The Analysis of the Unit Circle as a Planar Curve in Differential Geometry.

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[@datamatters8]

I've only watched a few of your videos so far. This lesson was terrific in that it was full of more detailed insights than I ever learned long ago, e.g. higher order derivatives. Thanks.

[@MathTheBeautiful]

Thank you - I'm glad you like it!

[@JonnyMath]

I was just looking at this today while studying kinematics!!! And I was wondering whether placing the velocity vector at the tip of the position vector is "wrong" because it should be at the origin and I got confused!!!😅🤣🤣🤣

[@MathTheBeautiful]

So this was helpful?

[@JonnyMath]

@@MathTheBeautiful Yes thanks!!!

[@JonnyMath]

I also made a video about vector calculus today explaining why the circumference is a function (vector function)😅🤣🤣🤣

[@tomholroyd7519]

If you tie a washer to a string and spin it around, notice that your hand is moving in a small circle. Or probably an ellipse. That movement of the "center" of rotation plays a role in the speed

[@tomholroyd7519]

I enjoy non-Cartesian logic. There's a Cartesian product (called conjunction), but there is also a non-Cartesian product (called fusion or smash product, or just "and") that has some advantages. I wonder about non-Cartesian coordinate systems. What makes it Cartesian?

[@Pluralist]

[@APaleDot]

When you negate the parameter, the orthogonal component of U' flips its direction, but not the parallel component.

[@MathTheBeautiful]

What do you mean - orthogonal to what object?

[@APaleDot]

@@MathTheBeautiful orthogonal to the original line you drew to define γ = 0.

[@waleedmashaqbeh]

I thought the parameterization of the unit circle does not involve angles and transrectal functions!