Pascals sætning.
Hvis en sekskant, ABCDEF, er indskrevet i et keglesnit (på figuren en ellipse), så vil skæringspunkterne, R, S og T, for de modstående sider ligge på en ret linje.
På figuren kan du flytte punkterne A, B, C, D, E og F.
Blaise Pascal, fransk matematiker og filosof (1623-1662).
Figure figure = Position [0,0] Size[x,y] Origin[x/2,y/2] Unit x/12 Color "white" Dynamic;
//Axes axes = Color "black";
//Grid grid = Color "blue";
//Units units = Color "black";
Variable a = 5;
Variable b = 3;
Ellipse ellipse = Center [0,0] Axes [a,b] Size 1.5 Color "black";
Point A = [1,3] Slider ellipse Size 2.5 Color "red";
Point B = [4,-2] Slider ellipse Size 2.5 Color "red";
Point C = [-3,2] Slider ellipse Size 2.5 Color "red";
Point D = [1.5,-3] Slider ellipse Size 2.5 Color "red";
Point E = [3,2.5] Slider ellipse Size 2.5 Color "red";
Point F = [-2,-2.5] Slider ellipse Size 2.5 Color "red";
Label labA = "A" At A Offset [10,-10] Color "black";
Label labB = "B" At B Offset [10,-10] Color "black";
Label labC = "C" At C Offset [10,-10] Color "black";
Label labD = "D" At D Offset [10,-10] Color "black";
Label labE = "E" At E Offset [10,-10] Color "black";
Label labF = "F" At F Offset [10,-10] Color "black";
Line AB1 = Start A Dir B-A Infinite Size 1 Color "gray";
Line BC1 = Start B Dir C-B Infinite Size 1 Color "gray";
Line CD1 = Start C Dir D-C Infinite Size 1 Color "gray";
Line DE1 = Start D Dir E-D Infinite Size 1 Color "gray";
Line EF1 = Start E Dir F-E Infinite Size 1 Color "gray";
Line FA1 = Start F Dir A-F Infinite Size 1 Color "gray";
Line AB = Start A Dir B-A Size 1.5 Color "red";
Line BC = Start B Dir C-B Size 1.5 Color "red";
Line CD = Start C Dir D-C Size 1.5 Color "red";
Line DE = Start D Dir E-D Size 1.5 Color "red";
Line EF = Start E Dir F-E Size 1.5 Color "red";
Line FA = Start F Dir A-F Size 1.5 Color "red";
Point R = intersect( A, B, D, E ) Size 2.5 Color "blue";
Point S = intersect( B, C, E, F ) Size 2.5 Color "blue";
Point T = intersect( C, D, F, A ) Size 2.5 Color "blue";
Label labR = "R" At R Offset [10,-10] Color "black";
Label labS = "S" At S Offset [10,-10] Color "black";
Label labT = "T" At T Offset [10,-10] Color "black";
Line l = Start R Dir T-R Infinite Size 1.5 Color "blue";