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My interests outside the classroom
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I have built and exhibited models built from LEGO bricks since I was 5; my current collection includes roughly 800,000 pieces. Pictures of my constructions (as of several years ago) can be found in this folder on Brickshelf.
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LEGO
bricks give rise to interesting mathematical questions
as well. Suppose you take n LEGO bricks (all the
same size and shape) and ask how many different ways
you can interlock the n bricks. This gives a
function which turns out to be exponential in n.
What is unknown is the number that is the "base" of
this exponential function (i.e. the entropy rate of
the system of interlocking bricks). For a
standard 2x4 LEGO brick, Duhuurs and Eilers give
estimates on the entropy rate in this
paper. For LEGO jumper plates and roof
tiles (sloped pieces), I wrote a paper with Ferris
State undergraduate Jon Wilson, which can be found here.
Estimates on the entropy of other types of LEGO bricks
and on combinations of multiple types of LEGO bricks
are largely unexplored, but most methods are
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