Analytic, Geometric, and Numeric Analysis of the


Douglas B. Meade 
WeiChi Yang 
Video  Sketch Pad 
Geom Expr 
Maple 10 
HTML  

§1  Introduction  
HTML  Geometric Solution of the Original Shrinking Circle Problem  
§2  The Original Shrinking Circle Problem  
HTML  Analytic Solution of the Original Shrinking Circle Problem  
HTML  Numeric Solution of the Original Shrinking Circle Problem (Table 1)  
§3  The Generalized Shrinking Circle Problem  
HTML  Lemma 1  
Derivations and Animations for Other Fixed Curves  
HTML  Ellipse  
HTML  Line  
HTML  Parabola  
Theorem 2  
§4  The Simplest Shrinking Sphere Problems  
HTML  Lemma 4 (including Figure 4)  
§5  The Generalized Shrinking Sphere Problems  
Derivations and Animations for Other Fixed Surfaces  
HTML  Ellipsoid  
HTML  Cone  
HTML  Paraboloid  
§6  Discussion of Numerical Limits and Visualization  
Numerical Difficulties for the Original Shrinking Circle Problem  
HTML  Visualizing the Generalized Shrinking Sphere with Discrete Samples (Figure 5)  
Visualizing the Generalized Shrinking Sphere with Geometric Objects (Figure 6)  
§7  Conclusion  
Icon  Name  Web Address 

Cabri 3D  http://www.cabri.com/  
ClassPad Manager  http://www.classpad.net/  
Geometry Expressions  http://www.geometryexpressions.com/  
Geometer's Sketchpad  http://www.dynamicgeometry.com/  
Maple  http://www.maplesoft.com/  
Mathematica  http://www.wolfram.com/ 