Chapter 3.4, Problem 50E

Given a hexagonal tiling of the plane, such as you mightfind on a kitchen floor, consider the basis of ${ℝ}^2$ consisting of the vectors $\stackrel{\to }{v},\stackrel{\to }{w}$ in the following sketch:

a. Find the coordinate vectors and

Hint: Sketch the coordinate grid defined by the basis $=\left(\stackrel{\to }{v},\stackrel{\to }{w}\right)$ .

b. We are told that $=\left[\begin{array}{l}3\\ 2\end{array}\right]$ . Sketch the point R. Is R a vertex or a center of a tile?

c. We are told that $=\left[\begin{array}{l}17\\ 13\end{array}\right]$ . Is S a center or avertex of a tile?