The Most Remarkable Theorem: Part III ( Theorema Egregium )

The final part in the series on the Theorema Egregium. The remarkable theorem of Carl F. Gauss.
#artofproblemsolving #theoremaegregium #gauss #gausslaw #gaussiancurvature #intrinsicgeometry
#vectorcalculus #tangentvectors #partialderivatives #firstfundamentalform #secondfundamentalform
#differentialgeometry #curves #surfaces #parametricequations #parametriccurves #parametricsurfaces

[@tombouie]

Thks & An enlightening adventure thru Math Physics (instead of the typical nightmare ;)

[@kilianklaiber6367]

Great content. Thanks a lot.

[@federicopagano6590]

Love the backgrounds ❤❤

[@purplestovekitchen]

Your statement about the eigenvalues being max and min values at 3:50 is only true for 2d vector space (so that there are only two eigenvalues - the max and min). 👍

[@alex1507er]

Your statement of Theorema Egregium is misleading. The Gaussian curvature is determined by the FIRST fundamental form (only).

[@BCarli1395]

Thank you for a very helpful explanation.

[@ToothbrushMan]

The residue is the sum of the angles minus 2pi, not pi.

[@figur3itout307]

Thanks for the feed back. I probably should have clarified that the version I presented was Gauss’ original version which he wrote in his famous paper concerning geodesic triangles specifically. The 2Pi form , if I am not mistaken, was the extension that O. Bonnet made to Gauss for regions bounded by nongeodesic curves, which allow for the extension to compact surfaces and as well as allow for Topological considerations. The so much about Gauss to talk about and not enough time, that much I am certain of. Thanks for being a part of my channel.

[@venkybabu8140]

When you think of time. It is a constant angle contours. So time is seen as the shortest path possible between different points. Even structures take the shape of an egg are more stable. A shape of the sphere is just closer to time though not exact. Even the sun is somewhat like egg shaped though far it looks spherical. They are egg shaped because it has to push through space for linearity of time. No two things have the same frequency. Resonance is always orthogonal.

[@sonarbangla8711]

Is it possible to easily understand twisters?

[@lanimulrepus]

The "Most Remarkable Theorem" gets the most remarkable introduction... Congratulations...

[@LeoniYUG]

Please, would you answer throughly my question: is the Theorema Egregium the foundation of the Levi~Civita calculus?

[@JojiThomas7431]

It is a great video. But I felt like you rushed through this video. Could have been better if you followed a slower pace, even if the video would become quite large.