Here are some vague ideas I would like explore in a workshop at
Mathcamp 2010. They
are untried, and I hope we can refine them and come up with more
ideas.
Google for "Flash Mob" to find interesting examples of public group
activities where many people read a pre-designed plan that is promoted
through a web site, then come together at a specific time to follow the
plan and do something interesting, and then disperse. See, for
example:
I would like to design and try out some math-oriented flash mob
activities, which I'll call "math-mobs." Below are some ideas I
have in mind. My plan for Mathcamp is that we first have a
session in which we develop these ideas further, come up with new
ideas, chose some, and make specific instructions of what participants
should do. Then we announce to the rest of the camp a time when we'll
try them out. Probably the try-out time would be the next day or
at least several hours later, so we can advertise to the whole camp and
more people can participate.
1. Giant Mobius strip. (Worlds largest?) Everyone brings a
bed sheet with them to a specified outdoor location. We stand in
a big circle, a sheet-length apart from each other. We hold the sheets
so they connect in a giant cylinder. Each person holds the top
corners of their sheet and the bottom corners of the next sheet.
But we have a twist in it as you go around, so it is a giant Mobius
strip. Probably the sheets would be folded in half the long way,
so they are not wider than a person's armspan. Next we do a slow
gentle rotation, a kind of "wave" that goes around the circle.
2. Giant Complete Graph. We have n
people come together and make K_n
using some kind of ribbon they bring with them. Perhaps each
person gets a roll of the flourescent surveyor's plastic "flagging
tape" (http://www.bestmaterials.com/detail.aspx?ID=8923). We
stand in a circle an arms length apart. Each person ties the end of
their roll of tape to their left wrist, then passes the roll to the
person 1 to their right. When you receive the roll from the person
on your left, you wrap it once around your left wrist and pass it 2
people to your right. Wrap it again, then pass it 3 people to the
right... After it goes n/2
people
to
the
right, the view from above will be a complete graph as in
these "string art" images:
http://en.wikipedia.org/wiki/Complete_graph
3. Human exponential tree. One person starts and extends his/her
two arms out in front. Two people then come and stand so an
extended hand is at their back. They each extend their
arms. Four people come and become the next level. Then
eight, etc. How far can this go on? At some point the next
level can not all fit, illustrating the practical limits of exponential
growth.
4. Square-root-of-five squares construction. Pick a place with a
square-grid tiled floor. Everyone brings one (or several?) of
five different things. (We specify five fruits?) One at a time
everyone adds an element to the growing pattern, one in each floor tile
to make the "knight's move" pattern that divides the grid into five
subgrids, each with square of five times the area, i.e., sqrt(5) times
the edge length. We leave it on display for some minutes, then
each person takes away as many items as they brought.
A
B
C
D
E A B C D E A B C D E D E A B C D E A B C D E A B C B C D E A B C D E A B C D E A E A B C D E A B C D E A B C D C D E A B C D E A B C D E A B A B C D E A B C D E A B C D E D E A B C D E A B C D E A B C B C D E A B C D E A B C D E A E A B C D E A B C D E A B C D C D E A B C D E A B C D E A B
5. Giant Tessellation. Everyone brings a handful of pencils and/or
pens. We don't write with them; they are just convenient "sticks"
to build with. Somehow we manage to lay them out on a floor
somewhere as the edges of an interesting tessellation. We look at it
for some minutes, then each person takes away as many items as they
brought. What would be a good tessellation for this? How would we
make it accurately enough given writing implements of varying lengths?
Addendum, August 2010
We tried out some of these ideas at Mathcamp 2010. See the
results here.
