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

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mes4.5 K18 days ago2 min read

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