GraphingCalculator 4;
Window 92 126 646 1263;
PaneDivider 332;
FontSizes 16;
BackgroundType 0;
BackgroundColor 10 0 20;
StackPanes 1;
Slider 0 180;
SliderSteps 180;
SliderMoving 1;
SliderDirection -1;
U 0 6.283185307179586;
V 0 6.283185307179586;
4D.X -1 1;
4D.Y -1 1;
4D.Z -1 1;
4D.W -1 1;
4D.Show4DxyPlane 0;
4D.Show4Daxes 0;
4D.Depth 1.7330909743;
4D.View 0.0907044105672264 -0.297266313767348 0.6881249164962376 0.655659628084767 0.298001350577371 -0.4386063133166485 -0.6934883187987625 0.487743425032779 -0.2011332764393695 -0.847976810869295 0.1145226007811978 -0.4768283834324809 0.9287159469218768 -0.01387691774415348 0.1801183635751077 -0.3238078074886469;
Text "Probing the 3-sphere with a rotating sphere
by Guido 'wugi' Wuyts, 2016
http://home.scarlet.be/wugi/qbComplex.html ";
Color 2;
Expr b=2^0.5;
Color 8;
Expr d=n*(2*pi/180);
Text "Rotating a sphere through a 3-sphere,
in the (u,v) plane, i.e. around the (x,y) plane (4D!).
b = radius of 3-sphere = sqrt(2)
d = sphere rotation angle in (u,v) plane
";
Color 6;
Expr vector(x,y,u,v)=vector(b*sin(u)*cos(v),b*sin(u)*sin(v),b*cos(u)*cos(d),b*cos(u)*sin(d));
Expr vector(-2,0,0,0),vector(2,0,0,0);
Expr vector(0,-2,0,0),vector(0,2,0,0);
Color 3;
Expr vector(0,0,0,0),vector(0,0,2,0);
Color 3;
Expr vector(0,0,0,0),vector(0,0,0,2);
Color 6;
Expr vector(0,0,0,0),vector(0,0,2*cos(d),2*sin(d));
Color 6;
Expr vector(0,0,0,0),vector(0,0,-(2*sin(d)),2*cos(d));