3D Curvature Example: Elliptical Helix

The elliptical helix r(t)=< 4 cos(2t), 2 sin(2t), t >,
0 ≤ t ≤ 2π .
  • Red: unit tangent vector, T(t)
  • Green: unit normal vector, N(t)
  • Blue: unit binormal vector, B(t)

  • 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

Created using Mathematica and LiveGraphics3D.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.