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: https://inleo.io/threads/view/mes/re-leothreads-2c8vbhp72
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GwdMY-E9_4LsmYmO-IxcoX
- Notes: https://peakd.com/hive-128780/@mes/omhbcxkw
- Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .
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