mes 3Speak Podcast

Plane Curves as Vector Functions and the Structure of a DNA Helix

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https://3speak.tv/watch?v=mes/urimnmus
In this video I discuss how plane curves can be represented as vector functions, and illustrate an example of a plane curve that spirals upwards into a helix. A plane curve has all points in 3D that lie on a single plane, such as a flat sheet or cylinder. Representing a cylinder as a plane curve obtains a circular spiral that rises upwards as the the parameter t increases. This represents a helix shape. I also recap on the DNA helix, which consists of two linked, parallel, and intertwined helixes. I also recap on RNA, which is typically a single strand helix, as well as the Central Dogma of Molecular Biology, which states:

Information can flow from DNA to/from RNA to protein, but never from protein to RNA or DNA.

#math #vectorfunctions #planecurves #biology #calculus

Timestamps:

  • Plane curves as vector functions: 0:00
  • Parametric equations of a horizontal parabola to vector form: 0:52
  • Recap on standard basis vectors i, j, and k: 2:07
  • Example 4: Vertical Helix: 2:40
    • Projection of the curve onto the x-y plane is a circle: 5:04
    • Vector function spirals upwards a helix along a cylinder: 6:30
    • Better illustration of the helix from my calculus book: 9:30
    • Graphing in GeoGebra 3D graphing calculator: 9:55
    • Recap on the DNA and RNA Helixes: 10:45
      • Central Dogma of Molecular Biology: Information doesn't flow from protein to RNA or DNA: 13:00

        • Notes and playlists:

        • Summary: https://inleo.io/threads/view/mes/re-leothreads-2lfbak842
        • 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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          mes 3Speak PodcastBy Math Easy Solutions