GSP4KQThat 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.$# ` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0498/Jan 29 20020#`
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$'%'&'8'8'8'9':') A`s@pt@4(@4B@B? OOx-axis: & nQ\aAx6(n6\.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.$LHalf-plane line
Arial nQ\aAx-axisKnQ\aAAnQ\aACT"nQ\aAD0%AnQ\aAA/nnQ\aAj -nnQ\aABn-nnQ\aAC-nnQ\aADQCn
/#Poincare Half-Plane Line
Setting: Poincare half-plane bounded by the x-axis
Given: Points A, B in the half-plane that do not lie on a common vertical line
Returns: The half-plane line (i.e. semicircle centered on the x-axis) which passes through A and B.
{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LHalf-plane segment
Ariale nQ\aAx-axispR%i@pt@@$nQ\aAEndpoint #21. Match Point DD$nQ\aAEndpoint #1Z;7Q@pt@@@nQ\aAA/nnQ\aAj -nnQ\aABn@
n-n nQ\aACQCn
/#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.$LHalf-plane length
Arialt nQ\aAx-axisoE$nQ\aAEndpoint #2@$nQ\aAEndpoint #1`nQ\aAC/nnQ\aAj -nnQ\aADn-nnQ\aAA-nnQ\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
Ariale*nQ\aAon angle side #2a
nQ\aAvertexe0%A
LL*nQ\aAon angle side #1a@ nQ\aAx-axise`nQ\aACnnQ\aAD/nnQ\aAj/nnQ\aAk -n nQ\aAE -n
nQ\aAF?n?n/nnQ\aAl/n
nQ\aAm/nnQ\aAn -nnQ\aAA/nnQ\aAo -nnQ\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.$LHalf-plane angle bisector
Arialsie nQ\aAx-axis*nQ\aAon angle side #2n8 nQ\aAvertexelNegKntss*nQ\aAon angle side #1n\UnQ\aAAnnQ\aAB/nnQ\aAj/nnQ\aAk -n nQ\aAC -n
nQ\aADnn/n
nQ\aAl/nnQ\aAm/nnQ\aAn/nnQ\aAo -nnQ\aAE -nnQ\aAF,nnQ\aAp/nnQ\aAq -nnQ\aAGn-nnQ\aAH-nnQ\aAIQCn$/#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
Ariale nQ\aAx-axisnQ\aAA.nQ\aAfoot of perpendicular$nQ\aA
#2 on linepnQ\aAA/nnQ\aAj -nnQ\aABnn/nnQ\aAk-n nQ\aAC-n nQ\aAD -n
nQ\aAEOCn
-nQ\aAF-nnQ\aAGQCnd/#Half-Plane Raise Perpendicular
Setting: Poincare half-plane bounded by the x-axis
Given: Points C, D in Poincare half-plane
Returns: The half-plane line through C which is perpendicular to the half plane line through C and D. Both lines are drawn in this construction.
Author: Steve Szydlik/July 2000
Revised for GSP 4.0 in February 2003{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LHalf-plane drop perpendicular
Arialsi nQ\aAx-axis$nQ\aA
#1 on line4$nQ\aA
#2 on lineLd;A$nQ\aAnot on linenQ\aAA/nnQ\aAj -nnQ\aAB?nnn-n nQ\aAC/n nQ\aAk-nnQ\aAD-nnQ\aAE-n
nQ\aAF-n
nQ\aAGQCn?.nQ\aAl -n nQ\aAHnnnQ\aAI/nnQ\aAm -nnQ\aAJn-nnQ\aAK-nnQ\aALQCn~/#Half-Plane Drop Perpendicular
Setting: Poincare half-plane bounded by the x-axis.
Given: Non-collinear points P, Q, C in the Poincare half-plane.
Returns: The half-plane line through C which is perpendicular to the Poincare line l containing P and Q. Both lines are drawn in this construction.
Author: Steve Szydlik/July 2000
Revised for GSP 4.0 in February 2003a{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ "LHalf-plane perpendicular bisector
Ariale nQ\aAx-axiso$nQ\aAendpoint #1$nQ\aAendpoint #2?nQ\aAE -nnQ\aAF/nnQ\aAj -nnQ\aAGn n n
nQ\aAHn -n
nQ\aAA
-n
nQ\aAB?n -nnQ\aAC -nnQ\aAD@
n-nnQ\aAIQCnnQ\aAJ/nnQ\aAk -nnQ\aAKn/nnQ\aAl -nnQ\aALn-nnQ\aAM-nnQ\aANQCnJ/#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.$&LHalf-plane circle by center and point
Arialsil"nQ\aA on circle nQ\aAcenterl nQ\aAx-axisl/nQ\aAjnnnQ\aAA/nnQ\aAk -nnQ\aABnn/n
nQ\aAl -nnQ\aAC?n-n
nQ\aAD-n
nQ\aAEnnnQ\aAF@
n-n nQ\aAGnnnQ\aAH/nnQ\aAm -nnQ\aAIn/#Half-Plane Circle by Center and Point
Setting: Poincare half-plane bounded by the x-axis
Given: Points O, P in the Poincare half-plane.
Returns: The half-plane circle centered at O with radius OP.
Author: Steve Szydlik/July 2000
Revised for GSP 4.0 in February 2003l{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$\,LHalf-plane circle by center and two points
Arialsil6nQ\aA#2 defining a radius segmentйNN6nQ\aA#1 defining a radius segment&nQ\aA
circle center nQ\aAx-axisc?nQ\aAH -nnQ\aAI/nnQ\aAj -n nQ\aAJn
n
nnQ\aAKn
-nnQ\aAD
-nnQ\aAE?n -nnQ\aAF -nnQ\aAG@
n-nnQ\aALnnnQ\aAM/nnQ\aAk -nnQ\aANn/nnQ\aAl -nnQ\aAOn-nnQ\aAP-nnQ\aAQQCn- nQ\aARn!n"nQ\aAS/n#"nQ\aAm -n$nQ\aATn%!?n%n%-n'&nQ\aAU/n%'nQ\aAn-n*&nQ\aAV-n*(nQ\aAW?n,).n+-nQ\aAo -n.'nQ\aAXn/n0nQ\aAY/n10nQ\aAp -n2nQ\aAZn3-n4nQ\aAA[1]s-n4nQ\aAB[1]sQCn65
- 7nQ\aAC[1]sn8n9nQ\aAD[1]s/n:9nQ\aAq -n;nQ\aAE[1]sn<n8</n8>nQ\aAr -n?nQ\aAF[1]s?n@-nA=nQ\aAG[1]s-nA=nQ\aAH[1]snBCnDnQ\aAI[1]s@
nE-nF=nQ\aAJ[1]s/nnQ\aAsnGnInQ\aAK[1]s/nJInQ\aAt -nKnQ\aAL[1]snLGnL/nNnQ\aAu -nOnQ\aAM[1]s?nPG-nQMnQ\aAN[1]s-nQMnQ\aAO[1]snRSnTnQ\aAP[1]s@
nGU-nVMnQ\aAQ[1]snGWnXnQ\aAR[1]s/nYXnQ\aAv -nHZnQ\aAS[1]sn[G:/#Half-Plane Circle by Center and Two Points
Setting: Poincare half-plane bounded by the x-axis
Given: Points O, C, D in the Poincare half-plane.
Returns: The half-plane circle centered at point O with radius OP congruent to CD.
Author: Steve Szydlik/July 2000
Revised for GSP 4.0 in February 2003{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LHalf-plane point reflection
Arialsit.nQ\aAM on reflecting line-plane raise perr*nQ\aAA to be reflected nQ\aAx-axis c;NnQ\aAA/nnQ\aAj -nnQ\aABnn/n nQ\aAk -n
nQ\aACn?n-n
nQ\aAD-n
nQ\aAEnnnQ\aAF@
n-nnQ\aAG-nnQ\aAH-nnQ\aAI-nnQ\aAJ-nnQ\aAKQCnQC/#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.$LHalf-plane midpoint
Arialo$nQ\aAendpoint #2$nQ\aAendpoint #1 nQ\aAx-axistnQ\aAC/nnQ\aAj -nnQ\aADn?n -n nQ\aAEn
nnQ\aAFn
-n
nQ\aAG-n
nQ\aAH?n -nnQ\aAI -nnQ\aAJ@
n-nnQ\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