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\def\credits{{\raisebox{3.25mm}{\parbox[t]{3.8in}{%\raggedright
{\color{red}Picture credits.}
Mona: Leonrado;
Al Gore: {\tt Futurama};
Map 1: {\tt en.\linebreak[0]wikipedia.\linebreak[0]org/\linebreak[0]wiki/\linebreak[0]Greenhouse\_\linebreak[0]gas};
Smokestacks: {\tt gbuapcd.\linebreak[0]org/\linebreak[0]complaint.\linebreak[0]htm};
Penguin: {\tt brentpabst.\linebreak[0]com/\linebreak[0]bp/\linebreak[0]2007/\linebreak[0]12/\linebreak[0]15/\linebreak[0]BrentGoesPenguin.\linebreak[0]aspx};
Map 2: {\tt flightpedia.\linebreak[0]org};
Segway: {\tt co2calculator.\linebreak[0]wordpress.\linebreak[0]com/\linebreak[0]2008/\linebreak[0]10};
Lobachevsky: {\tt en.\linebreak[0]wikipedia.\linebreak[0]org/\linebreak[0]wiki/\linebreak[0]Nikolai\_\linebreak[0]Lobachevsky};
Eschers: {\tt www.\linebreak[0]josleys.\linebreak[0]com/\linebreak[0]show\_\linebreak[0]gallery.\linebreak[0]php?\linebreak[0]galid=\linebreak[0]325};
}}}}
\def\web{{\url{http://drorbn.net/n16}}}
\def\Abstract{{\raisebox{3mm}{\parbox[t]{3.9in}{
{\color{red}Abstract.}
What's the hardest math I've ever used in real life? Me, myself, directly -
not by using a cellphone or a GPS device that somebody else designed? And
in ``real life'' --- not while studying or teaching mathematics?
I use addition and subtraction daily, adding up bills or calculating
change. I use percentages often, though mostly it is just ``add 15
percents''. I seldom use multiplication and division: when I buy in bulk, or
when I need to know how many tiles I need to replace my kitchen floor. I've
used powers twice in my life, doing calculations related to mortgages. I've
used a tiny bit of geometry and algebra for a tiny bit of non-math-related
computer graphics I've played with. And for a long time, that was all. In
my talk I will tell you how recently a math topic discovered only in the
1800s made a brief and modest appearance in my non-mathematical life. There
are many books devoted to that topic and a lot of active research. Yet for
all I know, nobody ever needed the actual formulas for such a simple reason
before.
Hence we'll talk about the motion of movie cameras, and the fastest way to
go from A to B subject to driving speed limits that depend on the locale,
and the ``happy segway principle'' which is a the heart of the least action
principle which in itself is at the heart of all of modern physics, and
finally, about that funny discovery of Janos Bolyai's and Nikolai Ivanovich
Lobachevsky's, that the famed axiom of parallels of the ancient Greeks need
not actually be true.
}}}}
\def\Goal{{\raisebox{3mm}{\parbox[t]{2.5in}{
{\color{red}Goal.} Find the least-blur path to go from Mona's left eye to
Mona's right eye in fixed time. Alternatively, fix your blur-tolerance, and
find the fastest path to do the same. For fixed blur, our camera moves
at a speed proportional to its distance from the image plane:
}}}}
\def\lion{{\raisebox{3mm}{\parbox[t]{3.6in}{
{\color{red}Bernoulli on Newton.} ``I recognize the lion by his paw''.
}}}}
\def\LeastAction{{\raisebox{3mm}{\parbox[t]{3.6in}{
{\color{red}The Least Action Principle.} Everywhere in physics, a system
goes from $A$ to $B$ along the path of least action.
\newline{\tiny With small print for quantum mechanics.}
}}}}
\def\funfacts{{\raisebox{3mm}{\parbox[t]{3.45in}{
{\color{red}Further Fun Facts.}
$\bullet$ In small scale, $\pi^H\to\pi^E$.
In large scale, $\pi^H\to\infty$.
\quad$\bullet$ The sum of the angles of a triangle is always less than
$\pi$. In fact, sum$+$area$=\pi$, so the largest possible area of a
triangle is $\pi$.
\quad$\bullet$ If your friend walks away, she'll drop out of sight before
you know it.
\quad$\bullet$ There are so many places just a stone throw away! But you'd
better remember your way back well!
}}}}
\def\parametrization{{\raisebox{3mm}{\parbox[t]{1.375in}{
\[ \theta'(t)=\sin\theta(t) \]
\[ \Downarrow \]
\[ \theta = 2\arctan e^t \]
}}}}
\def\etc{{\raisebox{0mm}{\parbox[t]{0.9in}{
Some further basic geometry also occurs:
}}}}
\def\ops{{\raisebox{0mm}{\parbox[t]{0.75in}{ \raggedright
{\color{red}Ops used.} $+$, $-$, $\times$, $\div$, $\sqrt{\ }$, $\cos$,
$\sin$, $\tan$, $\arccos$, $\arctan$, $\log$, $\exp$.
}}}}
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\def\CantonTower{{\raisebox{0mm}{\parbox[t]{1.25in}{
The Canton Tower in Guangzhou during the 2010 Asian Games Opening Ceremony,
as photographed by Colin Zhu. Its hyperboloid structure,
first explored by Russian engineer Vladimir Shukhov in the 1880s, is known
for its strength,
}}}}
\def\zhurl{{\url{http://www.flickr.com/photos/71834709@N00}}}
\def\loburl{{\url{http://www.youtube.com/watch?v=RNC-aj76zI4}}}
\def\Hyperboloid{{\raisebox{0mm}{\parbox[t]{2.5in}{
structural simplicity, and its relationship with
heyprbolic geometry and with Einstein's theory of relativity.
}}}}
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