Fundamental Mathematics from an Advanced Standpoint

Math 4303

Helmut Knaust, Department of Mathematical Sciences, UTEP, El Paso TX 79968
hknaust@utep.edu

Last Edits: 9/22/09

The Riemann Sphere Model of the Complex Numbers

Manipulate[Graphics3D[{AbsolutePointSize[8],Point[{x,y,0}],Point[{0,0,1}],
Point[{(1/((x^2)+(y^2)+1)) x,(1/((x^2)+(y^2)+1))  y,1-(1/((x^2)+(y^2)+1))} ],{Thick,Line[{{0,0,1},{x,y,0}}]},{Opacity[.8],Sphere[{0,0,1/2},1/2]}},FaceGrids->{{0,0,-1}},FaceGridsStyle->Directive[Red,Thin],Axes->True,AxesLabel->{"x","y","z"},BoxRatios->{4,4,1},ImageSize->600,BaseStyle->{14,Bold},PlotRange->{{-2.1,2.1},{-2.1,2.1},{0,1}}],{x,-2,2},{y,-2,2}]