light meter is placed opposite the penlight, the three opaque blocks are replaced by semi-transparent boxes with their attenuation coefficients (ACs) given (nice integers), and Bob explains that for a box the AC is log[intensity of light in / intensity out] so that the total attenuation displayed by the light meter is log[intensity at penlight / intensity measured by the light meter] = AC of row or column of grid = sum of ACs of boxes in the row or column. Can Alice figure out the placement of each box? Must Bob demonstrate the linear algebra required to solve the problem? Finally, four boxes with differing ACs (nice integers) are configured in the grid and Alice asked if she can determine the ACs of each box. Bob gives a grey level display for each result--hands-on tomography.

In my experience, very young kids with decent attention spans like such interactive challenges (no shock and awe approach, just simple reasoning).

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The Duel: Who Fired First?

Projections, Minkowski space, special relativity, and a legal paradox

A computer displays a line of observers outside a speeding train and a parallel line inside a train, all with respectively synchronized stop watches. Between the two lines and displaced along the length of the train are Galois and his frenemy with pistols poised. An animation captures the interest of the museum guests.

Two coordinate systems are superimposed with the origins of both systems coinciding at time $t=0$ well before the pistols are fired with respect to the observations of the ground crew.

A spacetime graph is displayed depicting the two events of the pistols being fired. In the classical Newtonian world, the two spatial coordinate lines are superimposed and depicted parallel to the two lines of observers with their origins displaced by the motion of the train by the time the shots are fired. The single time axis is depicted vertically perpendicular to both coordinate axes. The spatial displacement between the duelers is determined by drawing lines parallel to the single time axis through the point-events and down to the spatial axes, and analogously for the temporal displacement between the firings of the pistols. Let's have the two events happen simultaneously as recorded by the ground crew. Then the events will occur simultaneously according to the observers on the train also with exactly the same spatial displacement between the adversaries. These facts are easily demonstrated by the projections, and, indeed, are equivalent to the projections.

In the world of special relativity, the facts change. While keeping the time and space axes for observations by the ground observers unchanged, the time and space axes for the observers on the train must be displayed pivoted about the origin towards each other. Projections parallel to the skewed time axis though the events to the spatial axis reveal that the train observers will record a smaller spatial displacement between the duelers, and projections parallel to the skewed spatial axis reveal a non-zero temporal displacement in the events, i.e., the times the pistols are observed to have been fired are not equal as measured by the train observers.

A legal paradox! The ground observers might conclude the duelers are equally guilty of premeditated murderous intent whereas the train observers might accuse one of premeditated murderous intent and the other of reacting only in retaliation.

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I'd like to see a picture of a person throwing a ball (eg Michael Jordan) and next to it, the corresponding parabola in a Cartesian plane.

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Car parking by Lie group techniques!

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The Body Counter: Making Math Matter in Human Rights

An exhibit explaining the use of multiple systems estimation (MSE, a type of statistical inference) in human rights investigations and trials, based on Tina Rosenberg's article The Body Counter.

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