Connected Sum

Author

Eric W. Weisstein
March 27, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Topology/ConnectedSum.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ConnectedSum.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Graphics by
Todd Rowland
Wolfram Research, Inc.
March 27, 2003

Initialization

<<Graphics`Shapes`

Two Tori

Show[GraphicsArray[{
Graphics3D[{EdgeForm[],Torus[15,5,50,40],
TranslateShape[Torus[15,5,50,40],{50,0,0}]},Boxed->False],
Graphics3D[{EdgeForm[],Torus[15,5,50,40],TranslateShape[RotateShape[RotateShape[Cylinder[3,15,50],0,Pi/2,0],Pi/2,0,0],{25,0,0}],TranslateShape[Torus[15,5,50,40],{50,0,0}]},
Boxed->False]
}]]

Show[GraphicsArray[{
Graphics3D[{EdgeForm[],Torus[15,5,50,40],TranslateShape[Torus[15,5,50,40],{0,30,0}],TranslateShape[Torus[15,5,50,40],{0,-30,0}],TranslateShape[Torus[15,5,50,40],{50,0,0}],TranslateShape[Torus[15,5,50,40],{80,0,0}]},ViewPoint->{1,1,-2},Boxed->False],
Graphics3D[{EdgeForm[],Torus[15,5,50,40],TranslateShape[Torus[15,5,50,40],{0,30,0}],TranslateShape[Torus[15,5,50,40],{0,-30,0}],TranslateShape[RotateShape[RotateShape[Cylinder[3,15,50],0,Pi/2,0],Pi/2,0,0],{25,0,0}],TranslateShape[Torus[15,5,50,40],{50,0,0}],TranslateShape[Torus[15,5,50,40],{80,0,0}]},ViewPoint->{1,1,-2},Boxed->False]
}]]