For a surface in three dimension the focal surface, surface of centers or evolute is formed by taking the centers of the , which are the tangential spheres whose radii are the reciprocals of one of the principal curvatures at the point of tangency. Equivalently it is the surface formed by the centers of the circles which osculate the curvature lines. As the principal curvatures are the eigenvalues of the second fundamental form, there are two at each point, and these give rise to two points of the focal surface on each normal direction to the surface. Away from umbilical points, these two points of the focal surface are distinct; at umbilical points the two sheets come together. When the surface has a ridge the focal surface has a cuspidal edge, three such edges pass through an elliptical umbilic and only one through a hyperbolic umbilic. At points where the Gaussian curvature is zero, one sheet of the focal surface will have a point at infinity corresponding to the zero principal curvature. If is a point of the given surface, the unit normal and the principal curvatures at , then and are the corresponding two points of the focal surface. (Wikipedia).
This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
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From playlist Surface Area and Volume
From playlist Surface integrals
From playlist Surface integrals
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This video is about finding the Surface Area of Prisms and Pyramids
From playlist Surface Area and Volume
Light and Optics 5_1 Refractive Surfaces
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From playlist Physics - Light and Optics
MATH331: Riemann Surfaces - part 1
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From playlist The Riemann Sphere
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From playlist Surface integrals
This video covers Section 25.4 of Cutnell & Johnson Physics 10e, by David Young and Shane Stadler, published by John Wiley and Sons. The lecture is part of the course General Physics - Life Sciences I and II, taught by Dr. Boyd F. Edwards at Utah State University. This video was produced
From playlist Lecture 25A. The Reflection of Light: Mirrors
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From playlist optics
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From playlist Jean-Morlet Chair - Pollicott/Vaienti
Lec 8 | MIT 2.71 Optics, Spring 2009
Lecture 8: Telescopes; aberrations: chromatic, spherical, and coma Instructor: George Barbastathis, Colin Sheppard, Se Baek Oh View the complete course: http://ocw.mit.edu/2-71S09 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at htt
From playlist MIT 2.71 Optics, Spring 2009
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Don’t Memorise brings learning to life through its captivating educational videos. To Know More, visit https://infinitylearn.com/surge/study-materials/ncert-solutions/class-10/science/chapter-10-light-reflection-and-refraction/. ✅ Please Join Our Telegram Channel ►https://t.me/InfinityLea
From playlist Board Brahmastra || CBSE Class 10 Crash Course
Lec 7 | MIT 2.71 Optics, Spring 2009
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From playlist MIT 2.71 Optics, Spring 2009
Mr. H explains the difference between a converging and diverging lens in terms of their shape and the manner in which they refract light. Numerous examples, illustrations, and animations assist in the explanations. You can find more information that supports this video on our website:
From playlist Refraction and Lenses
UCI Physics 3C: Basic Physics III (Fall 2013) Lec 11. Basic Physics III View the complete course: http://ocw.uci.edu/courses/physics_3c_basic_physics_iii.html Instructor: Michael Smy, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw
From playlist Physics 3C: Basic Physics III
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From playlist Photolithography
Lec 9 | MIT 2.71 Optics, Spring 2009
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From playlist MIT 2.71 Optics, Spring 2009
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From playlist Natural Sciences