APPLETS | Description |
Geodesics on the Earth | This applet allows you to pick two locations on a map of Earth, and then compare the shortest path on the map to the shortest path on a sphere. |
Gaussian Curvature | This is a geogebra applet with a single slider controlling the curvature of a cylindrical-type surface, as well as images to help explain why the curvature will possess the sign it does. |
Map Projection Transitions | One can cycle through various map projections and actively affect the orientation of the globe to see how strange the distortions of maps can become. |
Hyperboloid Geodesics | An interactive Wolfram demo that shows the geodesics on a hyperboloid, which has negative curvature. |
Cube Geodesics | This applet shows that you can understand the shortest path between two points on a cube by instead looking at its net. I plan to use this to illustrate multiple facets of curvature. |
APPLET COLLECTIONS | Description |
Math Insight | A massive library of interactive applets, with particularly nice visualizations for multivariable calculus topics! |
PhET | University of Colorado Boulder website where you can find 90 applets that apply to a variety of K-12 STEM topics. |
Rossman/Chance Applet Collection | A collection of statistics related applets. They are minimalist in their design but effectively convey information. |
Falstad Physics Applets | A lot of physics based applets. They run really well in-browser and cover a wide range of topics in a variety of ways. I appreciate how responsive the applets are to changes in the parameters, many applets take longer. |
3 Dimensional Space | This website is pertinent to my subject of interest, as you can fly through a variety of fully rendered 3D curved geometries! It does hog up quite a bit of memory, however... |
OTHER RESOURCES | Description |
Discrete Differential Geometry | This youtube video by Keenan Crane explains curvature in a way that I find EXTREMELY helpful and hope it becomes more widespread. |
Intrinsic Curvature and Singularities | This video by Eugene Khutoryansky clearly articulates how we measure curvature by parallel transport along a loop. It also illustrates principle curvatures and singularities. |
Non-euclidean virtual reality | Here Henry Segerman shows an interactive VR hyperbolic space, where he shows you have to turn 90 degrees 5 times to get back to where you started! |
Making of SHRINKING PLANET | While this video does not directly pertain to curvature, it acts as an excellent video to show how the straight lines on any surface require no turning. Namely, turning a steering wheel. |
The History of Non-Euclidean Geometry | This is the final in a series documenting the history of non-euclidean geometry. Useful for contextualizing the topic in a clear way with motivations and intuition. |