3D Curvature Example: Exponential Spiral


The "spiral" r(t)=< e-t cos(t), e-t sin(t), e-t >,
0 ≤ t ≤ 2π
.
  • Yellow: Osculating Circle

Move the mouse pointer over the picture to begin the animation. It repeats in an endless loop. You can use the following controls:

  • Click+Drag: rotate the image
  • Shift+Click+Drag Up/Down: zoom in/out
  • Home: reset the image
  • Double Click: stop/restart the animation

Question: why does the motion slow down so much as the particle approaches the bottom? Will it ever reach the bottom?


Created using Mathematica and LiveGraphics3D.

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