Brianchons sætning.
Hvis en sekskant, ABCDEF, er omskrevet et keglesnit (på figuren en ellipse), så vil diagonalerne AD, BE og CF skæres i et punkt. Du kan ændre på sekskanten ved at flytte dens røringspunkter med ellipsen.
Charles Julien Brianchon, fransk matematiker (1783-1864)
Figure figure = Position [0,0] Size[x,y] Origin[x/2,y/2] Unit x/12 Color "white";
//Axes axes = Color "black";
//Grid grid = Color "blue";
//Units units = Color "black";
Variable a = 5;
Variable b = 2.5;
Ellipse ellipse = Center [0,0] Axes [a,b] Size 1.5 Color "black";
Point P1 = [5,0] Slider ellipse Size 2.5 Color "black";
Point P2 = [3,2.5] Slider ellipse Size 2.5 Color "black";
Point P3 = [-3,2.5] Slider ellipse Size 2.5 Color "black";
Point P4 = [-5,0] Slider ellipse Size 2.5 Color "black";
Point P5 = [-3,-2.5] Slider ellipse Size 2.5 Color "black";
Point P6 = [3,-2.5] Slider ellipse Size 2.5 Color "black";
Sequence ellipse ( P1 P2 P3 P4 P5 P6 );
Variable retn1 = [ -a/b*P1:1, b/a*P1:0 ];
Variable retn2 = [ -a/b*P2:1, b/a*P2:0 ];
Variable retn3 = [ -a/b*P3:1, b/a*P3:0 ];
Variable retn4 = [ -a/b*P4:1, b/a*P4:0 ];
Variable retn5 = [ -a/b*P5:1, b/a*P5:0 ];
Variable retn6 = [ -a/b*P6:1, b/a*P6:0 ];
Point A = intersect( P1, P1 + retn1, P2, P2 + retn2 ) Size 2.5 Color "red";
Point B = intersect( P2, P2 + retn2, P3, P3 + retn3 ) Size 2.5 Color "red";
Point C = intersect( P3, P3 + retn3, P4, P4 + retn4 ) Size 2.5 Color "red";
Point D = intersect( P4, P4 + retn4, P5, P5 + retn5 ) Size 2.5 Color "red";
Point E = intersect( P5, P5 + retn5, P6, P6 + retn6 ) Size 2.5 Color "red";
Point F = intersect( P6, P6 + retn6, P1, P1 + retn1 ) 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 l1 = Start A Dir B-A Size 1.5 Color "red";
Line l2 = Start B Dir C-B Size 1.5 Color "red";
Line l3 = Start C Dir D-C Size 1.5 Color "red";
Line l4 = Start D Dir E-D Size 1.5 Color "red";
Line l5 = Start E Dir F-E Size 1.5 Color "red";
Line l6 = Start F Dir A-F Size 1.5 Color "red";
Line AD = Start A Dir D-A Size 1.5 Color "blue";
Line BE = Start B Dir E-B Size 1.5 Color "blue";
Line CF = Start C Dir F-C Size 1.5 Color "blue";