## 311 – HW5

March 31, 2015

(I am counting as HW3 the homework exercises supervised by Sam Coskey during the two weeks following Isabel’s birth, and as HW4 the two written exercises assigned by Sam that I collected on March 17.)

This exercise is due April 7 at the beginning of lecture.

Provide a proof verifying that the function $d:\mathbb R^2\times\mathbb R^2\to\mathbb R$ given by

$d((x,y),(z,w))=\sqrt{2(x-z)^2+2(y-w)^2-3(x-z)(y-w)}$

is a distance function.