1 Using graph #1 use Euler’s formula on vertices, rgions and edges to confirm thr number of edges. Count them to be sure.
1 Using graph #1 use Euler’s formula on vertices, rgions and edges to confirm thr number of edges. Count them to be sure.
2. Does graph #1 have an Euler path? Why or why not.? Use Euler’s Criterion.
3. Find the number of permutations of a rectangle. A regular dodecahedron (12 sided)
4.a) List the four rigid motions on the plane
b) What are the three regular tessellations (tilings)of a plane
c) What are the five Platonic solids
5. Starting with a square, construct a golden rectangle. How do you obtain a golden spiral?
6.Find the number of degrees in an angle of a regular dodecagon
7. Given a figure representing an art gallery, use the given procedure to find the number and placement of the guards to protect the gallery
8a..In Figure #1 use an algorithm in the text starting from vertex A to find the shortest path to any other vertex
8b) Use the procedure given in the text to find a minimal spanning tree that connects all the vertices in Figure #1 without having any circuits
9)Carefully state the Pythagorean Theorem, and outline a proof
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