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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #30 · Multivariable Calculus · Gradient & optimization

In three dimensions, Steiner minimizes the total distance … from four points

These problems minimize the Steiner distance $f = d_{1} + d_{2} + d_{3}$ and related functions. A computer is needed for 33 and.

In three dimensions, Steiner minimizes the total distance $f (x, y, z) = d_{1} + d_{2} + d_{3} + d_{4}$ from four points. Show that grad $d_{1}$ is still a unit vector (in which direction)? At what angles do four unit vectors add to zero?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #30

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