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parabel.zul
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parabel.zul
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window(-1,1,-1,1);
/*
Parabel, Tangente und Brennpunkt.
Wenn Sie x bewegen, bewegt sich der Punkt (x,x^2) und die Tangente
an die Parabel mit. Um zu sehen, daá es sich tats„chlich um die
Tangente handelt, zeichnen Sie die Ortslinie von (x,x^2).
Der Berennpunkt F sammelt tats„chlich die von oben einfallenden
und an der Parabel reflektierten Lichtstrahlen.
*/
"Point_1"(hidden)=point(-0.846914,-0.82716);
"Point_2"(hidden)=point(0.77284,-0.82716);
"Line_1"()=line("Point_1","Point_2");
"x=1"(showname,symbol:cross)=pointon("Line_1",-0.0864198,-0.82716);
"Object_39"(hidden),"Line_9"()=rectangular("Point_1","Line_1");
"x"(color:green,showname)=pointon("Line_1",-0.190123,-0.82716);
"Circle_5"(hidden,color:cyan)=circle("Point_1","x=1");
"y=1"(showname,symbol:cross),"Cut_10"(hidden,color:cyan)=intersection("Line_9","Circle_5");
"Circle_6"(hidden,color:cyan)=circle("Point_1","x");
"Cut_13"(hidden,color:cyan),"Cut_12"(hidden,color:cyan)=intersection("Line_9","Circle_6");
"Line_10"(hidden,color:cyan)=line("x=1","Cut_13");
"Object_49"(hidden,color:cyan),"Line_11"(hidden,color:cyan)=parallel("x","Line_10");
"x^2"(color:green,showname)=intersection("Line_9","Line_11");
"Object_52"(hidden,color:cyan),"Line_12"(hidden,color:cyan)=rectangular("x","Line_1");
"Object_54"(hidden,color:cyan),"Line_13"(hidden,color:cyan)=rectangular("x^2","Line_9");
"(x,x^2)"(color:cyan,showname,symbol:circle)=intersection("Line_12","Line_13");
"Line_14"(hidden,color:brown)=line("Point_1","(x,x^2)");
"Object_58"(hidden,color:brown),"Line_15"(hidden,color:brown)=parallel("x=1","Line_14");
"Cut_16"(hidden,color:brown)=intersection("Line_15","Line_13");
"Object_61"(hidden,color:brown),"Line_16"(hidden,color:brown)=rectangular("Cut_16","Line_13");
"Object_63"(hidden,color:brown),"Circle_7"(hidden,color:brown)=circle3("Cut_16","Point_1","x");
"Cut_18"(hidden,color:brown),"Cut_17"(hidden,color:brown)=intersection("Circle_7","Line_16");
"Circle_8"(hidden,color:brown)=circle("Cut_17","Cut_16");
"Cut_20"(hidden,color:brown),"Cut_19"(hidden,color:brown)=intersection("Line_16","Circle_8");
"Line_17"(color:brown)=line("(x,x^2)","Cut_19");
"Circle_9"(hidden,color:blue)=circle("(x,x^2)","x");
"Cut_22"(hidden,color:blue),"Cut_21"(hidden,color:blue)=intersection("Line_12","Circle_9");
"Ray_1"(color:blue)=ray("(x,x^2)","Cut_22");
"Object_75"(hidden,color:blue),"Line_18"(hidden,color:blue)=rectangular("(x,x^2)","Line_17");
"Object_77"(hidden,color:blue),"Line_19"(hidden,color:blue)=rectangular("Cut_22","Line_18");
"Cut_24"(hidden,color:blue),"Cut_23"(hidden,color:blue)=intersection("Circle_9","Line_19");
"Line_20"(hidden,color:blue)=line("(x,x^2)","Cut_24");
"F"(color:blue,showname,symbol:circle)=intersection("Line_9","Line_20");
"Segment_3"(color:blue)=segment("(x,x^2)","F");
"Cut_27"(hidden,color:pink)=intersection("Line_1","Line_17");
"Circle_10"(hidden,color:pink)=circle("(x,x^2)","Cut_27");
"Cut_29"(hidden,color:pink),"Cut_28"(color:pink)=intersection("Ray_1","Circle_10");
"Cut_31"(hidden,color:pink),"Cut_30"(hidden,color:pink)=intersection("Line_17","Circle_10");
"Angle_2"(color:pink)=angle("Cut_31","(x,x^2)","Cut_29");
"Angle_3"(color:pink)=angle("F","(x,x^2)","Cut_30");