GSP4 KQThat 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.$# ` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0498/Jan 29 20020#` Arial  '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':') A`s@pt@4(@ 4B@B?   OOx-axis: &  nQ\aAx6(n 6\.B@: &n  nQ\aAy='n  -#{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LHalf-plane line Arial  nQ\aAx-axisKnQ\aAAnQ\aACT"nQ\aAD0%A  nQ\aAA/n nQ\aAj -n nQ\aABn  -n nQ\aAC -n nQ\aADQ Cn  /#Poincare Half-Plane Line Setting: Poincare half-plane bounded by the x-axis Given: Points A, B in the half-plane that do not lie on a common vertical line Returns: The half-plane line (i.e. semicircle centered on the x-axis) which passes through A and B. {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.$ LHalf-plane segment Arial e nQ\aAx-axispR%i@pt@@$nQ\aA Endpoint #21. Match Point DD$nQ\aA Endpoint #1Z;7Q@pt@@  @nQ\aAA/n nQ\aAj -n nQ\aABn @ n  -n  nQ\aACQ Cn /#Poincare Half-Plane Segment Given: Poincare half-plane bounded by the x-axis Given: Points A, B in the half-plane that are not on a common vertical line Returns: The arc of a circle with endpoints A and B, lying in the upper half plane and centered on the x-axisn{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.$LHalf-plane length Arial t nQ\aAx-axisoE$nQ\aA Endpoint #2@$nQ\aA Endpoint #1`  nQ\aAC/n nQ\aAj -n nQ\aADn  -n nQ\aAA -n nQ\aAB%0n   N<0>%0n   9<0>%0n   $<0>%0n   <0>0 !n z c<0> b.  Z0  ``  `` "distance#/#Half-Plane Length Setting: Poincare half-plane bounded by the x-axis Given: Points C, D in the Poincare half-plane Returns: The Poincare length of the segment CD. Note that since the half-plane model is not isometric, the Poincare length of the segment is generally different from its Euclidean length. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LHalf-plane angle measure Arial e*nQ\aAon angle side #2a  nQ\aAvertexe0%A LL*nQ\aAon angle side #1a@ nQ\aAx-axise`   nQ\aAC nnQ\aAD/n nQ\aAj/n nQ\aAk -n  nQ\aAE -n  nQ\aAF? n  ? n  /n nQ\aAl/n  nQ\aAm/n nQ\aAn -n nQ\aAA/n nQ\aAo -n nQ\aAB)1n   (<0>nQ\aAThetaJ/#Half-Plane Angle Measure Setting: Poincare half-plane bounded by the x-axis Given: Points P, C, Q in the Poincare half-plane Returns: The measure of the Poincare angle PCQ. This is the measure of the Euclidean angle between the Poincare segments joining P and C, and C and Q. Author: Steve Szydlik/February 2003t{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.$LHalf-plane angle bisector Arialsi e nQ\aAx-axis*nQ\aAon angle side #2n8 nQ\aAvertexelNegKntss*nQ\aAon angle side #1n\U   nQ\aAA nnQ\aAB/n nQ\aAj/n nQ\aAk -n  nQ\aAC -n  nQ\aADn  n  /n  nQ\aAl/n nQ\aAm/n nQ\aAn/n nQ\aAo -n nQ\aAE -n nQ\aAF,nnQ\aAp/n nQ\aAq -n nQ\aAGn  -n nQ\aAH -n nQ\aAIQ Cn$/#Half-Plane Angle Bisector Setting: Poincare half-plane bounded by the x-axis Given: Points P, C, Q in the Poincare half-plane Returns: The Poincare half-plane line which is the angle bisector of angle PCQ. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003{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.$ LHalf-plane raise perpendicular Arial e nQ\aAx-axisnQ\aAA.nQ\aAfoot of perpendicular$nQ\aA #2 on linep  nQ\aAA/n nQ\aAj -n nQ\aABn n /n nQ\aAk -n  nQ\aAC -n  nQ\aAD -n  nQ\aAEO Cn    - nQ\aAF -n nQ\aAGQ Cnd/#Half-Plane Raise Perpendicular Setting: Poincare half-plane bounded by the x-axis Given: Points C, D in Poincare half-plane Returns: The half-plane line through C which is perpendicular to the half plane line through C and D. Both lines are drawn in this construction. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LHalf-plane drop perpendicular Arialsi  nQ\aAx-axis$nQ\aA #1 on line4 $nQ\aA #2 on lineLd;A$nQ\aA not on line  nQ\aAA/n nQ\aAj -n nQ\aAB? n n n  -n  nQ\aAC/n  nQ\aAk -n  nQ\aAD -n  nQ\aAE -n  nQ\aAF -n  nQ\aAGQ Cn?   . nQ\aAl -n  nQ\aAHn  nnQ\aAI/n nQ\aAm -n nQ\aAJn  -n nQ\aAK -n nQ\aALQ Cn~/#Half-Plane Drop Perpendicular Setting: Poincare half-plane bounded by the x-axis. Given: Non-collinear points P, Q, C in the Poincare half-plane. Returns: The half-plane line through C which is perpendicular to the Poincare line l containing P and Q. Both lines are drawn in this construction. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003a{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.$ "LHalf-plane perpendicular bisector Arial e nQ\aAx-axiso$nQ\aA endpoint #1$nQ\aA endpoint #2?    nQ\aAE -n nQ\aAF/n nQ\aAj -n nQ\aAGn  n   n nQ\aAHn  -n  nQ\aAA -n  nQ\aAB? n  -n nQ\aAC -n nQ\aAD@ n  -n  nQ\aAIQ Cn  nQ\aAJ/n nQ\aAk -n nQ\aAKn /n nQ\aAl -n nQ\aALn  -n nQ\aAM -n nQ\aANQ CnJ/#Half-Plane Perpendicular Bisector Setting: Poincare half-plane bounded by the x-axis. Given: Points C, D in the Poincare half-plane. Returns: The half-plane perpendicular bisector of segment CD. Segment CD is also drawn in this construction. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003l{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.$&LHalf-plane circle by center and point Arialsi l"nQ\aA on circle nQ\aAcenterl nQ\aAx-axisl/ nQ\aAjn  nnQ\aAA/n nQ\aAk -n nQ\aABn n /n  nQ\aAl -n  nQ\aAC? n   -n  nQ\aAD -n  nQ\aAEn  nnQ\aAF@ n  -n  nQ\aAGn  nnQ\aAH/n nQ\aAm -n nQ\aAIn /#Half-Plane Circle by Center and Point Setting: Poincare half-plane bounded by the x-axis Given: Points O, P in the Poincare half-plane. Returns: The half-plane circle centered at O with radius OP. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003l{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$\,LHalf-plane circle by center and two points Arialsi l6nQ\aA#2 defining a radius segmentйNN6nQ\aA#1 defining a radius segment&nQ\aA circle center nQ\aAx-axisc ?    nQ\aAH -n nQ\aAI/n nQ\aAj -n  nQ\aAJn  n   n nQ\aAKn  -n  nQ\aAD -n  nQ\aAE? n  -n nQ\aAF -n nQ\aAG@ n  -n  nQ\aALn  nnQ\aAM/n nQ\aAk -n nQ\aANn /n nQ\aAl -n nQ\aAOn  -n nQ\aAP -n nQ\aAQQ Cn -  nQ\aARn ! n"nQ\aAS/n #"nQ\aAm -n $nQ\aATn %!? n %n % -n '&nQ\aAU/n %'nQ\aAn -n *&nQ\aAV -n *(nQ\aAW? n ,).n +-nQ\aAo -n .'nQ\aAXn / n0nQ\aAY/n 10nQ\aAp -n 2nQ\aAZn 3 -n 4nQ\aAA[1]s -n 4nQ\aAB[1]sQ Cn65 -  7nQ\aAC[1]sn 8 n9nQ\aAD[1]s/n :9nQ\aAq -n ;nQ\aAE[1]sn <n 8</n 8>nQ\aAr -n ?nQ\aAF[1]s? n @ -n A=nQ\aAG[1]s -n A=nQ\aAH[1]sn BC nDnQ\aAI[1]s@ n E -n F=nQ\aAJ[1]s/n nQ\aAsn G nInQ\aAK[1]s/n JInQ\aAt -n KnQ\aAL[1]sn LGn L/n NnQ\aAu -n OnQ\aAM[1]s? n PG -n QMnQ\aAN[1]s -n QMnQ\aAO[1]sn RS nTnQ\aAP[1]s@ n GU -n VMnQ\aAQ[1]sn GW nXnQ\aAR[1]s/n YXnQ\aAv -n HZnQ\aAS[1]sn [G:/#Half-Plane Circle by Center and Two Points Setting: Poincare half-plane bounded by the x-axis Given: Points O, C, D in the Poincare half-plane. Returns: The half-plane circle centered at point O with radius OP congruent to CD. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LHalf-plane point reflection Arialsi t.nQ\aAM on reflecting line-plane raise perr*nQ\aAA to be reflected nQ\aAx-axis c;N  nQ\aAA/n nQ\aAj -n nQ\aABn n /n  nQ\aAk -n  nQ\aACn  ? n   -n  nQ\aAD -n  nQ\aAEn  nnQ\aAF@ n  -n nQ\aAG -n nQ\aAH -n  nQ\aAI -n nQ\aAJ -n  nQ\aAKQ CnQ C/#Half-Plane Point Reflection Setting: Poincare half-plane bounded by the x-axis. Given: Points M, A in the Poincare half-plane. Returns: The image A' of point A upon reflection in the Poincare line m that is perpendicular to segment AM. In other words, AA' is perpendicular to M and AM is congruent to A'M. Both lines through M are drawn in this construction. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003{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.$LHalf-plane midpoint Arial o$nQ\aA endpoint #2$nQ\aA endpoint #1 nQ\aAx-axist  nQ\aAC/n nQ\aAj -n nQ\aADn ? n  -n  nQ\aAEn   n nQ\aAFn   -n  nQ\aAG-n  nQ\aAH? n  -n nQ\aAI -n nQ\aAJ@ n  -n nQ\aAKH/#Half-Plane Midpoint Setting: Poincare half-plane bounded by the x-axis. Given: Points C, D in the Poincare half-plane. Returns: The half-plane midpoint M of segment CD, so that M lies on CD and CM is congruent (in the Poincare sense) to DM. Author: Steve Szydlik/July 2000 Revised for GSP 4.0 in February 2003n