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ghs2022.xml~
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ghs2022.xml~
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<NOTE date="Oct 28, 2017" theme="default" notes="yes">
<TITLE>MathMagic</TITLE>
<FRAME t="2"><TOP>Get off the earth!</TOP>
<XPOS w="10" x="1" y="-2">\only<1>{<IMG web="goeclean1.png" scl="0.5">How many men?</IMG>}%
\only<2>{<IMG web="goeclean2.png" scl="0.5">How many men?</IMG>}%
\only<3>{<IMG web="goeclean3.png" scl="0.5">How many men?</IMG>}%
\only<4>{<IMG web="goeclean4.png" scl="0.5">How many men?</IMG>}%
</XPOS>
</FRAME>
<FRAME t="2"><TOP>Mathematical perspective</TOP>
\only<1>{<IMG web="linegoe1.pdf" scl="0.6"></IMG>}%
\only<2>{<IMG web="linegoe2.pdf" scl="0.6"></IMG>}%
</FRAME>
<FRAME t="2"><TOP>Making your own</TOP>
\only<1>{<IMG web="fun0a.png" scl="0.3"></IMG>}%
\only<2>{<IMG web="fun0b.png" scl="0.3"></IMG>}%
\only<3>{<IMG web="fun0a.png" scl="0.3"></IMG>}%
\only<4>{<IMG web="fun1.png" scl="0.3"></IMG>}%
\only<5>{<IMG web="fun2a.png" scl="0.3"></IMG>}%
\only<6>{<IMG web="fun2b.png" scl="0.3"></IMG>}%
\only<7>{<IMG web="fun3a.png" scl="0.3"></IMG>}%
\only<8>{<IMG web="fun3b.png" scl="0.3"></IMG>}%
\only<9>{<IMG web="fun4a.png" scl="0.3"></IMG>}%
\only<10>{<IMG web="fun4b.png" scl="0.3"></IMG>}%
\only<11>{<IMG web="fun5a.png" scl="0.3"></IMG>}%
\only<12>{<IMG web="fun5b.png" scl="0.3"></IMG>}%
\only<13>{<IMG web="fun6a.png" scl="0.3"></IMG>}%
\only<14>{<IMG web="fun6b.png" scl="0.3"></IMG>}%
\only<15>{<IMG web="funfulla.png" scl="0.3"></IMG>}%
\only<16>{<IMG web="funfullb.png" scl="0.3"></IMG>}%
</FRAME>
<HEAD1>Puzzle</HEAD1>
<FRAME><TOP>Puzzle of the five cups</TOP>
\centerline{\huge Invariance}
</FRAME>
<HEAD1>Magic</HEAD1>
<FRAME t="2"><TOP>Cut</TOP>
\only<1>{<IMG web="hummer1.png"></IMG>}%
\only<2>{<IMG web="hummer2.png"></IMG>}%
\only<3>{<IMG web="hummer3.png"></IMG>}%
</FRAME>
<FRAME t="2"><TOP>Flip top two together</TOP>
\only<1>{<IMG web="hummer1.png"></IMG>}%
\only<2>{<IMG web="hummer4.png"></IMG>}%
\only<3>{<IMG web="hummer5.png"></IMG>}%
</FRAME>
<FRAME t="2"><TOP>Instructions</TOP>
<UL>
<LI>Give a random cut.</LI>
<LI>Remember the bottom card.</LI>
<LI>Take the top card to the bottom.</LI>
<LI>Flip the top card.</LI>
<LI>Random cut.</LI>
<LI>Flip top two cards together.</LI>
<LI>Repeat the above two steps <M>3</M> times.</LI>
<LI>Give me the packet.</LI>
</UL>
</FRAME>
<HEAD1>Euler</HEAD1>
<FRAME t="2"><TOP>From high school days</TOP>
\only<1>{<IMG web="euler1.pdf" scl="0.5"></IMG>}%
\only<2>{<IMG web="euler2.pdf" scl="0.5"></IMG>}%
\only<3>{<IMG web="euler3.pdf" scl="0.5"></IMG>}%
\only<4>{<IMG web="euler4.pdf" scl="0.5"></IMG>}%
</FRAME>
<FRAME t="2"><TOP>Euler's theorem</TOP>
Consider a diagram consisting of some points
joined by some lines such that you can go from any point to any
other point. Then you can draw this diagram without lifting your
pen and without reusing any line if and only if
<Q>either
<Q>only an even number of lines meet at each point</Q>
or
<Q>an odd number of lines meet at exactly two points</Q>
</Q>
</FRAME>
<FRAME t="2"><TOP>An example</TOP>
<SEQ>
<IMG web="eul1.pdf" scl="0.5"></IMG>
<IMG web="eul2.pdf" scl="0.5"></IMG>
</SEQ>
</FRAME>
<FRAME t="2"><TOP>Mind reading magic</TOP>
</FRAME>
<HEAD2>Explanation</HEAD2>
<FRAME t="2"><TOP>Did I do it without <RED>any</RED> information?</TOP>
\only<1>{<IMG web="people1.pdf" scl="0.5"></IMG>}%
\only<2->{<IMG web="people2.pdf" scl="0.5"></IMG>}%
\uncover<3->{How many such patterns are possible?}
<VGAP/>
\uncover<4>{Ans: <M>2^5.</M>}
</FRAME>
<FRAME t="2"><TOP>A deck of (at most) 32 cards</TOP>
\uncover<2->{Hmmm...so you used an arranged deck!}%
<VGAP/>
\uncover<3->{But did we not shuffle it thoroughly?}%
<XPOS x="1" y="6" w="10">\only<4>{<IMG web="deckcycle1.pdf" scl="0.5"></IMG>}%
\only<5>{<IMG web="deckcycle2.pdf" scl="0.5"></IMG>}%
\only<6->{<IMG web="deckcycle3.pdf" scl="0.5"></IMG>}%
</XPOS>
<XPOS x="5" y="6" w="10">\only<4-6>{<IMG web="cy1.pdf" scl="0.5"></IMG>}%
\only<7>{<IMG web="cy2.pdf" scl="0.5"></IMG>}%
</XPOS>
</FRAME>
<FRAME t="2"><TOP>OK, cyclical arrangement. But how?</TOP>
<XPOS x="2" y="2" w="10">
\only<2>{<IMG web="8cards1.pdf" scl="0.5"><M>2^3=8</M> cards</IMG>}%
\only<3>{<IMG web="8cards2.pdf" scl="0.5">Is this arrangement OK?</IMG>}%
\only<4>{<IMG web="8cards3a.pdf" scl="0.5">Is this arrangement OK?</IMG>}%
\only<5>{<IMG web="8cards3b.pdf" scl="0.5">Is this arrangement OK?</IMG>}%
\only<6>{<IMG web="8cards4a.pdf" scl="0.5">Is this arrangement OK?</IMG>}%
\only<7>{<IMG web="8cards4b.pdf" scl="0.5">Is this arrangement OK?</IMG>}%
</XPOS>
<XPOS x="6" y="2" w="10">
\only<4,6>{<IMG web="tinjan1.pdf" scl="0.3"></IMG>}%
\only<5,7>{<IMG web="tinjan2.pdf" scl="0.3"></IMG>}%
</XPOS>
</FRAME>
<FRAME t="2"><TOP>So we need...</TOP>
...a cyclical pattern where all consecutive triples have distinct
red-black patterns.
\only<1>{<IMG web="allpat0.pdf" scl="0.5"></IMG>}%
\only<2>{<IMG web="allpat1.pdf" scl="0.5"></IMG>}%
\only<3>{<IMG web="allpat2.pdf" scl="0.5"></IMG>}%
\only<4>{<IMG web="allpat3.pdf" scl="0.5"></IMG>}%
\only<5>{<IMG web="allpat4.pdf" scl="0.5"></IMG>}%
\only<6>{<IMG web="allpat5.pdf" scl="0.5"></IMG>}%
\only<7>{<IMG web="allpat6.pdf" scl="0.5"></IMG>}%
\only<8>{<IMG web="allpat7.pdf" scl="0.5"></IMG>}%
\only<9->{<IMG web="allpat8.pdf" scl="0.5"></IMG>}%
\uncover<9->{How to find such a pattern?}
\uncover<10>{Does one really exist at all?}
</FRAME>
<COMMENT>
Local Variables:
two-part: ("<FRAME><TOP>" "</TOP>\n</FRAME>")
End:
</COMMENT>
</NOTE>