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qE 5admWF A9H _\}6WB>ׯRH" /^ IHa&LR! 5bjRo%@`Cr\	 <
ʭIQ1	vK"t} 5j%SX8r\$2 )ħ 	 +KY|P\l.ʠ%aJDXY& E%>5a
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Fƕr&9uK嬺0	m[vWe`0IJUETZр e5`eo`$\ϐco*SB[da  5)`Q2I*@S#Jk]ٮ.6gfٞ e&'&`|eùNZ cA\ 5`^L&33$bv 	kGC}}uDiE)f WoKyvj\6fѬ 5ffۀ))Y22&
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ۙrrGL` 5DT*׀dV,1(	$KF,Rd ^Q6@x+2e@YUf qb!ukZnc#[y-*f2 7&lܐ
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Zh  PJ P_; PF pX"@t PLE pX(7  P>E&X?T  X   X	@  X!  X	c  PE  PF pW&X"@mPE  Pd pX
#ր PpPpX[X PF PFP*F   	v   g-3         (  <P ALIGN="LEFT"><FONT FACE="Times New Roman" SIZE="12" COLOR="#FFFFFF"><A HREF="http://home.earthlink.net/~spencerdoolin/relativity/wavereflect.htm">Table of</A></FONT></P><P ALIGN="LEFT"><FONT FACE="Times New Roman" SIZE="12" COLOR="#FFFFFF"><A HREF="http://home.earthlink.net/~spencerdoolin/relativity/wavereflect.htm">Contents</A></FONT></P>   녠     ]^}U   ts_E袞   !kc    uL5N.p      5wqܮM.
#ǺtܹwqR        -˪8[,WV ~Ѷ&NQ       5)
7E@sw񒷛\#2|  f    5;T«n)hP``{YãSh?93        5+t$
VͿ߾V5	X|  f    57h];~JQ7.6ԣco*#        5,7ΟnzmLr>?%DߴTr.U%Dӳ       5*(N7+1~hCSTNj8s  	        @     	"Ck '    u*r@       5ʙW9~԰ *   e > GK      ===GD     ===  Kn>3.%~Qt?o    fff 333    h<@  qqqGD     ===   fff2aj>8ELpTG#BA/$@BNu.dS1v-
(yih*i܏ G$[py"<|N"G:Cy L`nZNpZ    	 e >     ]Av&n9Ͱ\  fff h<@  qqq      333 0aj8IL-TG!BA/$@BnuNB>V%ڴ:	!>G:ӄ~#y`$ܦ  u ;V[l,rD9Ap9v U
a:Ah>     fff%mP< &GͰ\#   
 e&    ]Av&n9Ͱ\     `zAhuC9,7C  fff          333   fff2@xnq.@INb6Ԅ9!臅u0C0mP#b5CnT.Ha6X#P_$L5~X\asW.pRP762;PA6B@ufe7. ,l   2    e&    `pCtr;!9dF`          	   
          0  _parent frame RightArrow _visible gotoAndStop      N    O   N O   N      R 	       qpv  @            	   
          /  _parent frame LeftArrow _visible gotoAndStop      N    GO   N O   N      R 	       !py @   $    X	]`m  	      4 .     XO m        x׍x     XO m        x׍x     X
O m        ^׀     XO m        ^׀ N    `/x 	      Ntx`k`k^xx <Xkpx^x <  >xPXkpxjx*z] <@rx~xz]`k "    XRm 	      ǅ` C    wϥ}      %Ϡ~}k>/.]N     #  	        @        jU	I      %`| &    X
pm        A^x <  \    o{V&,YŢ        5= wu%O_B\p S _ ( 
HÐ R9  BT$ p 	       !'I  \>ו!   ~"8f  ڳ]?4   s;!Ӕ'  g^JSB  bl,쀐  7DG	  Ǝ6
  NQ	ۀ  bqnt  ^ՒSt@   
   x 4U  	   gT`klClC< <|Cfx`k <Ntx`k`k^xx <Xkpx^x <>xPXkpxjx <N|CrxxPx <nXkx <fxXkx`k <Zx`k`kpx <Xk <lChC|C|ClC`k <\krxpxbP~xz]hCpxdx< <Xkpx^x <hC|C <hCz] <|ChCn`k <BP <|CxPhC`k^x <|Crx <nXkjx`k <hC|C <Xk <  0lChC|C|ClC`k <ZxhC|C <\klC`kXkxP`kxP <fxx <|Cfx`kxP`k <Xkz] <z]~x\kfx <\krxpxbP~xz]hCrxpx<  v[Pfx`k <Xk\k|ChCrxpx <z]|CXkxP|C`k^x <rx~x|C <Xkz] <XkZxrxx`k< < <ThC|Cfx <Ntx`k`k^xx <Xkpx^x <>xPXkpxjx <|Crxdx`k|Cfx`kxF< <"xxxx <bP`k`k|C <bPxPrxn <|Cfx`k <z]|CrxxP`k<    w_`q 	      A:hCz]\klCXkhCn`kxP.C < <Pfx`k <nXk|Cfx <hCpx <|CfxhCz] <^x`knrxpxz]|CxPXk|ChCrxpx <nXkx <Zx`k <Xk <lChC|C|ClC`k <hC\kjxh<  ?6x <|Cfx`k <`kpx^x <rxbP <|Cfx`k <^x`knrxpxz]|CxPXk|ChCrxpx <BP <bPhCdx~xxP`k^x <rx~x|C <fxrx <|Crx <\kXklC\k~xlCXk|C`k <  A?fx`kxP`k <|Cfx`k <Xkx`kz] <`kxP`k <bPxPrxn <Ntx`k`k^xx*z] <tx`kxPz]tx`k\k|ChCx`k< <Zx~x|C <hC|C <|Crxrxjx <n`k <  v
z]rxn`k <|ChCn`k<  ?Pfx`k <lCXk|C`kxP <txXkxP|C <rxbP <|CfxhCz] <^x`knrx <Xkz] <^xrxpx`k <bPrxxP <nx <
P|Cfx`k <txxPrxdxxPXknn`kxP*z]P <  CZx`kpx`kbPhC|C< <z]rx <|CfxXk|C <BP <\krx~xlC^x <bPhCdx~xxP`k <rx~x|C <|Cfx`k <XklCdxrxxPhC|Cfxn <|Crx <nXkjx`k <Xk <Zx`k|C|C`kxP <  !^x`knrxpxz]|CxPXk|ChCrxpx <hCpx <|Cfx`k <px`kXkxP <bP~x|C~xxP`k< ]   p IȀ` 	      8P`klClC <n`k <XkZxrx~x|C <`kxPxPXk|CXk <hCbP <xrx~x <Xkpx|C <|Crx< <Zx~x|C <xP`kXklChCk`k <|CfxXk|C <BP <  5hClClC <txxPrxZxXkZxlCx <Zx`k <xP`k\kxP`kXk|ChCpxdx <|CfxhCz] <^x`knrx <bPxPrxn <z]\kxPXk|C\kfx< < <  A/BP*n <z]~xxP`k <xrx~x <hClClC <bPhCpx^x <DJPN <rxbP <lChC|C|ClC`k <nhCz]|CXkjx`kz]< .    x T] U  	   W<x`kpx <|Cfxrx~xdxfx <|Cfx`k <\kXkxP|Crxrxpx <z]fxrxz] <Ntx`k`k^xx <Xk\k\k`klC`kxPXk|ChCpxdx <Xkpx^x <^x`k\k`klC`kxPXk|ChCpxdx <|CfxxPrx~xdxfxrx~x|C <|Cfx`k <|CxPhCtx<  RBP <Xk\k|C~xXklClCx <^xhC^x <|Cfx`k <nXk|Cfx <txxP`k|C`kpx^xhCpxdx <Ntx`k`k^xx <Xkz] <dxrxhCpxdx <|Cfx`k <z]Xkn`k <z]tx`k`k^x <|Cfx`k <fxrxlC`k <|ChCn`k<  v[Ntx`k`k^xx <|CXkjx`kz] <rxbLbP <bPxPrxn <fxhCz] <fxrx~xz]`k <Xk|C <*xx <rxbP <|Cfx`k <z]tx`k`k^x <rxbP <lChCdxfx|C< < <JxP <*xxx <bP`k`k|C <tx`kxP <nhC\kxPrxz]`k\krxpx^x<  6   ! wx        5裡A7kAñ<, 	   "   !  @   Q   # hQQ 	      4XSˍ`  TiJ5C0Bƿ
=.kǀ $   $ Xk 	      Ntx`k`k^xx   % x $Y 	   "Nrx <fx`kpx <Ntx`k`k^xx <xP`kXk\kfx`kz] <|Cfx`k <z]|CrxxP`k< <  ^|ChCn`k <0 <^xhCz]|CXkpx\k`kCz]tx`k`k^x< <z]rx <hCpx <|CfxhCz] <\kXkz]`k< <>xPXkpxjx <Xkpx^x <|Cfx`k <z]|CrxxP`kjx`k`ktx`kxP <n`kXkz]~xxP`k <|CfxXk|C < <Ntx`k`k^xx <|Crxrxjx <$x <  AnhC\kxPrxz]`k\krxpx^x <|Crx <xP`kXk\kfx <|Cfx`k <z]|CrxxP`k<  (@rx <^xrx <|Cfx`kx <n`kXkz]~xxP`k <|CfxhCz]< <xrx~x <nhCdxfx|C <Xkz]jx2k  [   & qUqP     %d`m-[ @  aB[~$%/   $:H-A @ _-H0   	   '   &  @    8   ( wx         	ǆ} ~p] `^   8   ) wx   f     	ǆ} ~p] `^   8   * wx        	ǆ} ~p] `^    +   (   )   *        this setLights _root description At 1.25 microseconds, Speedy will be measured to have reached the 1000 foot line.  This signal will not 
 reach Frank for another microsecond.  It is only after 2.25 microseconds have passed that Frank can 
 measure this.  ?  ?         R  O   N GO   N GO   ,   (   )   *       & this setLights _root description At 2.5 microseconds, Speedy flips the switch at the halfway point.  The light from the
 clock at the store and from the clock at Franks house, they will both read .5 microseconds.
 This is the place on the trip where Speedy sees the same time on both clocks.  ?  @         R  O   N GO   N GO E  -   (   )   *         this setLights _root description At 3.75 microseconds, Speedy reaches the 3000 foot line.  Notice that though he is almost to the
 store, the light from him leaving Franks house has still not reached the store.  ?  @         R  O   N GO   .   (   )   *       	 this setLights _root description At 3.75 microseconds, Speedy reaches the 3000 foot line.  Notice that though he is almost to the
 store, the light from him leaving Franks house has still not reached the store. At 5 microseconds, Speedy reaches the store and turns around.  A short argument (less than a 
 nanosecond) ensues with the storekeeper about whose watch is wrong.  As Speedy turns around, 
 major changes in his perspective are the key to understanding the Twin Paradox.
  ?        R  O   N GO  O   N GO   N GO    /   (   )   *        ?  @        this   setLights R  _root 8  description  Speedy is on his way back from the store. O   0   (   )   *       5 this setLights _root description Once again Speedy reaches the symmetry point.  This time he will read the Storekeeper
 and Frank's clocks at 5.5 microseconds.  (Hint:  the light left 2 microseconds ago.
 What time is it at Frank's Place and the Store right now?  Hint 2:  What button did
 you just click?)  ?  @         R  O   N GO   N GO   N GO    1   (   )   *        ? !@        this   setLights R  _root G  description  Frank still doesn't know that Speedy is on his way back. O    2   (   )   *         this setLights _root description Speedy reaches back to Frank's place.  However, Speedy's watch reads 6 microseconds, while Frank's watch
 reads 10 microseconds.  What happened?  ?
        R  O   N GO   3   (   )   *         this setLights _root description At 4 microseconds, The storekeeper first sees that Speedy is leaving Frank's house.  Since he knows 
 the distance to Frank's house, and the speed of light, he is able to calculate that Frank left 4
 microseconds ago.  ?        R  O   N GO   N GO (   4 `!       	9x Wpk &   5 Xum       =Ğ <k (   6 `!       	Ax Wpk #   7 X_ m       I=] (   8 `!       	Mx Wpk &   9 X	um       QĞ <k (   : `       	Ux Wpk %   ; Xn m       9׀?xw #   < X_ m       E=] 	  = ׿          ( _root.description Let's say Speedy triggers a light switch at each 1000 foot position along the way to the store.Click each button to see where Speedy and the light waves are at the time stated.  (I use "usec" because "msec" might be confused with milliseconds which are 1000 times longer.)Click the buttons to see where speedy is and where the light waves are. d  >   (   )   *         this setLights _root description At 9 microseconds, Frank sees Speedy stop at the store and turn around.  He knows that the light took 4
  microseconds to get from the store to him, so he measures that Speedy reached the store in 5 microseconds.  ?	        R  O   N GO #   ? X	_ m       Y=] 3  @ w ` 	   8Hrx <`k <hClClC <z]`k`k <fxXk|C <fxXktxtx`kpx`k^x <bPxPrxn <Ntx`k`k^xx*z] <tx`kxPz]tx`k\k|ChCx`k<  AR6`kbPrxxP`k <z]tx`k`k^xx <lC`kXkx`kz] <bPrxxP <|Cfx`k <z]|CrxxP`k< <`kx`kxPx|CfxhCpxdx <z]`k`knz] <|Cfx`k <z]Xkn`k <Xkz] <hC|C <^xrx`kz] <|Crx <>xPXkpxjx<    A X
@ m        ^    B XO m        x׍x    C XO m        s^׀    D XO m        {^׀     E k	I      % | &   F Xpm        9gx < ,  G x 4n`Հ 	   \Tfx`kpx <Ntx`k`k^xx <|CXkjx`kz] <rxbPbP <Xk|C <*xx <rxbP <|Cfx`k <z]tx`k`k^x <rxbP <lChCdxfx|C< <fxrx`kx`kxP< <fx`k <z]`k`kz] <|Cfx`k <`kpx|ChCxP`k <z]\k`kpx`k <lC`kpxdx|Cfx  *\krxpx|CxPXk\k|C`k^x <|Crx <&xx <rxbP <hC|C*z] <rxxPhCdxhCpxXklC <lC`kpxdx|Cfx< X  H `` 	   WPfx`k <lChCdxfx|C <fxhC\kfx <hCz] <xP`kXk\kfxhCpxdx <Ntx`k`k^xx <bPxPrxn <|Cfx`k <z]|CrxxP`k <Xk|C <|CfxhCz] <txrxhCpx|C <T4N <"x <nhC\kxPrxz]`k\krxpx^xz] <rxlC^x<  \Hrx <|CfxXk|C <Ntx`k`k^xx <hCz] <nrxxhCpxdx <|CrxXkxP^x <hC|C< <fxrx`kx`kxP< <hC|C <hCz] <rxpxlCx <x"xxx <bP`k`k|C <XkXkx< <Xkpx^x <hC|C <hCz] <rxpxlCx <x<"x <  AnhC\kxPrxz]`k\krxpx^xz] <rxlC^x<  RPrx <Ntx`k`k^xx< <hC|C <z]`k`knz] <|CfxXk|C <|Cfx`k <z]|CrxxP`k <fxXkz] <Xk\k|C~xXklClCx <nrxx`k^x <x<&x <z]`k\krxpx^xz] <hCpx|Crx <|Cfx`k <bP~x|C~xxP`k< K  I p Jƀ`. 	   ; < <
P4\k|C~xXklClCx <fx`k <hClClC <lCXk|C`kxP <bPhCpx^x <|CfxXk|C <|Cfx`k <z]|CrxxP`k <fxXkz] <nrxx`k^x < x<x   <     >nhC\kxPrxz]`k\krxpx^xz] <hCpx|Crx <|Cfx`k <bP~x|C~xxP`k<<< <^x~xxPhCpxdx <fxhCz] <|CxPhCtx <|Crx <|Cfx`k <z]|CrxxP`k< <  A7Ntx`k`k^xx <dxrx`kz] <bPrxxP < x <nhC\kxPrxz]`k\krxpx^xz]< <|Cfx`k <z]|CrxxP`k <dxrx`kz] <|CfxxPrx~xdxfx <  v6 xC<&x0x<*x <nhC\kxPrxz]`k\krxpx^xz]< < x<x <^x`kz]xpx\kfxxPrxpxhCkXk|ChCrxpxx<*x <|ChCn`kP  "^xhClCXk|C`k^x <z]`k\krxpx^xz] <0 <$x <nhC\kxPrxz]`k\krxpx^xz]<P     J i[     %x_|   K x 4 U  	   @Tfx`kpx <Ntx`k`k^xx <xP`kXk\kfx`kz] <|Cfx`k <\k`kpx|C`kxP< <fxhCz] <Xk|C\kfx <z]Xkxz] <x<$x <nhC\kxPrxz]`k\krxpx^xz]<  ^@`k <z]`k`kz] <|CfxXk|C <|Cfx`k <\klCrx\kjxz] <Xk|C <>xPXkpxjx*z] <fxrx~xz]`k <Xkpx^x <|Cfx`k <z]|CrxxP`k <Zxrx|Cfx <z]Xkx <x<$x <nhC\kxPrxz]`k\krxpx^xz] <Xk|C <|CfxhCz] <|ChCn`k<  AdPfx`k <\k`kpx|C`kxPz] <rxbP <|Cfx`kz]`k <Xkx`kz] <hClClC <Zx`k <"xxx <bP`k`k|C <Zx`kfxhCpx^x <|Cfx`khCxP <z]rx~xxP\k`kz] <bPxPrxn <fxhCz] <tx`kxPz]tx`k\k|ChCx`k< < <
P*xx <rxbP <|Cfx`k <  v.^xhCz]|CXkpx\k`k <lChCdxfx|C <|CxPXkx`klCz] <hCpx <fxXklCbP <Xk <nhC\kxPrxz]`k\krxpx^x<P   L w7`A 	   ;4\k|C~xXklClCh< <BP <lCXk|C`kxP <xP`kXklChCk`k^x <|CfxXk|C <|Cfx`k <\k`kpx|C`kxPz] <rxbP <|Cfx`k <Xkx`k <hCz] <  6HJP <"xxx <bP`k`k|C <Zx`kfxhCpx^x <|Cfx`k <z]|CrxxP`k< < <Pfx`k <|ChCn`k <Xk|C <|Cfx`k <z]|CrxxP`k <  A.hCz] <pxrx < x<x
Px<$xx<&xP0"x<x <nhC\kxPrxz]`k\krxpx^xz]< < <Pfx`k <x<$x   <     v/nhC\kxPrxz]`k\krxpx^x <Xkx`k <lC`kbP|C < x<&x <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx< <rxxP <  ) x<&xC<&x0&x <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx< <bPxPrxn <Ntx`k`k^xx*z] <  0tx`kxPz]tx`k\k|ChCx`k< <Xkpx^x <z]fxrx~xlC^x <|Cfx~xz] <Zx`k <&xx*xxx0"x*xxx <bP`k`k|C <  -Zx`kfxhCpx^x <|Cfx`k <z]|CrxxP`k< <hC|Cfx <Xk <xPXk^xhC~xz] <rxbP <&xxxx <bP`k`k|CP     M oE     %_| y   N hS   	      DhCdxfx|C <bPxPrxn <>xPXkpxjx*z] <8lCrx\kjx <  z]XkxhCpxdx <x <nhC\kxPrxz]`k\krxpx^x   O x $@U  	   a4bP|C`kxP < x <nhC\kxPrxz]`k\krxpx^xz]< <Ntx`k`k^xx <xP`kXk\kfx`kz] <|Cfx`k <z]|CrxxP`k< < <@`k <xP`kXk^xz] <|Cfx`k <lChCdxfx|C <bPxPrxn <>xPXkpxjx*z] <\klCrx\kjx< <z]XkxhCpxdx <x <  fnhC\kxPrxz]`k\krxpx^x< < <>xPrxn <fxhCz] <tx`kxPz]tx`k\k|ChCx`k< <>xPXkpxjx*z] <8lCrx\kjx <hCz] <z]lCrx`k^x <^xrxpx< < <Nrx <|CfxXk|C <lChCdxfx|C <^xhC^xpx*|C <lC`kXkx`k <>xPXkpxjx*z] <  Ac\klCrx\kjx <~xpx|ChClC <x<&x&x <nhC\kxPrxz]`k\krxpx^xz] <bPxPrxn <Ntx`k`k^xx*z] <tx`kxPz]tx`k\k|ChCx`k< < <PfxhCz] <Xkz] <x< x"x <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx< < <JxP <x x"xx <  vBbP`k`k|C <Zx`kfxhCpx^x <fxhCn< < <4px^x <|Cfx`k <lChCdxfx|C <fxXkz] <|CxPXkx`klC`k^x <x x"xx <bP`k`k|C <z]hCpx\k`k <|Cfx`kpx<     P jU     %`_| f  Q ԡ   	   Tfx`kpx <Ntx`k`k^xx <z]|Crxtxz] <fxXk|C <fxXktxtx`kpxz]2k  8Pfx`k <lChCdxfx|C <bPxPrxn <>xPXkpxjx*z] <\klCrx\kjx <NPBPDD <z]Xkxz] <rxpx`k <nhC\kxPrxz]`k\krxpx^x<  A7Zx~x|C <pxrx <|Cfx`k <z]rx~xxP\k`k <hCz] <z]|CXk|ChCrxpxXkxPx< <Xkpx^x <"xxxx <bP`k`k|C <XkXkx< < <  v^BPpxz]|C`kXk^x <rxbP <fxXkxhCpxdx <Zx`k`kpx <xP`klC`kXkz]`k^x <x< x"x <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx< <pxrx <hC|C <Xkz] <xP`klC`kXkz]`k^x <"x <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx<  .Hrx <hC|C <z]`k`knz] <>xPXkpxjx <fxXkz] <lC`kXktx`k^x <hCpx|Crx <|Cfx`k <bP~x|C~xxP`kP J  R р$ 	   `Hrx <Ntx`k`k^xx <|C~xxPpxz] <Xkpx^x <xP~xpxz] <|Cfx`k <rx|Cfx`kxP <^xhCxP`k\k|ChCrxpx< < <Pfx`k <lChCdxfx|C <bPxPrxn <>xPXkpxjx*z] <\klCrx\kjx <z]|ChClClC <z]Xkxz] <XkZxrx~x|C <x <  cnhC\kxPrxz]`k\krxpx^x< <6RP <>xPXkpxjxz] <\klCrx\kjx <hCz] <xP~xz]fxhCpxdx <|CrxXkxP^x <Ntx`k`k^xx <Xk|C <*xx <rxbP <|Cfx`k <z]tx`k`k^x <rxbP <lChCdxfx|C< < <Nrx <fx`kxP`k <Xkz] <  A`>xPXkpxjx <fx`kpx <fxhCz] <\klCrx\kjx <z]XkhC^x <x <nhC\kxPrxz]`k\krxpx^x2k < <T`k <px`k`k^x <|Crx <bPhCdx~xxP`k <rx~x|C <fxXk|C <>xPXkpxjx*z] <\klCrx\kjx <z]Xkxz] <pxrx <Xkpx^x <  ve`kx|CxPXktxrxlCXk|C`k< < <BPpx <|CfxxP`k`k <nhC\kxPrxz]`k\krxpx^xz]< <fx`kpx <Ntx`k`k^xx <XkxPxPhCx`kz] <Xk|C <>xPXkpxjx*z] <fxrx~xz]`k< <>xPXkpxjx*z] <\klCrx\kjx <hClClC <z]Xkx <xx <  cnhC\kxPrxz]`k\krxpx^xz]< < <TfxhClC`k < x <z]`k\krxpx^xz] <txXkz]z] <bPrxxP <Ntx`k`k^xx< <x<*x <z]`k\krxpx^xz] <txXkz]z] <bPrxxP <>xPXkpxjx< < <Nrx <>xPXkpxjx*z] <\klCrx\kjx <n~xz]|C <  epxrx <z]Xkx <*x<x <nhC\kxPrxz]`k\krxpx^xz]< < <Nrx <|Cfx`k <bx <nhC\kxPrxz]`k\krxpx^x <lChCdxfx|Cb <lC`kbP|C <>xPXkpxjx*z] <\klCrx\kjx <(x<x <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx <bPxPrxn 5  6>xPXkpxjx*z] <tx`kxPz]tx`k\k|ChCx`k <rxxP <xx <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx <bPrxxP <Ntx`k`k^xx<   S p `%H 	   RBPbP <|Cfx`k <lChCdxfx|C <lC`kbP|C <xx <nhC\kxPrxz]`k\krxpx^xz] <Xkdxrx< <hC|C <z]fxrx~xlC^x <rxxPhCdxhCpxXk|C`k <
Pxx <nhC\kxPrxz]`k\krxpx^xz]Px
P*xxx <  IbP`k`k|CCnhC\kxPrxz]`k\krxpx^xP0,x&xxx <bP`k`k|C <Zx`kfxhCpx^x <>xPXkpxjx< <Xkpx^x <fxXkx`k <Xk <xPXk^xhC~xz] <rxbP <xxxx <bP`k`k|C<  vL@`kxP`k*z] <Xk <vx~x`kz]|ChCrxpx<<< < <Tfx`kxP`k <hCz] <>xPXkpxjx*z] <b$x<$x <nhC\kxPrxz]`k\krxpx^x <Xkx`kb <Xk|C <|CfxhCz] <txrxhCpx|C2k   T x $U  	   _L`kn`knZx`kxP <|CfxXk|C <>xPXkpxjx*z] <Xk|C\kfx <pxrx <xP`kXk^xz] <*x<x <nhC\kxPrxz]`k\krxpx^xz]< < <4px^x <|Cfx`k <lChCdxfx|C <|CfxXk|C <Ntx`k`k^xx <z]`k`kz] <z]Xkxz] <x <  anhC\kxPrxz]`k\krxpx^x< < <Jx`kxP <|Cfx`k <px`kx|C < x <nhC\kxPrxz]`k\krxpx^xz]< <Ntx`k`k^xx <hClClC <z]`k`k <>xPXkpxjx*z] <Xk|C\kfx <hCpx <bPXkz]|CbPrxxPXkxP^x< <nrxxhCpxdx <  A&bPxPrxn <x <nhC\kxPrxz]`k\krxpx^x <|Crx <xx <nhC\kxPrxz]`k\krxpx^xz]<  vKPfx`k <lChCdxfx|C <bPxPrxn <Xkpxxfx`kxP`k <Zx`k|C`k`kpx <x <Xkpx^x <*x<x <nhC\kxPrxz]`k\krxpx^xz] <hCz] <XklCxP`kXk^xx <~xpx^x`kxPXkx<    U `-# 	      DhCdxfx|C <bPxPrxn <  >xPXkpxjx*z] <8lCrx\kjx <  Az]XkxhCpxdx <$x<$x <  vnhC\kxPrxz]`k\krxpx^xz]    V `,# 	      DhCdxfx|C <bPxPrxn <  >xPXkpxjx*z] <8lCrx\kjx <  A	z]XkxhCpxdx <x <  vnhC\kxPrxz]`k\krxpx^x<   W x $@  	   dBPbP <>xPXkpxjx*z] <Xk|C\kfx <\k~xxPxP`kpx|ClCx <z]Xkxz] <*x<x <nhC\kxPrxz]`k\krxpx^xz]< <|Cfx`kpx <|Cfx`k <$x<$x <nhC\kxPrxz]`k\krxpx^x <Xkx`k <hCz] <x<(x <nhC\kxPrxz]`k\krxpx^xz] <  XXklCrxpxdx <|Cfx`k <Xkx <
PbPxPrxn <>xPXkpxjx*z] <tx`kxPz]tx`k\k|ChCx`kP <rxxP <"x<$x <nhC\kxPrxz]`k\krxpx^xz] <
PbPxPrxn <Ntx`k`k^xx*z] <tx`kxPz]tx`k\k|ChCx`kP  ARNrx <|Cfx`k <Xkx`k <hClClC <Zx`k <"x<$xx*xxx0 x&xxx <bP`k`k|C <Zx`kfxhCpx^x <>xPXkpxjx <Xkpx^x <fxXkx`k <Xk <xPXk^xhC~xz] <rxbP <"x$xxx <bP`k`k|C<  dF`kXkpxfxhClC`k <|Cfx`k <\klCrx\kjx <Xk|C <|Cfx`k <z]|CrxxP`k <xP`kXk^xz] <$x <nhC\kxPrxz]`k\krxpx^xz] <Xkpx^x <fxXkz] <pxrx|C <x`k|C <xP`klC`kXkz]`k^x <hC|C*z] <$x<$x <nhC\kxPrxz]`k\krxpx^x <  UXkx`k< < <Tfx`kxP`k <hClClC <Ntx`k`k^xx <Zx`k <fx`kpx <|Cfx`k <$x<$x <nhC\kxPrxz]`k\krxpx^x <Xkx`k <hCz] <xP`klC`kXkz]`k^x <bPxPrxn <|Cfx`k <z]|CrxxP`k2k t   X `5  	      DhCdxfx|C <bPxPrxn <z]|CrxxP`k  z]XkxhCpxdx <$x<$x <  AnhC\kxPrxz]`k\krxpx^xz]<    Y hS   	      DhCdxfx|C <bPxPrxn <>xPXkpxjx*z] <8lCrx\kjx <  z]XkxhCpxdx <$x<$x <nhC\kxPrxz]`k\krxpx^xz]   Z x $`< 	   aJbP <\krx~xxPz]`k <|Cfx`k <$x<$x <nhC\kxPrxz]`k\krxpx^x <Xkx`k <hClClC <Zx`k <xP`klC`kXkz]`k^x <<$x <nhC\kxPrxz]`k\krxpx^xz] <XkbP|C`kxP <|Cfx`k <$x <nhC\kxPrxz]`k\krxpx^x <Xkx`k<  e>xPrxn <Ntx`k`k^xx*z] <tx`kxPz]tx`k\k|ChCx`k <hC|C <hClClC <Zx`k <<$xC<&x0<*x x x <nhC\kxPrxz]`k\krxpx^xz]< < <PxPXkx`klChCpxdx <Xk|C <*xxx <bP`k`k|CCnhC\kxPrxz]`k\krxpx^x< <fx`k <  AghClClC <Zx`k <&x&x(x <bP`k`k|C <XklCrxpxdx <|Cfx`k <Xkx <ZxXk\kjx< < <F`kXkpxfxhClC`k <|Cfx`k <rx|Cfx`kxP <Xkx`k <`kxtxXkpx^xz] <bPxPrxn <Xk <xPXk^xhC~xz] <rxbP <"x$xxx <bP`k`k|C <|Crx <Xk <  v+xPXk^xhC~xz] <rxbP < <$x x x x <bP`k`k|C< <hCpx <<*x x x <nhC\kxPrxz]`k\krxpx^xz]< v  [ x $ p  	   GNtx`k`k^xx <pxrx <xP`kXk\kfx`kz] <|Cfx`k <fxXklCbPXkx <txrxhCpx|C< < <@hCz] <Xk|C\kfx <z]Xkxz] <x<$x <nhC\kxPrxz]`k\krxpx^xz]<  ZPfx`k <b$x<$x <nhC\kxPrxz]`k\krxpx^x <Xkx`kb <bPxPrxn <>xPXkpxjx*z] <fxrx~xz]`k <fxXkz] <xP`kXk\kfx`k^x <Xk <xPXk^xhC~xz] <rxbP <"x$xxxx$xxx0&xxxx <bP`k`k|C<  vbPfx`k <b$x<$x <nhC\kxPrxz]`k\krxpx^x <Xkx`kb <bPxPrxn <|Cfx`k <z]|CrxxP`k <Zx`kfxhCpx^x <fxhCn <hCz] <rxpxlCx <x<$xP<*x x x0<&x&x(x <nhC\kxPrxz]`k\krxpx^x <rxlC^x< < <BP|C*z] <  "xPXk^xhC~xz] <hClClC <|Cfx`kxP`kbPrxxP`k <Zx`k <&x&x(x <bP`k`k|C<    \ hS   	      DhCdxfx|C <bPxPrxn <>xPXkpxjx*z] <8lCrx\kjx <  z]XkxhCpxdx <$x<$x <nhC\kxPrxz]`k\krxpx^xz]    ] hT$   	      DhCdxfx|C <bPxPrxn <N|CrxxP`k*z] <8lCrx\kjx <  z]XkxhCpxdx <$x<$x <nhC\kxPrxz]`k\krxpx^xz]<   ^ x $@ 	   `Tfx`kpx <|Cfx`k <b&x <nhC\kxPrxz]`k\krxpx^x <Xkx`kb <lC`kXkx`kz] <|Cfx`k <z]|CrxxP`k <Ntx`k`k^xx <hClClC <n`kXkz]~xxP`k <|CfxXk|C <xC<&x0x<&x&x(x <nhC\kxPrxz]`k\krxpx^xz] )  SfxXkx`k <txXkz]z]`k^x <z]hCpx\k`k <fx`k <lC`kbP|C <|Cfx`k <z]|CrxxP`k< < <@`k <hClClC <Zx`k <x<&x&x(xx*xxx0x x x x <bP`k`k|C <XklCrxpxdx <|Cfx`k <Xkx< }   _ hS   	      DhCdxfx|C <bPxPrxn <>xPXkpxjx*z] <\klCrx\kjx  z]XkxhCpxdx <$x<$x <nhC\kxPrxz]`k\krxpx^xz]    ` hS   	      DhCdxfx|C <bPxPrxn <N|CrxxP`k*z] <8lCrx\kjx <  z]XkxhCpxdx <$x<$x <nhC\kxPrxz]`k\krxpx^xz] {   a hRD   	      DhCdxfx|C <bPxPrxn <N|CrxxP`k*z] <\klCrx\kjx <  z]XkxhCpxdx <&x <nhC\kxPrxz]`k\krxpx^xz]   b x D  	   fx< x x x <nhC\kxPrxz]`k\krxpx^xz] <lCXk|C`kxP <fx`k <hCz] <Xk|C <|Cfx`k <z]|CrxxP`k< < <@`k <XkxPxPhCx`kz] <Xk|C <|Cfx`k <z]Xkn`k <|ChCn`k <Xkz] <|Cfx`k <b&x <nhC\kxPrxz]`k\krxpx^x <Xkx`kb 3  bPxPrxn <|Cfx`k <z]|CrxxP`k<  v'>rxxP <Ntx`k`k^xh< <&x <nhC\kxPrxz]`k\krxpx^xz] <fxXkx`k <txXkz]z]`k^x<  '>rxxP <>xPXkpxjx< <xx <nhC\kxPrxz]`k\krxpx^xz] <fxXkx`k <txXkz]z]`k^x<   c x @ 	   YVrx~x <hClClC <Zx`k <fxXktxtxx <|Crx <jxpxrx <|CfxXk|C <BP <hClClC <Zx`k <Xk|C|C`kntx|ChCpxdx <|Crx <nXkjx`k <|CfxhCz] <^x`knrxpxz]|CxPXk|ChCrxpx <`kXkz]hC`kxP <|Crx <  ~xpx^x`kxPz]|CXkpx^x <hCpx <|Cfx`k <px`kXkxP <bP~x|C~xxP`k< 	  d  ?j   ,  this frame Guy _xscale LeftArrow _visible       O     d   O   O       &  Â^LeftArrow    &  0RightArrow   |&B   q  ) 	  l(
     nM  t    &%   Scene (   )  ր   &*   Guy 7  j?l8  -D9  ]
@ 8 9 ?     Guy   _xscale <   O 7   owF8 " Kra-<@ : # jI@ 7 ?     Guy 	  _x    O 8 Kr^F: $ ʟ ; % pwl @ 8 : ; ?    Guy _x time speed _xscale Math sqrt n timeLit scale Circles max _yscale Circle7 Circle6 Circle5 Circle4 Circle3 Circle2 Circle1 Circle0 Array this Scene _y  setLights  time speed y     d       O   d            RO      NH M   	          d   O             NO              H    	 	
     
 N         	     RO 
 N         	     RO P V 
           @              H   
 N    O 
 N    O 
 N  N N  d   GO 
 N  N NO   8O P G         H G  
 N  N N     d   GO P     67 '   Circle0    69 ' ׭@ Circle1    6; ' u  Circle2    6= ' E@ Circle3    6? ' &e  Circle4    6A ' @@ Circle5    6C ' R  Circle6    6E ' L Circle7 G + skA I , s{sA K - sJA M . ;@  O / ;S/`  Q 0 ;D`  S 1 ;t]`  U 2 ;f!`  W 3 sh Y 4 cπZ 5 IЀ[ 6 [Ȁ\ 7 ຾ ] 8 d^ 9 *_ : iz ` ; ~αa < B`b = hDc > ;muP e ? 9p@ 7 9 ; = ? A C E G I K M O Q S U W Y Z [ \ ] ^ _ ` a b c e ?7     Guy _xscale _x    d   O   8O 7 @ k8@ ?     Guy   _x         O  I9  A @9  B 9 	 C I9 
 D FN@  % ș@  W ( E ) F n * @  C 7 G vN`@ 7 8 ' p : H lB ; I =  @ : ;  Y9  9  i9 	 ?9 
 9   %% ș@ J@( J )  * @ 6 7 K noE 8 cJƳZ: ' DJ  < L Q= ' 34=w @   	 
   * 7 : < =   %   6  @ 6  Guy   aN@  A 9 ! B ]i9 " C 9 # D 9 $  U% ș@ c( M )  * N  + O m/B8 r$k @    # $ % ( ) * + 8   z=`  n  Y 	  jI
  &   m  s@   6  	 Scene  P   h_  ' 0D	 ! N  " Q l7E@    ! "  I A 9 B 	 C I
 D A E  ș@  W    @ J  5ߠ  R j?@    ' 34L `   I	 A 9
 B  C I D A  E  ș@  @   @ K0 U  S oI! N * @   T j?! J@   !   ' 0` " U Dꀊ# V 
$ W j?@  HRO  _X耈	 耈
 耈 EX耈 耈 M ș@     @ " H]   >/" X SР# Y Z$ Z kOe @  FC\  	 
 (h t   ș@ ά   @  `   34>" [ k8# \ ĭ5$ ] BJ@ " #  UUUMJ  M	 	
 Y 3 z	  ș@ <I   @ * ?   ;>{" ' HREJ  $ ^ nR@% _ M:& ` K4' a H@ " % & '  w3DW 	.	 I.
 V. 	. I. %  ș@ I   @ * w5  B"N" b oB# ` hv $ a D @   	 
         " # $ ?+     this   RightArrow N  _visible  O  c no; @  @ @ @      & d  Text @   
