Example 7: Using Computers (GeoGebra) to Draw Space Curves

In this video I graph out several complicated space curves using GeoGebra's amazing 3D graphing calculator. These curves are the toroidal spiral, trefoil knot, and a twisted cubic. I illustrate the importance of perspective when viewing these three dimensional curves, by graphing the projections along each major coordinate plane. I also show that we can better visualize space curves by graphing them on 3D surfaces. For example, the twisted cubic is just the intersection curve between a parabolic and cubic cylinder!

#math #3D #spacecurves #GeoGebra #calculator

Timestamps

• Example 7: Space curves are more difficult to draw than plane curves: 0:00
• Toroidal spiral: 0:31
• Trefoil knot: 1:06
• Graphing the Trefoil knot and Toroidal spiral in GeoGebra: https://www.geogebra.org/calculator/gyfv87f2 1:33
• Example 7: Twisted Cubic: 3:13
  • Views of the Twisted Cubic: 7:03
  • Twisted Cubic in GeoGebra: https://www.geogebra.org/calculator/vxv5heat 7:28
• Visualizing Space Curves on Surfaces: 8:37
  • Twisted cubic on a parabolic cylinder: 9:46
  • Graphing Twisted Cubic on the intersection of two cylinders in GeoGebra: 11:18

Notes and playlists

• Summary: @mes/re-leothreads-2c8vbhp72
• Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GwdMY-E9_4LsmYmO-IxcoX
• Notes: @mes/omhbcxkw
• Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .

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