Intro to Differential Geometry 📐

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In this lecture of differential geometry you will be learning about the curve Astroid,. Taking ahead from the earlier lesson of parameterization, in this lesson explores more about parameterization using the astroid curve. You will learn about vector valued function, the velocity vector and how a particle traces a path around the curve and what is a tangent line. Putting all these things together, you will find some nice visuals along with animations that will make your understanding of this lesson profound.

00:00 - 03:12 - Recap of the earlier lesson
03:13 - 08:35 - What is Astroid curve
08:36 - 10:04 - Astroid curve tracing
10:05 - 12:44 - Quadrants of the Astroid Curve
12:45 - 16:23 - How an Astroid curve is formed
16:24 - 21:49 - What is vector valued function
21:50 - 24:44 - What is velocity vector
24:45 - 28:33 - Velocity vector of an Astroid curve
28:34 - 29:04 - What is tangent line
29:05 - 32:13 - Tangent line, velocity vector and position vector
32:14 - 32:32 - Tangent line equation of a circle
32:33 - 32:36 - What is the equation of tangent line
32:37 - 37:23 - Tangent line of an Astroid curve
37:24 - 37:51 - Conclusion

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