Extreme points on flattened spheres The equation x2n + y2n
Chapter 12, Problem 52(choose chapter or problem)
Extreme points on flattened spheres The equation x2n + y2n + z2n = 1, where n is a positive integer, describes a flattened sphere. Define the extreme points to be the points on the flattened sphere with a maximum distance from the origin. a. Find all the extreme points on the flattened sphere with n = 2. What is the distance between the extreme points and the origin? b. Find all the extreme points on the flattened sphere for integers n 7 2. What is the distance between the extreme points and the origin? c. Give the location of the extreme points in the limit as nS _. What is the limiting distance between the extreme points and the origin as nS _?
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