Traktrice.
En traktrice fremkommer, når man flytter punktet Q ud ad x-aksen og hele tiden lader P bevæge sig hen mod Q, således at afstanden PQ forbliver den samme. Som professor Jessen sagde: “Forestil Dem en mand, som går langs bredden af en tilfrosset sø, mens han trækker en lille, genstridig hund efter sig.” Du kan starte trækket ved at trykke på “PLAY”.
Figure figure = Position [0,0] Size[x,y] Origin[x/8,y*4/5] Unit x/8 Color "white";
Axes axes = Color "black";
Grid grid = Color "blue";
Units units = Color "black";
Function tractrix( Number x ) = 2*[x-(1-exp(-2*x))/(1+exp(-2*x)),2*exp(-x)/(1+exp(-2*x))];
Timer tid = From 0 To 3 Step 0.01 Tick 25;
RadioButton playbutton = Text [ "Play"; "Stop" ] Action [ start tid; stop tid ]
Position [500,20] Size [80,25];
PushButton resetbutton = Text "Rewind" Action reset tid, reset playbutton Position [500,60] Size [80,25];
Point P = tractrix(tid) Size 2.5 Color "red";
Point Q = 2*[tid,0] Size 2.5 Color "blue";
Label P_label = "P" At P Offset [10,0] Color "black";
Label Q_label = "Q" At Q Offset [10,0] Color "black";
Line PQ = Start P Dir Q-P Size 1.5 Color "blue";
ParametricCurve trak = tractrix(t) From -2 To 6 Size 0.5 Color "gray";
ParametricCurve trak1 = tractrix(t) From 0 To tid Size 1.5 Color "red";