GSP4 lTQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.y$ LWorkspace` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#HArial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':'lj V> TQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.y$ LCredits` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#HArial0 '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':')P~@Pu@4( 4\.B@: &  nQ\aAx6( 6\.B@: &  nQ\aAy='  0. <0><0>>  h  h Khttp://www.keypress.com/sketchpad/general_resources/advanced_sketch_gallery>>6nQ\aAWeb: Advanced Sketch Gallery <  < !http://www.keypress.com/sketchpad8nQ\aAWeb: Sketchpad Resource Center-#{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$*LHyperbolic compass: CentrePt BoundaryPtsArial0nQ\aAP`i@nQ\aAC<?bX<@?er.nQ\aAC'<rV@bX<@?er.nQ\aAC'@? ? . nQ\aAj/ nQ\aAk - nQ\aAC - nQ\aAD nQ\aAA?  .  nQ\aAl.  nQ\aAm -  nQ\aAE/ nQ\aAn - nQ\aAB#*(    p= $:m.@nQ\aAL[1] {A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$2LHyperbolic perpendicular: Basept Linept1 Linept2Arial0nQ\aAC f@nQ\aABC''nQ\aAA -?  . nQ\aAj<?bX<@?er.?  "  {A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$"(LHyperbola through 3 points: Pt1 Pt2 Pt3Arial0nQ\aACPq@nQ\aAB\.eC@F@nQ\aAA[?8F@   nQ\aAG nQ\aAH<?bX<@?er.?  ?  .  nQ\aAj"   <?bX<@?er.?   ?  . nQ\aAk"   -  nQ\aAD<?bX<@?er.nQ\aAD'<rV@bX<@?er.nQ\aAD'@? ?  nQ\aAE. nQ\aAl. nQ\aAm/ nQ\aAn - nQ\aAI - nQ\aAJ? . nQ\aAo - nQ\aAK/ nQ\aAp -  nQ\aAF#*( ! !  p= $:m.@nQ\aAL[1]{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LMinkowski distance: Pt1 Pt2Arial0nQ\aABnQ\aAA<?bX<@?er.<rV@bX<@?er.?  ?   - nQ\aAA%0    <0>%0    <0>0 !  j  9<0>:/ J00$$eMDw$ww@  `` nQ\aAdist {A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LMinkowski angle Pt1 Vertex Pt2Arial0nQ\aAP[2]2nQ\aATnQ\aAP[1]2<?bX<@?er.?  / nQ\aAj/ nQ\aAk/ nQ\aAl - nQ\aAA - nQ\aAB. nQ\aAm. nQ\aAn -  nQ\aAC -  nQ\aAD/3   k<0>nQ\aAm[1]/3  <0>nQ\aAm[2]0 ! n <0> N0 0 & &eMDw+Xw~Sw.x `` nQ\aAangle{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$:0LIntersection between two hyperbolas: hyp1 hyp2tArial0nQ\aAL[2]r45nQ\aAL[1]r=S'nQ\aAS[1]r=Sa nQ\aAA nQ\aAB nQ\aAC  nQ\aAD<?bX<@?y Bjrn ?   ?  .  nQ\aAj"     nQ\aAE<?bX<@?y Bjrn ?  ?  . nQ\aAk"   -  nQ\aAFA3    <0>nQ\aAm[1]B3    !<0>nQ\aAm[2]A3   <<0>B3    Y<0>0 !r  u<0> R0 %%eMDw$ww ``  `` nQ\aAm[3] nQ\aAG nQ\aAH nQ\aAI  nQ\aAJ<?bX<@?y Bjrn ?   ?  . "nQ\aAl"  #!  %nQ\aAK&<?bX<@?y Bjrn ?  &'?  . &)nQ\aAm"  *( - $+nQ\aALA3 ,   <0>nQ\aAm[4]B3 ,   <0>nQ\aAm[5]A3    <0>B3    <0>0 !/-0.r  <0> R0 ""eMDw$ww ``  `` nQ\aAm[6]0 ! .b * <0>:/ B0 ) )eMDw$ww``nQ\aAm[7]0 !.-1~ *'<0> ^0MeM ``  ``  `` nQ\aAm[8]0 !.-1 *A<0>gn  b0#\w+  `` `` ```` nQ\aAm[9]0 !324 *[<0> h0#\w+  ` ```  ` nQ\aAm[10]0 !324 *<0>gn  h0MeM ` ```  ` nQ\aAm[11]0 !5n *<0> N0 #\w+ ` `` `nQ\aAm[12]0 !16-.n *<0>:/ N0 MeM` `` `nQ\aAm[13]E857nQ\aAME868nQ\aAN{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$)FLIntersecting a straight line and a hyperbola: Linept1 Linept2 Hyp Arial0nQ\aAL[1]attnQ\aAGuunQ\aAFvv'nQ\aAS[1]aww nQ\aAA nQ\aAB nQ\aAC?  ?     nQ\aAD <?bX<@?1 Linep?   .  nQ\aAj"     nQ\aAE<?bX<@?1 Linep?  . nQ\aAk"   - nQ\aAFA3    <0>nQ\aAm[1]B3    !<0>nQ\aAm[2]A3    ;<0>B3    W<0>0 !r  s<0> R0 #\w+ ``  `` nQ\aAm[3]A3   B/<0>B3   BK<0>A3   Bg<0>B3   B<0>0 !r <0> R0 #\w+ ``  `` nQ\aAm[4]0 ! f 4<0> F0#\w+```nQ\aAm[5]0 !! j N<0>:/ J0#\w+````nQ\aAm[6]0 !!n h<0> N0 #\w+`````nQ\aAm[7]0 !" # <0> h0MeM ` ```  ` nQ\aAm[8]0 !" # <0>gn  h0#\w+ ` ```  ` nQ\aAm[9]0 ! $!f <0>:/ F0#\w+```0 ! %!f <0> F0#\w+```E8$&nQ\aAGE8%'nQ\aAH{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$$6LIntersection of null lines with hyperbola: Basept hypArial0nQ\aAL[1]tpr@nQ\aADr\V@Pu@'nQ\aAS[1]tP~@h4Fr@A3    <0>B3    <0> nQ\aAA nQ\aAB nQ\aAC?      nQ\aAD  nQ\aAE <?bX<@?pBjrn ?   .  nQ\aAj"   <?bX<@?pBjrn ?   ?  .  nQ\aAk"   - nQ\aAFA3    ;<0>B3    V<0>A3    q<0>B3    <0>0 !r  <0> R0  ! !eMDw+Xw~Sw; ``  `` nQ\aAm[1]0 !n  <0>:/ N0  " "eMDw+Xw~Sw;` `` `E8nQ\aAG0 !n  <0> N0 $$eMDw+Xw~Sw;` `` `E8nQ\aAH<?bX<@?pBjrn <?=p@bX<@?pBjrn ?  !?  "{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$`LMinkowski ellipse F1 F2 PtArial0nQ\aAQ/pz@nQ\aAF[2]nQ\aAF[1]<?bX<@?pBjrn nQ\aAF'[1]?  . nQ\aAq/ nQ\aAr - nQ\aAI/ nQ\aAs. nQ\aAt%0    =<0>  ?  <?bX<@?pBjrn ?  <rV@bX<@?pBjrn ?   - nQ\aAA%0    <0>%0    <0>0 ! j <0>:/ J00$$eMDw$ww@  `` nQ\aAdist/ nQ\aAu - nQ\aAJ%0    <0>0 !  b *<0> B0h##eMDw+Xw~Sw*``  nQ\aAK ?   - nQ\aAL $r<f@b <r<f@bX<@?pBjrn nQ\aAQ'' <?bX<@?pBjrn nQ\aAQ''P C "! #nQ\aAB?  $nQ\aAj -  nQ\aAM%0 &   s<0>%0 &   X<0> -  nQ\aAN%0 )  <0>%0 )   <0>0 !*'+(z <0> Z0h ! !eMDw+Xw~Sw*  ``  `` 0 ! , b 4<0>:/ B0h % %eMDw+Xw~Sw*`` -nQ\aAc[1] -  .nQ\aAO. /nQ\aAv - 0nQ\aAP? /1nQ\aAk1<rV@bX<@?pBjrn ?  13 - 4nQ\aAC%0 51   <0>%0 5   <0>0 ! 76j  <0> J00$$eMDw$ww@  `` nQ\aAdist0 ! 8r b<0> R0 h ) )eMDw+Xw~Sw*`  `  9nQ\aAc[2] - :nQ\aAQ/ ;nQ\aAw - <nQ\aAR=<?bX<@?pBjrn ?  => - :nQ\aAS/ @nQ\aAx - AnQ\aATB<rV@bX<@?pBjrn ?  BC - ?DnQ\aAD%0 =E   <0>%0 EB   <0>0 ! FGj !<0>:/ J00$$eMDw$ww@  `` nQ\aAdist0 ! Hb <0> B0h # #eMDw+Xw~Sw*``0 ! HIr 9<0> R0 h ' 'eMDw+Xw~Sw*` ` 0 ! Jn <0>:/ N0 h##eMDw+Xw~Sw*`  `  KnQ\aAc[3] - LnQ\aAU/ MnQ\aAy - NnQ\aAV - LnQ\aAW/ PnQ\aAz - QnQ\aAX? 1nQ\aAl - %SnQ\aAE -nQ\aAc[4] - UnQ\aAY. VnQ\aAa -  WnQ\aAZ?  VnQ\aAm - Y2nQ\aAF? ZTnQ\aAn? VnQ\aAo - [\nQ\aAG? ]/nQ\aAp - %^nQ\aAH#*( _#$%T[]^_  ?nQ\aAL[1]{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ELMinkowski Hyperbola F1 F2 PtArial0nQ\aAQ[0]U33`@nQ\aAFn@! Qv@nQ\aACB1s2@7~{@<?bX<@?y Bjrn nQ\aAC'?  / nQ\aAp/ nQ\aAq. nQ\aAr - nQ\aAH - nQ\aAI?  ?    -  nQ\aAJ%0   hm<0>%0   h<0>. nQ\aAs. nQ\aAt  $r<f@b@    $r<f@b@   - nQ\aAK%0   h<0>%0    h<0> - nQ\aAL%0   h<0>%0    h<0>0 !z h<0> Z00!!eMDw+Xw~Sw.x  ``  `` 0 ! b C<0> B00 # #eMDw+Xw~Sw.x``  nQ\aAc[1] - nQ\aAM? nQ\aAj  $r<f@b0 ! b <0>:/ B00 & &eMDw+Xw~Sw.x``  "nQ\aAc[2] - #nQ\aAB? $!nQ\aAk? $nQ\aAl $ $r<f@b?  '! - ( nQ\aAA'<r<f@bX<@?y Bjrn nQ\aAB'''<?bX<@?y Bjrn nQ\aAB''P C'+* ,nQ\aAC? '-nQ\aAm - .&nQ\aAD? )/nQ\aAn - 0%nQ\aAE? 1nQ\aAo - .2nQ\aAF#*( 3,-./0123  ?nQ\aAL[1]?  $0 ! b h<0> B00 " "eMDw+Xw~Sw.x``<?bX<@?y Bjrn ?  7$<rV@bX<@?y Bjrn ?  $9 - 8:nQ\aAG%0 ;  h<0>%0 ;$  h<0>0 ! <=j h<0>:/ J00$$eMDw$ww@  `` nQ\aAdist0 ! >6n h<0> N0 0))eMDw+Xw~Sw.x` `   ?nQ\aAc[3].  nQ\aAu - A@nQ\aAN/ BAnQ\aAv - C nQ\aAO D $r<f@b