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Transcript

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

A plane curve has all points in 3D that lie on a single plane, such as a flat sheet or cylinder.

YouTube - Notes - Playlist - Vector Functions playlist

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

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