Curvature and Osculating Circle for a 2D Parametric Curve in GeoGebra

Рет қаралды 1,755

4 жыл бұрын

In this video we use GeoGebra to graph a 2D parametric curve, a point on the curve, and the osculating circle of the curve at the point. We can then animate the point and watch the osculating circle change. In Graphics 2 we add a function that calculates the curvature of the function at the point. Once we're done we can watch the relationship between the curvature of the function and the radius of the osculating circle.
Key things to know: graphing functions, points, sliders, osculating circles, curvature.
This is a topic you might encounter in a Calculus III, Multivariable, or Vector Calculus class, depending on the course name!
You can play around with GeoGebra in your web browser at GeoGebra.org

Пікірлер: 5

@danerferhadi8127 Жыл бұрын

Awesome! You can also do this in 3D space, where you put the oscillating circle onto a plane which is constructed using the tangent point and either the unit tangent vector, the normal vector, or the binormal vector

@danv8718 3 жыл бұрын

Really great demonstration. Your Geogebra videos are the best!

@turksvids 3 жыл бұрын

Thanks so much! I've been so focused on creating videos of my notes for the last half year that I haven't had time to do any fun GeoGebra stuff! Looking forward to getting back to that someday soon... :)

@danv8718 3 жыл бұрын

@@turksvids Thank you for posting! I've learned tons of useful and interesting Geogebra stuff watching your videos.

@nisrinashufah7158 3 жыл бұрын

hi! your demonstration is really helpful for my assignment. but i still confused in the last one. on part calculate the curvature, why my work is always 0 for each v? my vector function is 446.85 cos(0.4759 t)i+446.85 sin(0.4759 t)j. thank you so much. i hope you read this comment