Explore BrainMass
Share

Explore BrainMass

    Gaussian Curvature

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let f(x,y) be an infinitely differentiable function. Suppose that

    a. f(0,0) = 0
    b. f_x(0,0) = 0 and f_y(0,0) = 0.

    Consider the surface z = f(x,y). Show that K(0,0) = f_xx(0,0) f_yy(0,0) - f_xy(0,0)^2.

    © BrainMass Inc. brainmass.com October 10, 2019, 3:40 am ad1c9bdddf
    https://brainmass.com/math/curves/gaussian-curvature-429703

    Solution Preview

    For a general surface of the form z = f(x,y) where f is infinitely differentiable, the Gaussian curvature at the point (x0,y0,f(x0,y0)) ...

    Solution Summary

    We derive a formula for the Gaussian curvature of a particular type of surface at a particular point.

    $2.19