Pappus’ sætning.
Hvis hjørnerne i en sekskant, ABCDEF, ligger skiftevis på to linjer, så vil skæringspunkterne, X, Y og Z, mellem modstående sider i sekskanten ligge på en ret linje.
På figuren kan du flytte på punkterne A, B, C, D, E og F.
Pappus af Alexandria, græsk matematiker (ca 290 - ca 350).
Figure figure = Position [0,0] Size[x,y] Origin[x/3,y/2] Unit x/12 Color "white" Dynamic;
//Axes axes = Color "black";
//Grid grid = Color "blue";
//Units units = Color "black";
Line l1 = Start [-1,3] Dir [1,3] Infinite Size 1.5 Color "black";
Line l2 = Start [-1,3] Dir [1,-4] Infinite Size 1.5 Color "black";
Point A = [-1.5,1] Slider l1 Size 2.5 Color "red";
Point B = [-0.5,0.5] Slider l2 Size 2.5 Color "red";
Point C = [-2,-0.5] Slider l1 Size 2.5 Color "red";
Point D = [0,-1.5] Slider l2 Size 2.5 Color "red";
Point E = [-3,-2.5] Slider l1 Size 2.5 Color "red";
Point F = [-0.2,-0.2] Slider l2 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 X = intersect( A, B, D, E ) Size 2.5 Color "blue";
Point Y = intersect( B, C, E, F ) Size 2.5 Color "blue";
Point Z = intersect( C, D, F, A ) Size 2.5 Color "blue";
Label labX = "X" At X Offset [10,-10] Color "black";
Label labY = "Y" At Y Offset [10,-10] Color "black";
Label labZ = "Z" At Z Offset [10,-10] Color "black";
Line l = Start X Dir Z-X Infinite Size 1.5 Color "blue";