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\href{http://www.math.toronto.edu/~drorbn/Copyleft/}{\textcopyleft}$\mid$
\href{http://www.math.toronto.edu/~drorbn/}{Dror Bar-Natan}:
\href{http://www.math.toronto.edu/~drorbn/Talks/}{Talks}:
\href{http://www.math.toronto.edu/~drorbn/Talks/Treehouse-1410/}{Treehouse-1410}:
\hfill {\sl Video, handout, links at}

\vskip 0.5mm
{\large\bf\red The 17 Tiling Patterns:
{\p Gotta catch 'em all!}}
\hfill{\sl \url{http://drorbn.net/Treehouse}}

\vskip 1.5mm
{\small Treehouse Talks, Friday October 17, 2014, Beeton Auditorium, Toronto
Reference Library, 789 Yonge Street, 6:30PM}

\vfill
\begin{multicols}{2}

{\bf\red Abstract.} My goal is to get you hooked, captured and unreleased
until you find all 17 in real life, around you.

We all know know that the plane can be filled in different periodic
manners: floor tiles are often square but sometimes hexagonal, bricks are
often laid in an interlaced pattern, fabrics often carry interesting
patterns. A little less known is that there are precisely 17 symmetry
patterns for tiling the plane; not one more, not one less. It is even less
known how easy these 17 are to identify in the patterns around you, how fun
it is, how common some are, and how rare some others seem to be.

{\p Gotta catch 'em all!}

\columnbreak

\parpic[r]{\includegraphics[width=1.25in]{../../2014-08/17Worlds/ConwayEtAl.jpg}}
{\bf\red Reading.} An excellent book on the subject is {\em The Symmetries
of Things} by J.~H.~Conway, H.~Burgiel, and C.~Goodman-Strauss, CRC
Press, 2008.

Another nice text is {\em Classical Tessellations and Three-Manifolds}
by J.~M.~Montesinos,  Springer-Verlag, 1987.

{\bf\red Question.} In what ways can you make \$2 change, using
coins denominated $\frac12$, $\frac23$, $\frac34$, $\frac45$,
$\frac56$, etc.?

{\def\f#1#2{\frac{#1}{\red\mathbf #2}}
{\bf\red Answer.}
$2=\f12+\f12+\f12+\f12=\f23+\f23+\f23=\f34+\f34+\f12=\f56+\f23+\f12$,
and that's it.
}

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{\bf\color{red}Tilings worksheet.} Classify the following
pictures according to the following possibilities: \Da=2222, \Db=333,
\Dc=442, \Dd=632, \De=*2222, \Df=*333, \Dg=*442, \Dh=*632, \Di=4*2,
\Dj=3*3, \Dk=2*22, \Dl=22*, \Dm=**, \Dn=*o, \Do=oo, \Dp=22o, and \Dq=0
(the pictures come in \{context, pattern\} pairs).

\begin{center}
\includegraphics[width=8in]{WorkSheetS.jpg}
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\null\vfill\includegraphics[width=8in]{WorkSheet-0.jpg}\vfill{\p Gotta!}
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\null\vfill\includegraphics[width=8in]{WorkSheet-1.jpg}\vfill{\p Gotta!}
\newpage
\null\vfill\includegraphics[width=8in]{WorkSheet-2.jpg}\vfill{\p Gotta!}
\end{center}

%This worksheet: \url{http://drorbn.net/Treehouse/Gotta.pdf}

%Solutions and more:
%\url{http://www.math.toronto.edu/~drorbn/Gallery/Symmetry/Tilings/}

%Talk: \url{http://drorbn.net/Treehouse/}

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