#### Geometry

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Question

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The square metric. De?ne the distance between two points (x_1, y_1) and (x_2, y_2) in R2

by D((x_1, y_1), (x_2, y_2)) = max{|x_2 ? x_1|,|y_2 ? y_1|}^4

(a) Verify that D is a metric.

(b) Find all points (x, y) in R2 such that D((0,0), (x, y)= 1. Draw a sketch in the cartesian plane