**Homework #5
Due Tuesday, October 27
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**Find all the cube roots of***i*.**Draw any non-convex quadrilateral such that no two sides are the same length. Draw an ``Escher-like'' tiling of the plane by modifying the sides of this quadrilateral in the manner that we discussed in class. You may use Geometer's Sketchpad to do this if you wish.****Explain how you can be absolutely certain that we have found all 21 possible planar clusters. Some suggestions: What are the possible numbers of polygons that can be in a cluster? For each possible number, what are the possible numbers of triangles that can be in a cluster? For each possible number of triangles, what are the possible numbers of squares? Etc.****Consider two points and in space.**- What are the coordinates of the midpoint of the segment ?
- Suppose we wish to divide the segment by a point
*C*such that*AC*:*CB*=3:2. Determine the coordinates of*C*.

**Determine coordinates of the vertices of the polyhedron determined by the space cluster 3-4-3-4. Use Maple to draw it. Print out the result.****Read the article on imaginary numbers and the two articles on tilings that are on reserve in the Education Library.**

- Make good drawings of the possible tilings by planar clusters.
- Find samples of border wallpaper and regular wallpaper with interesting repeating patterns.

Wed Nov 4 12:25:34 EST 1998