Aristotle's Wheel Paradox

Author

Eric W. Weisstein
June 25, 2012

This notebook downloaded from http://mathworld.wolfram.com/notebooks/RecreationalMath/AristotlesWheelParadox.nb.

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

©2012 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Animation by
Javier H. Ospina H.  
December 9, 2004

Graphic

Animation by Javier H. Ospina H. (December 9, 2004)

V5

movie=With[{rsmall=0.8,rbig=1.6},
Table[Show[Graphics[{
{
GrayLevel[0.5],
Circle[{0,0},rsmall,{-Pi/2,3Pi/2}],
Circle[{2 Pi,0},rsmall,{-Pi/2,3Pi/2}],
Circle[{0,0},rbig,{-Pi/2,3Pi/2}],
Circle[{2 Pi,0},rbig,{-Pi/2,3Pi/2}],
Line[{{0,-rbig},{2 Pi,-rbig}}],
Line[{{0,-rsmall},{2 Pi,-rsmall}}],
Line[{{0,0},{0,-rbig}}],
Line[{{2Pi,0},{2Pi,-rbig}}]
},
{
Blue,
Circle[{t,0},rbig,{3Pi/2-t,3Pi/2}],
Circle[{t,0},rsmall,{3Pi/2-t,3Pi/2}]
},
{Red,Thickness[0.007],
Circle[{t,0},rbig,{-Pi/2,3Pi/2-t}],
Circle[{t,0},rsmall,{-Pi/2,3Pi/2-t}],
Line[{{0,-rbig},{t,-rbig}}],
Line[{{0,-rsmall},{t,-rsmall}}]
},
{Purple,
Line[{{t,0},{rbig Cos[-t-Pi/2]+t,rbig Sin[-t-Pi/2]}}]
}
},
PlotRange->{{-rbig-0.1,2 Pi rbig-rbig},{-rbig-0.5,rbig+0.5}},AspectRatio->Automatic
]],{t,0, 2 Pi,Pi/24}]
];

<<Utilities`GIF`;

Export[gifs<>"AristotlesWheel.gif",movie]//Timing

V6

GraphicsGrid[Partition[movie[[1;;49;;6]],3],Spacings->{60,50}]