Sisäinen laskutoimitus avoimella ja suljetulla välillä
1. Operaatio o avoimella välillä
${
1. Operaatio o avoimella välillä
#CODEBASE = "http://cs.uef.fi/matematiikka/java/javasketchpad"
$}
#CODEBASE = "../jsp"
#ARCHIVE="jsp4.jar"
#WIDTH = 600
#HEIGHT = 100
#ALIGN = Center
*Frame = 0
*TextFont = "Helvetica"
*TextBold = 1
*TextSize = 18
*LabelFont = "Courier"
*LabelBold = 1
*MeasureFont = "Courier"
*MeasureSize = 14
*MeasureBold = 1
*MeasureInDegrees = 1
*DirectedAngles = 0
*BackRed = 255
*BackGreen = 255
*BackBlue = 235
$reset FixedText(585,15,'Reset = ''R''')[red,bold,justifyRight];
FixedText(585, 45,'R')[plain,font('Helvetica'),bold, black,justifyCenter];
$O FixedPoint(300,50)[ black, label('0')];
$ykk FixedPoint(325,50)[ white, label('1'), hidden];
$L Line($ykk,$O)[black];
$c FixedPoint(500,50)[black, label('c')];
$negc VectorTranslation($O,$c,$O)[black, label('-c')];
$cvalue Ratio/Points($O,$ykk,$c,200,0,'c = ')[red];
$cfake FixedPoint(499,50)[black, label('c'),hidden];
$negcfake VectorTranslation($O,$cfake,$O)[black, label('-c'),hidden];
$Scnegc Segment($cfake,$negcfake)[hidden];
$u Point on object($Scnegc,0.11)[red, label('u'),layer(5)];
$v Point on object($Scnegc,0.6)[blue,label('v'),layer(5)];
$uvalue Ratio/Points($O,$ykk,$u,200,15,'u = ')[red,hidden];
$vvalue Ratio/Points($O,$ykk,$v,200,30,'v = ')[blue,hidden];
$uovvalue Calculate(200,65,'uov = ','AB+ AB* CC* / 1+ /')($uvalue,$vvalue,$cvalue)[magenta, hidden];
$uov Dilation/MarkedRatio($ykk,$O,$uovvalue)[magenta, label('u o v'), layer(2)];
2. Operaatio o suljetulla välillä
${
SLT Graafinen tehtävä 1a: vauhtien summa suhteellisuusteoriassa, suljetulle välille rajoitettu
#CODEBASE = "http://cs.uef.fi/matematiikka/java/javasketchpad"
$}
#CODEBASE = "../jsp"
#ARCHIVE="jsp4.jar"
#WIDTH = 600
#HEIGHT = 100
#ALIGN = Center
*Frame = 0
*TextFont = "Helvetica"
*TextBold = 1
*TextSize = 18
*LabelFont = "Courier"
*LabelBold = 1
*MeasureFont = "Courier"
*MeasureSize = 14
*MeasureBold = 1
*MeasureInDegrees = 1
*DirectedAngles = 0
*BackRed = 255
*BackGreen = 255
*BackBlue = 220
$reset FixedText(585,15,'Reset = ''R''')[red,bold,justifyRight];
FixedText(585, 45,'R')[plain,font('Helvetica'),bold, black,justifyCenter];
$O FixedPoint(300,50)[ black, label('0')];
$ykk FixedPoint(325,50)[ white, label('1'), hidden];
$L Line($ykk,$O)[black];
$c FixedPoint(500,50)[black, label('c')];
$negc VectorTranslation($O,$c,$O)[black, label('-c')];
$cvalue Ratio/Points($O,$ykk,$c,200,0,'c = ')[red];
$Scnegc Segment($c,$negc)[hidden];
$u Point on object($Scnegc,0.75)[red, label('u'),layer(5)];
$v Point on object($Scnegc,0.3)[blue,label('v'),layer(5)];
$uvalue Ratio/Points($O,$ykk,$u,200,15,'u = ')[red,hidden];
$vvalue Ratio/Points($O,$ykk,$v,200,30,'v = ')[red,hidden];
$Duc Distance($u,$c,0,20,'|u-c| =')[magenta, hidden];
$Dvnegc Distance($v,$negc,0,40,'|v+c| =')[magenta, hidden];
$flaguov01 Calculate( 200, 70, 'summa = ','0 A B+-@sqrt')($Duc,$Dvnegc)[magenta, hidden];
$uov01 Translation/FixedAngle/MarkedDistance($O, $flaguov01, 0)[magenta, label('u o v'), layer(2)];
$Dvc Distance($v,$c,0,20,'|v-c| =')[red,hidden];
$Dunegc Distance($u,$negc,0,40,'|u+c| =')[red,hidden];
$flaguov02 Calculate( 200, 70, 'summa = ','0 A B+-@sqrt')($Dvc,$Dunegc)[magenta, hidden];
$uov02 Translation/FixedAngle/MarkedDistance($O, $flaguov02, 0)[magenta, label('u o v'), layer(2)];
$uovvalue Calculate(200,65,'uov = ','AB+ AB* CC* / 1+ /')($uvalue,$vvalue,$cvalue)[red, hidden];
$uov Dilation/MarkedRatio($ykk,$O,$uovvalue)[magenta, label('u o v'), layer(2)];
2. Ulkoinen laskutoimitus avoimella ja suljetulla välillä
2A. Operaatio * avoimella välillä
${
2A. Operaatio * avoimella välillä
#CODEBASE = "http://cs.uef.fi/matematiikka/java/javasketchpad"
$}
#CODEBASE = "../jsp"
#ARCHIVE="jsp4.jar"
#WIDTH = 600
#HEIGHT = 120
#ALIGN = Center
*Frame = 0
*TextFont = "Helvetica"
*TextBold = 1
*TextSize = 18
*LabelFont = "Courier"
*LabelBold = 1
*MeasureFont = "Courier"
*MeasureSize = 14
*MeasureBold = 1
*MeasureInDegrees = 1
*DirectedAngles = 0
*BackRed = 235
*BackGreen = 255
*BackBlue = 255
$reset FixedText(585,15,'Reset = ''R''')[red, bold, justifyRight];
FixedText(585, 48,'R')[plain,font('Helvetica'),bold, black, justifyCenter];
FixedText(585, 103,'R')[plain,font('Helvetica'),bold, red, justifyCenter];
$LUpp FixedPoint(0,85)[hidden];
$LLow FixedPoint(0,120)[hidden];
$RLow FixedPoint(600,120)[hidden];
$RUpp FixedPoint(600,85)[hidden];
$RectA Polygon($LUpp,$LLow,$RLow,$RUpp,$LUpp)[yellow];
$RO FixedPoint(300,105)[black, label('0')];
$Ref Translation($RO,25,0)[hidden];
$Ray Ray($Ref,$RO)[black, hidden];
$Rykk FixedPoint(325,105)[white, label('1')];
$RL Line($Rykk,$RO)[red];
$a Point on object($RL,3)[label('a'), red, layer(5)];
$avalue Ratio/Points($RO,$Rykk,$a,200,15,'a = ')[red, hidden];
$O FixedPoint(300,50)[ black, label('0')];
$ykk FixedPoint(325,50)[ white, label('1'), hidden];
$L Line($ykk,$O)[black];
$c FixedPoint(500,50)[black, label('c')];
$negc VectorTranslation($O,$c,$O)[black, label('-c')];
$cvalue Ratio/Points($O,$ykk,$c,200,0,'c = ')[red, hidden];
$cfake FixedPoint(499,50)[black, label('c'),hidden];
$negcfake VectorTranslation($O,$cfake,$O)[black, label('-c'),hidden];
$Scnegc Segment($cfake,$negcfake)[hidden];
$u Point on object($Scnegc,0.75)[red, label('u'),layer(5)];
$uvalue Ratio/Points($O,$ykk,$u,0,15,'u = ')[red, hidden];
$Au Calculate(200,65,'B = ','A CB+ CB- / @ln__ *')($avalue,$uvalue,$cvalue)[red, hidden];
$auvalue Calculate(200,65,'au = ','A 2.718281828 B^ 1 - 2.718281828 B^ 1+ / *')($cvalue,$Au)[red, hidden];
$au Dilation/MarkedRatio($ykk,$O,$auvalue)[red, label('a*u'), layer(2)];
$Saau Segment($a,$au)[red];
$Suau Segment($u,$au)[red, layer(10)];
2B. Operaatio * suljetulla välillä
${
2B. Ulkoinen laskutoimitus suljetulla välillä
#CODEBASE = "http://cs.uef.fi/matematiikka/java/javasketchpad"
$}
#CODEBASE = "../jsp"
#ARCHIVE="jsp4.jar"
#WIDTH = 600
#HEIGHT = 120
#ALIGN = Center
*Frame = 0
*TextFont = "Helvetica"
*TextBold = 1
*TextSize = 18
*LabelFont = "Courier"
*LabelBold = 1
*MeasureFont = "Courier"
*MeasureSize = 14
*MeasureBold = 1
*MeasureInDegrees = 1
*DirectedAngles = 0
*BackRed = 220
*BackGreen = 255
*BackBlue = 255
$reset FixedText(585,15,'Reset = ''R''')[red, bold, justifyRight];
FixedText(585, 48,'R')[plain,font('Helvetica'),bold, black, justifyCenter];
FixedText(585, 103,'R')[plain,font('Helvetica'),bold, red, justifyCenter];
$LUpp FixedPoint(0,85)[hidden];
$LLow FixedPoint(0,120)[hidden];
$RLow FixedPoint(600,120)[hidden];
$RUpp FixedPoint(600,85)[hidden];
$RectA Polygon($LUpp,$LLow,$RLow,$RUpp,$LUpp)[yellow];
$RO FixedPoint(300,105)[black, label('0')];
$Ref Translation($RO,25,0)[hidden];
$Ray Ray($Ref,$RO)[black, hidden];
$Rykk FixedPoint(325,105)[white, label('1')];
$RL Line($Rykk,$RO)[red];
$a Point on object($RL,3)[label('a'), layer(5)];
$avalue Ratio/Points($RO,$Rykk,$a,200,35,'a = ')[red, hidden];
$O FixedPoint(300,50)[ black, label('0')];
$ykk FixedPoint(325,50)[ white, label('1'), hidden];
$L Line($ykk,$O)[black];
$c FixedPoint(500,50)[black, label('c')];
$negc VectorTranslation($O,$c,$O)[black, label('-c')];
$cvalue Ratio/Points($O,$ykk,$c,200,0,'c = ')[red, hidden];
$Scnegc Segment($c,$negc)[hidden];
$u Point on object($Scnegc,0.75)[red, label('u'),layer(5)];
$uvalue Ratio/Points($O,$ykk,$u,200,15,'u = ')[red, hidden];
$A Calculate(200,65,'B = ','A CB+ CB- / @ln__ *')($avalue,$uvalue,$cvalue)[red, hidden];
$cuvalue Calculate(200,65,'cu = ','A 2.718281828 B^ 1 - 2.718281828 B^ 1+ / *')($cvalue,$A)[red, hidden];
$au Dilation/MarkedRatio($ykk,$O,$cuvalue)[magenta, label('a*u'), layer(2)];
$DaO Distance($a,$RO,0,20,'|a-0| =')[magenta, hidden];
$flaga0 Calculate( 200, 70, 'flaga0 = ','0 A - @sqrt')($DaO)[magenta, hidden];
$au0 Translation/FixedAngle/MarkedDistance($O, $flaga0, 0)[magenta, label('a*u'), layer(2)];
$Duc Distance($u,$c,0,20,'|u-c| =')[magenta,hidden];
$flagaposuc Calculate( 200, 70, 'flagaposuc = ','A @sgn_ B @sgn_ - 1 - @sqrt')($avalue,$Duc)[magenta, hidden];
$auaposc Translation/FixedAngle/MarkedDistance($c, $flagaposuc, 0)[magenta, label('a*u'), layer(2)];
$Dupoisc Distance($u,$negc,0,20,'|u+c| =')[magenta,hidden];
$flaganeguc Calculate( 200, 70, 'flaganeguc = ','0 A @sgn_ - B @sgn_ - 1 - @sqrt')($avalue,$Dupoisc)[magenta, hidden];
$auanegc Translation/FixedAngle/MarkedDistance($c, $flaganeguc, 0)[magenta, label('a*u'), layer(2)];
$Saau Segment($a,$au)[red];
$Saau0 Segment($a,$au0)[red];
$Saauposc Segment($a,$auaposc)[red];
$Saaunegc Segment($a,$auanegc)[red];
$Suau Segment($u,$au)[red, layer(10)];
$Suau0 Segment($u,$au0)[red, layer(10)];
$Suauposc Segment($u,$auaposc)[red, layer(10)];
$Suaunegc Segment($u,$auanegc)[red, layer(10)];
Martti E. Pesonen 19.4.2006