{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{PSTYLE "Norm al" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Map le Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 126 "Referat von Milena Prei \337 und Michael Dorsch, Isolde-Kurz-Gymnasium Reutlingen \+ 07.11.2001" }}{PARA 0 "" 0 "" {TEXT 259 5 "T hema" }{TEXT -1 48 ": Geraden in 2D und 3D mit dem geometry-package." }}{PARA 0 "" 0 "" {TEXT 260 9 "\334bersicht" }{TEXT -1 113 ": Mit 3 ge gebenen Punkten soll eine Gerade (2D bzw.3D) aufgestellt, berechnet un d optisch veranschaulicht werden." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 25 "- Schnittpunkte berechnen" }}{PARA 0 "" 0 "" {TEXT -1 27 "- Eigenschaften der Objekte" }}{PARA 0 "" 0 "" {TEXT -1 43 "- Abstand der Geraden voneinander berechnen" }}{PARA 0 " " 0 "" {TEXT -1 43 "- Winkel, die die Geraden bilden, berechnen" }} {PARA 0 "" 0 "" {TEXT -1 24 "- Punktprobe durchf\374hren" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 0 "" } {TEXT 256 0 "" }{TEXT 257 0 "" }{TEXT 258 7 "Geraden" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 156 " Anmerkung: Die in Geraden 3D verwendeten Befe hle tauchen nicht alle auch in Geraden 2D auf, da der Schwerpunkt dies es Referates im Dreidimensionalen liegt." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Geraden 2D" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 15 "with(geometry):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 " Definieren der Punkte A, B und C. Es wird immer zuerst der Na me angegeben und dann die Koordinaten des jeweiligen Punktes." } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "point(A ,1,2),point(B,3,5),point(C,2,-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%% \"AG%\"BG%\"CG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "draw(\{A,B,C\},symbol=circle,scaling=cons trained,axes=normal,thickness=4);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'POINTSG6'7$$\"\"\"\"\"!$\"\"#F)-%&STYLEG6#%% LINEG-%'COLOURG6&%$RGBG$\"*++++\"!\")F)F)-%*THICKNESSG6#\"\"%-%'SYMBOL G6#%'CIRCLEG-F$6'7$$\"\"$F)$\"\"&F)F,F0F7F;-F$6'7$F*$!\"#F)F,F0F7F;-%* AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F'FB;FIFD" 1 2 0 1 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 " Festlegen der Geraden g durch die Punkte A und B ." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "lin e(g,[A,B]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"gG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 " Mit dem Befehl detail(g) erf\344hrt man die Ei nzelheiten der Geraden g." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "detail(g);" }}{PARA 6 "" 1 "" {TEXT -1 24 " na me of the object: g" }}{PARA 6 "" 1 "" {TEXT -1 29 " form of the obj ect: line2d" }}{PARA 6 "" 1 "" {TEXT -1 91 " assume that the name of the horizonal and vertical axis are _x and _y" }} {PARA 6 "" 1 "" {TEXT -1 41 " equation of the line: -1-3*_x+2*_y = 0 " }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 " Der Befehl Equation liefert die Geradengleichung in Koordinatenfo rm" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Eq uation(g,\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(!\"\"\"\"\"% \"yG!\"$%\"xG\"\"#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 183 " Der \+ Plotbefehl mit geom3d ist sehr einfach: Es gen\374gt schon ein \"> dra w(g); um einen Plot zu bekommen. Mit den folgenden Erg\344nzungen kann man den Plot dann noch anschaulicher machen:" }{MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "draw(g,scaling=constrained,axes=nor mal);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURV ESG6%7U7$$\"#5\"\"!$\"++++]:!\")7$$\"+++++'*!\"*$\"++++!\\\"F-7$$\"+++ ++#*F1$\"++++I9F-7$$\"+++++))F1$\"++++q8F-7$$\"+++++%)F1$\"++++58F-7$$ \"\")F*$\"++++]7F-7$$\"+++++wF1$\"++++!>\"F-7$$\"+++++sF1$\"++++I6F-7$ $\"+++++oF1$\"++++q5F-7$$\"+++++kF1$\"++++55F-7$$\"\"'F*$\"+++++&*F17$ $\"+++++cF1$\"+++++*)F17$$\"+++++_F1$\"+++++$)F17$$\"+++++[F1$\"+++++x F17$$\"+++++WF1$\"+++++rF17$$\"\"%F*$\"+++++lF17$$\"+++++OF1$\"+++++fF 17$$\"+++++KF1$\"+++++`F17$$\"+++++GF1$\"+++++ZF17$$\"+++++CF1$\"+++++ TF17$$\"\"#F*$\"+++++NF17$$\"+++++;F1$\"+++++HF17$$\"+++++7F1$\"+++++B F17$$\"+++++!)!#5$\"+++++F17$$!\"#F*$!+++++DF17$$!+++++CF1$!+++++JF17$$!+++ ++GF1$!+++++PF17$$!+++++KF1$!+++++VF17$$!+++++OF1$!+++++\\F17$$!\"%F*$ !+++++bF17$$!+++++WF1$!+++++hF17$$!+++++[F1$!+++++nF17$$!+++++_F1$!+++ ++tF17$$!+++++cF1$!+++++zF17$$!\"'F*$!+++++&)F17$$!+++++kF1$!+++++\"*F 17$$!+++++oF1$!+++++(*F17$$!+++++sF1$!++++I5F-7$$!+++++wF1$!++++!4\"F- 7$$F-F*$!++++]6F-7$$!+++++%)F1$!++++57F-7$$!+++++))F1$!++++q7F-7$$!+++ ++#*F1$!++++I8F-7$$!+++++'*F1$!++++!R\"F-7$$FjrF*$!++++]9F--%&STYLEG6# %%LINEG-%'COLOURG6&%$RGBG$\"*++++\"F-F*F*-%*AXESSTYLEG6#%'NORMALG-%(SC ALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F][lF(Fe\\l" 1 2 0 1 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 " Aufstellen einer weiteren Geraden - diesmal Gerade h durch die Punkt e A,C:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "line(h,[A,C]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"hG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "detail(g);" }}{PARA 6 "" 1 " " {TEXT -1 24 " name of the object: g" }}{PARA 6 "" 1 "" {TEXT -1 29 " form of the object: line2d" }}{PARA 6 "" 1 "" {TEXT -1 39 " e quation of the line: -1-3*y+2*x = 0" }}{PARA 6 "" 1 "" {TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "draw(h,scaling=constrained ,axes=normal);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 " 6&-%'CURVESG6%7U7$$\"#5\"\"!$!+++++M!\")7$$\"+++++'*!\"*$!++++SKF-7$$ \"+++++#*F1$!++++!3$F-7$$\"+++++))F1$!++++?HF-7$$\"+++++%)F1$!++++gFF- 7$$\"\")F*$!+++++EF-7$$\"+++++wF1$!++++SCF-7$$\"+++++sF1$!++++!G#F-7$$ \"+++++oF1$!++++?@F-7$$\"+++++kF1$!++++g>F-7$$\"\"'F*$!+++++=F-7$$\"++ +++cF1$!++++S;F-7$$\"+++++_F1$!++++![\"F-7$$\"+++++[F1$!++++?8F-7$$\"+ ++++WF1$!++++g6F-7$$\"\"%F*$!+++++5F-7$$\"+++++OF1$!+++++%)F17$$\"++++ +KF1$!+++++oF17$$\"+++++GF1$!+++++_F17$$\"+++++CF1$!+++++OF17$$\"\"#F* $!+++++?F17$$\"+++++;F1$!+++++S!#57$$\"+++++7F1Fdr7$$\"+++++!)FbrF_q7$ $\"+++++SFbrF[p7$F*$\"+++++gF17$F`rFI7$$!+++++!)FbrF57$$!+++++7F1$\"++ ++!3\"F-7$$!+++++;F1$\"++++S7F-7$$!\"#F*$\"+++++9F-7$$!+++++CF1$\"++++ g:F-7$$!+++++GF1$\"++++? " 0 "" {MPLTEXT 1 0 44 "draw([g,h],scaling=constrained,axes=normal);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6%7U7$$\"#5\"\"!$\"+ +++]:!\")7$$\"+++++'*!\"*$\"++++!\\\"F-7$$\"+++++#*F1$\"++++I9F-7$$\"+ ++++))F1$\"++++q8F-7$$\"+++++%)F1$\"++++58F-7$$\"\")F*$\"++++]7F-7$$\" +++++wF1$\"++++!>\"F-7$$\"+++++sF1$\"++++I6F-7$$\"+++++oF1$\"++++q5F-7 $$\"+++++kF1$\"++++55F-7$$\"\"'F*$\"+++++&*F17$$\"+++++cF1$\"+++++*)F1 7$$\"+++++_F1$\"+++++$)F17$$\"+++++[F1$\"+++++xF17$$\"+++++WF1$\"+++++ rF17$$\"\"%F*$\"+++++lF17$$\"+++++OF1$\"+++++fF17$$\"+++++KF1$\"+++++` F17$$\"+++++GF1$\"+++++ZF17$$\"+++++CF1$\"+++++TF17$$\"\"#F*$\"+++++NF 17$$\"+++++;F1$\"+++++HF17$$\"+++++7F1$\"+++++BF17$$\"+++++!)!#5$\"+++ ++F17 $$!\"#F*$!+++++DF17$$!+++++CF1$!+++++JF17$$!+++++GF1$!+++++PF17$$!++++ +KF1$!+++++VF17$$!+++++OF1$!+++++\\F17$$!\"%F*$!+++++bF17$$!+++++WF1$! +++++hF17$$!+++++[F1$!+++++nF17$$!+++++_F1$!+++++tF17$$!+++++cF1$!++++ +zF17$$!\"'F*$!+++++&)F17$$!+++++kF1$!+++++\"*F17$$!+++++oF1$!+++++(*F 17$$!+++++sF1$!++++I5F-7$$!+++++wF1$!++++!4\"F-7$$F-F*$!++++]6F-7$$!++ +++%)F1$!++++57F-7$$!+++++))F1$!++++q7F-7$$!+++++#*F1$!++++I8F-7$$!+++ ++'*F1$!++++!R\"F-7$$FjrF*$!++++]9F--%&STYLEG6#%%LINEG-%'COLOURG6&%$RG BG$\"*++++\"F-F*F*-F$6%7U7$F($!+++++MF-7$F/$!++++SKF-7$F5$!++++!3$F-7$ F:$!++++?HF-7$F?$!++++gFF-7$FD$!+++++EF-7$FI$!++++SCF-7$FN$!++++!G#F-7 $FS$!++++?@F-7$FX$!++++g>F-7$Fgn$!+++++=F-7$F\\o$!++++S;F-7$Fao$!++++! [\"F-7$Ffo$!++++?8F-7$F[p$!++++g6F-7$F`p$FisF-7$FepFiy7$FjpFfx7$F_qFbw 7$FdqF^v7$Fiq$!+++++?F17$F^rFfs7$FcrFcr7$FhrF_q7$F^sF[p7$F*$\"+++++gF1 7$FfsFI7$F[tF57$F`t$\"++++!3\"F-7$Fet$\"++++S7F-7$Fjt$\"+++++9F-7$F_u$ \"++++g:F-7$Fdu$\"++++? " 0 "" {MPLTEXT 1 0 21 "intersection(SP,g,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#SPG" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 " Anzeigen der Koordinaten der Sch nittpunkte:" }{MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "coordinates(SP);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"\" \"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 127 " Einzeichnen der beiden G eraden g und h, der Punkte A, B, C und des Schnittpunktes SP (der hier mit dem Punkt A \374bereinstimmt):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "draw([g,h,A,B,C,SP],scaling=constra ined,axes=normal);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6+-%'POINTSG6%7$$\"\"\"\"\"!$\"\"#F)-%&STYLEG6#%%LINEG-%' COLOURG6&%$RGBG$\"*++++\"!\")F)F)-F$6%7$$\"\"$F)$\"\"&F)F,F0-F$6%7$F*$ !\"#F)F,F0F#-%'CURVESG6%7U7$$\"#5F)$\"++++]:F67$$\"+++++'*!\"*$\"++++! \\\"F67$$\"+++++#*FO$\"++++I9F67$$\"+++++))FO$\"++++q8F67$$\"+++++%)FO $\"++++58F67$$\"\")F)$\"++++]7F67$$\"+++++wFO$\"++++!>\"F67$$\"+++++sF O$\"++++I6F67$$\"+++++oFO$\"++++q5F67$$\"+++++kFO$\"++++55F67$$\"\"'F) $\"+++++&*FO7$$\"+++++cFO$\"+++++*)FO7$$\"+++++_FO$\"+++++$)FO7$$\"+++ ++[FO$\"+++++xFO7$$\"+++++WFO$\"+++++rFO7$$\"\"%F)$\"+++++lFO7$$\"++++ +OFO$\"+++++fFO7$$\"+++++KFO$\"+++++`FO7$$\"+++++GFO$\"+++++ZFO7$$\"++ +++CFO$\"+++++TFO7$F*$\"+++++NFO7$$\"+++++;FO$\"+++++HFO7$$\"+++++7FO$ \"+++++BFO7$$\"+++++!)!#5$\"+++++FO7$FA$!+++++DFO7$$!+++++CFO$!+++++JFO7$$! +++++GFO$!+++++PFO7$$!+++++KFO$!+++++VFO7$$!+++++OFO$!+++++\\FO7$$!\"% F)$!+++++bFO7$$!+++++WFO$!+++++hFO7$$!+++++[FO$!+++++nFO7$$!+++++_FO$! +++++tFO7$$!+++++cFO$!+++++zFO7$$!\"'F)$!+++++&)FO7$$!+++++kFO$!+++++ \"*FO7$$!+++++oFO$!+++++(*FO7$$!+++++sFO$!++++I5F67$$!+++++wFO$!++++!4 \"F67$$F6F)$!++++]6F67$$!+++++%)FO$!++++57F67$$!+++++))FO$!++++q7F67$$ !+++++#*FO$!++++I8F67$$!+++++'*FO$!++++!R\"F67$$FftF)$!++++]9F6F,F0-FD 6%7U7$FH$!+++++MF67$FM$!++++SKF67$FS$!++++!3$F67$FX$!++++?HF67$Fgn$!++ ++gFF67$F\\o$!+++++EF67$Fao$!++++SCF67$Ffo$!++++!G#F67$F[p$!++++?@F67$ F`p$!++++g>F67$Fep$!+++++=F67$Fjp$!++++S;F67$F_q$!++++![\"F67$Fdq$!+++ +?8F67$Fiq$!++++g6F67$F^r$FeuF67$FcrFc[l7$FhrF`z7$F]sF\\y7$FbsFhw7$F*$ !+++++?FO7$FjsFbu7$F_tF_t7$FdtF]s7$FjtFiq7$F)$\"+++++gFO7$FbuFao7$FguF S7$F\\v$\"++++!3\"F67$Fav$\"++++S7F67$FA$\"+++++9F67$Fiv$\"++++g:F67$F ^w$\"++++? " 0 "" {MPLTEXT 1 0 14 "distance(A,B) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"#8\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "distance(A,C);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"#<\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "distance(B,C);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#*$-%%sqrtG6#\"#]\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 " Die \+ Entfernung der Punkte kann man sich mit segment veranschaulichen:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "segment(AB, [A,B]), segment( BC, [B,C]), segment(CA, [C,A]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " draw(\{AB,BC,CA,A,B,C\},symbol=circle,axes=normal,thickness=1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%%#ABG%#BCG%#CAG" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6+-%'POINTSG6'7$$\"\"\"\"\"!$\"\"#F )-%&STYLEG6#%%LINEG-%'COLOURG6&%$RGBG$\"*++++\"!\")F)F)-%*THICKNESSG6# F(-%'SYMBOLG6#%'CIRCLEG-F$6'7$$\"\"$F)$\"\"&F)F,F0F7F:-F$6'7$F*$!\"#F) F,F0F7F:-%'CURVESG6'7$F&F@F,F0F7F:-FK6'7$FGF&F,F0F7F:-FK6'7$F@FGF,F0F7 F:-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F'FA;F HFC" 1 2 0 1 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Geraden 3D" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 " F\374r Geraden in 3D wird n icht with(geometry) ge\366ffnet, sondern with(geom3d), was auf dem Cas siopeia _w(geom3d) entspricht." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(geo m3d):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Das Definieren der Punk te funktioniert genauso wie bei 2D, nur dass eben die y-Komponente noc h hinzukommt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "point(A,1, 2,3),point(B,3,5,4),point(C,2,-2,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6%%\"AG%\"BG%\"CG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 " Die Einzel heiten zu den jeweiligen Punkten (hier exemplarisch mit A) kann man si ch wieder mit detail ausgeben lassen." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "detail(A);" }}{PARA 6 "" 1 "" {TEXT -1 24 " name of the object: A" }}{PARA 6 "" 1 "" {TEXT -1 30 " form of the object: point3d" }}{PARA 6 "" 1 "" {TEXT -1 38 " coor dinates of the point: [1, 2, 3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "draw(\{A,B,C\},symbol=circle,scaling=constrained,axes=normal,t hickness=4);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6( -%'POINTSG6%7%$\"\"\"\"\"!$\"\"#F)$\"\"$F)-%*THICKNESSG6#\"\"%-%'SYMBO LG6#%'CIRCLEG-F$6%7%F,$\"\"&F)$F1F)F.F2-F$6%7%F*$!\"#F)$\"\"(F)F.F2-%( SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%'NORMALG-%%VIEWG6%;F'F,;F?F9;F ,FA" 1 2 0 1 0 2 1 1 4 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "line(g,[A,B]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"gG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "det ail(g);" }}{PARA 6 "" 1 "" {TEXT -1 24 " name of the object: g" }} {PARA 6 "" 1 "" {TEXT -1 29 " form of the object: line3d" }}{PARA 6 "" 1 "" {TEXT -1 91 " assume that the name of the parameter \+ in the parametric equations is _t " }}{PARA 6 "" 1 "" {TEXT -1 54 " assume that the name of the axis are _x, _y, and _z" }} {PARA 6 "" 1 "" {TEXT -1 62 " equation of the line: [_x = 1+2*_t, _y = 2+3*_t, _z = 3+_t]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Eq uation(g,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,&\"\"\"F%%\"tG\"\"# ,&F'F%F&\"\"$,&F)F%F&F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " draw(g,scaling=constrained,axes=normal,color=blue);" }}{PARA 13 "" 1 " " {GLPLOT3D 400 300 300 {PLOTDATA 3 "6&-%'CURVESG6$7$7%$!+S[AXV!\"*$!+ es$y,'F*$\"*\"e(QF$F*7%$\"+S[AXjF*$\"+EPy,5!\")$\"+>ChscF*-%'COLOURG6& %$RGBG\"\"!F;$\"*++++\"F4-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%'N ORMALG-%%VIEWG6%;F(F0;F+F2;F-F5" 1 2 0 1 0 2 1 1 4 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "li ne(h,[A,C]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"hG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "detail(h);" }}{PARA 6 "" 1 "" {TEXT -1 24 " name of the object: h" }}{PARA 6 "" 1 "" {TEXT -1 29 " form of the object: line3d" }}{PARA 6 "" 1 "" {TEXT -1 91 " assum e that the name of the parameter in the parametric equ ations is _t " }}{PARA 6 "" 1 "" {TEXT -1 54 " assume that the name \+ of the axis are _x, _y, and _z" }}{PARA 6 "" 1 "" {TEXT -1 62 " equa tion of the line: [_x = 1+_t, _y = 2-4*_t, _z = 3+4*_t]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "draw(h,scaling=constrained,axes=nor mal,color=red);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6&-%'CURVESG6$7$7%$!*glxS(!\"*$\"+Qi5j*)F*$!+Qi5jRF*7%$\"+glxSFF*$!+Q i5j\\F*$\"+Qi5j**F*-%'COLOURG6&%$RGBG$\"*++++\"!\")\"\"!F=-%(SCALINGG6 #%,CONSTRAINEDG-%*AXESSTYLEG6#%'NORMALG-%%VIEWG6%;F(F0;F2F+;F-F4" 1 2 0 1 0 2 1 1 4 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 87 "draw(\{g,h,A,B,C\},symbol=circle,scaling=const rained,axes=normal,thickness=1,color=blue);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6*-%'POINTSG6%7%$\"\"\"\"\"!$\"\"#F )$\"\"$F)-%*THICKNESSG6#F(-%'SYMBOLG6#%'CIRCLEG-F$6%7%F,$\"\"&F)$\"\"% F)F.F1-F$6%7%F*$!\"#F)$\"\"(F)F.F1-%'CURVESG6&7$7%$\"+)******\\#!#5$\" +++++]!\"*F)7%$\"+++++IFM$!+)*******fFM$\"+++++6!\")F.F1-%'COLOURG6&%$ RGBGF)F)$\"*++++\"FU-FD6&7$7%$!+-+++]FM$!+++++qFMF)7%$\"+,+++ " 0 "" {MPLTEXT 1 0 21 "intersection (SP,g,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#SPG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "coordinates(SP);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 " Anmerkung: Mit dem Befehl coordinates( ) kann man sich auch die \+ Koordinaten von A,B oder C nochmals ausgeben lassen: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "coordinates(A);" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 15 "coordinates(B);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "coordinates(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"\"\"#\" \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"$\"\"&\"\"%" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7%\"\"#!\"#\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 200 " Mit distance kann man sich die geringste Entfernung der beiden Geraden voneinander ausrechnen - hier logischerweise auf Grund der Tatsache, dass sich g und ha schneiden - ist der Abstand gleich N ull." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "distance(g,h);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 " Berechnen der Winkel, den die beiden Geraden bilden mit \+ dem Befehl FindAngel:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "FindAngle(g,h)*180/Pi; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%'arccosG6#,$*&-%%sqrtG6#\"#9\"\"\"-F+6#\"#LF.#\"\"\"\"#xF. %#PiG!\"\"\"$!=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+--3zt!\")" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 86 " Nun kann man sich die Entfernungen der einzelnen \+ Punkte voneinander ausgeben lassen: " }{MPLTEXT 1 0 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "distance(A,B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"#9\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "distance(C,SP);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6# \"#L\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 180 " Dass dies auch ta ts\344chlich richtig ist, erkennt man, wenn man nach dem Abstand zwisc hen A und dem Schnittpunkt SP fragt: Da m\374sste Null rauskommen, da \+ beide Punkte identisch sind:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dis tance(A,SP);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 202 " Punktprobe mit Hilfe von IsOnObject: Hi er liegt A auf h und auf g, da hier A der Schnittpunkt der beiden Gera den ist. Der Punkt C liegt aber nicht auf der Geraden g: Was uns Maple mit \"false\" mitteilt." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "IsOnObject(A,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "IsOnObject(A,h );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "IsOnObject(C,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 111 "Zur nochmaligen Veranschaulichung k\366nnen die 3 Punkte A,B und C mit segment auch zum Dreieck verbun den werden:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "segment(AB, \+ [A,B]), segment(BC, [B,C]), segment(CA, [C,A]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%#ABG%#BCG%#CAG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "draw(\{AB,BC,CA,A,B,C\},symbol=circle,axes=normal,thickness=1, orientation=[10,70]);" }}{PARA 13 "" 1 "" {GLPLOT3D 255 191 191 {PLOTDATA 3 "6,-%'POINTSG6%7%$\"\"\"\"\"!$\"\"#F)$\"\"$F)-%*THICKNESSG 6#F(-%'SYMBOLG6#%'CIRCLEG-F$6%7%F,$\"\"&F)$\"\"%F)F.F1-F$6%7%F*$!\"#F) $\"\"(F)F.F1-%'CURVESG6%7$F7F>F.F1-FD6%7$F>F&F.F1-FD6%7$F&F7F.F1-%(SCA LINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%'NORMALG-%%VIEWG6%;F'F,;F?F8;F,FA -%+PROJECTIONG6%$\"#5F)$\"#qF)F(" 1 2 0 1 0 2 1 1 4 1 1.000000 70.000000 10.000000 1 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 " Man si eht: Egal ob mit segment (oben) oder mit der herk\366mmlichen Variante (unten): Die Geraden sind die gleichen." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "line(j,[B,C]);draw([g,h,j],scaling=constrained,axes=n ormal,color=blue,orientation=[10,70]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"jG" }}{PARA 13 "" 1 "" {GLPLOT3D 398 298 298 {PLOTDATA 3 "6)- %'CURVESG6$7$7%$!+S[AXV!\"*$!+es$y,'F*$\"*\"e(QF$F*7%$\"+S[AXjF*$\"+EP y,5!\")$\"+>ChscF*-%'COLOURG6&%$RGBG\"\"!F;$\"*++++\"F4-F$6$7$7%$!+T[A XVF*$\"+O**3QBF4$!+O**3Q=F47%$\"+T[AXjF*$!+O**3Q>F4$\"+O**3QCF4F7-F$6$ 7$7%$\"+z*Hg/\"F4$\"+])4As&F4FF7%FB$!+)Qd;k%F4$\"+_uc.EF4F7-%(SCALINGG 6#%,CONSTRAINEDG-%*AXESSTYLEG6#%'NORMALG-%%VIEWG6%;FBFS;FXFU;FFFZ-%+PR OJECTIONG6%$\"#5F;$\"#qF;\"\"\"" 1 2 0 1 0 2 1 1 4 1 1.000000 70.000000 10.000000 1 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "michael.dors ch@gmx.de " }}{PARA 0 "" 0 "" {TEXT -1 21 " milena.preiss@gmx.de" }}}} {MARK "4" 0 }{VIEWOPTS 1 1 0 1 1 1803 }