Solve part 1 only Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²).1. Find the second fundamental form of o.2. Compute the normal curvature and the geodesic curvature of the circle(t) = (sin t, cos t, 1) on the above paraboloid.

1 Consider the paraboloid parameterized by σu,v=u,v,u2+v2. We have to find the second fundamental…

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Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental form of o.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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Solve part 1 only

Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²).
1. Find the second fundamental form of o.
2. Compute the normal curvature and the geodesic curvature of the circle
(t) = (sin t, cos t, 1) on the above paraboloid.

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