During the summer, I teach at the Hampshire College Summer Studies in Mathematics (HCSSiM).
In the following five pictures, you see the result of string pieces choreographed by the Dr. Schaffer and Mr. Stern Dance Ensemble. (More detail on their pedagogical work is at the Math Dance site.)
Clockwise, beginning with the top: Andrew Uzzell, Karol Przbytkowski (seated),
Matt Tretin, Daniel Studenmund, Martin Vieth (center), Gavin Dow, Danny Scheinerman,
Niko Warner, Nelson Chiu, Maria Guirguis. Lying in the background is Leathan
Graves-Highsmith.
This is a dodecahedron from multiple string loops, from HCSSiM 2003. The students
used diagrams and instructions I wrote from discussions with Karl Schaffer.
Clockwise: Emily Bargar in green, Ian MacLeod, Jamie Conway, Sho Uemura, Talia
Hurwich, Alex Kunin, from HCSSiM 2004. In the left-hand photo, the students
are discussing how to transform an octahedron into a tetrahedron, which has
been completed in the right-hand photo.
Clockwise from left: Jan Siwanowicz (HCSSiM 1993), with Azi Horowitz, Jacob Izraelevitz, Alex Bowen (visitor), Michael Gottlieb, Max Woerner-Chase, Richard Bowen, ???, Noah Blach, and Aaron Wilkowski, from HCSSiM 2005. This is a single-strand dodecahedron.
Left to Right: Amanda Redlich, John Choi, Jeff Amlin, Albert Wang,
Sergei Lupashin, Emily Riehl, Ian Wang
This icosahedron is from HCSSiM 2000. The students were given the original Schaffer/Stern
instructions and directed by me and then by my junior staff Matt Riddle.
My Polytopes and More maxi class at HCSSiM 2006 was trying to decide on a definition for regular polyhedra. As part of their investigations, they invented some infinite polyhedra (Coxeter-Petrie polyhedra, in fact)...
June Jhe with his 6-squares-around-each-vertex creation
Nate Harman with his 4-hexagons-around-each-vertex and 6-hexagons-around-each-vertex models
Not to be outdone, Emma Cohen and Hannah Alpert constructed an 8-triangles-around-each vertex polyhedron, and then concluded that it couldn't be regular.
HCSSiM 2005 had a doughnut-making party. Below are before-frying and after-frying photos of the Sierpinski Triangle doughnut, made (I believe) by Andy Feldman. Note also the lame triple-holed torus (proabably made by me).
No doughnut-making party is complete without frosting doughnuts, and what better frosting pattern than a graph embedding? Here Noah Blach shows off his embedding of K_6 on the two-holed torus.
Emily Bargar, Susie Ko, and Max Engelstein generalized Pascal's Triangle to
Pascal's Tetrahedron. Here they are at HCSSiM 2004 creating a model of it from
packing peanuts, marker, and toothpicks.
Jacob Kushkuley (HCSSiM 2004) made a really large hyperbolic hat (named ZeZe
by Emily Bargar, pictured earlier) with 8 triangles around each vertex. What
is difficult to see in these photos is that he had attempted to create a closed
surface by attaching free edges wherever possible and thus creating doughnut-like
holes. In other words, this partial embedding is of very high genus.
My topological graph theory maxi (HCSSiM 2004) suddenly decided to form a human
Petersen graph. Each person is a vertex, extending two arms and a leg representing
the three edges emanating from each vertex. In the right-hand photo we'd decided
it would be a good idea to actually form a connected graph; too bad the photographer's
finger got a bit in the way.
Outer pentagon, clockwise: Jon Strassfeld wearing his yellow pig shirt, Brendan
Foley, Jonah Blasiak (junior staff), Rachel Kirsch, and David Lonoff.
Inner penta-star, clockwise (not by edge-adjacency, but by the usual people-adjacency):
me in my yellow pig dress, Hannah Alpert, Sho Uemura, Alex Kunin, and Bret Wilson.
In these photos, the students are having a contest to see which team can construct the tallest tower from 8.5"x11" paper (from a recycle bin, of course). That's Paul Kwak (HCSSiM 2003) standing on a chair in the first photo and the remaining photos are from HCSSiM 2000, featuring (first picture) John Basias, Albert Wang, Jeff Snow, Michael VonKorff, Emily Riehl, John Darius Mangual and (second picture) Johnny Wang, Ian Wang, Amanda Redlich, Rita Loiotile, John Basias. (There are some folk unidentified because I can't see their faces well enough from the angle of the photo to identify them.)
