1. Ans:
V=4, E=5, F=3
V-E+F=4-5+3=2
2. Ans
V=7, E=12, F=7
7-12+7=2
V=1, E=0, F=1
1-0+1=2
#1 and # 2 are pretty straightforward. There will be a straightforward problem on the quiz :
(note: in all of the pictures, the numbers in blue count regions, the red dots are vertices, and the numbers in green count edges)
|
1. Ans: |
2. Ans
V=7, E=12, F=7 |
| 3. Kind of a trick problem. Ans: V=1, E=0, F=1 1-0+1=2 |
Now, all of the others are harder: there are things that can go wrong besides just counting stuff incorrectly. Check out these pictures, and decide which you think are correct and why:
4.
5.
6.
#7-9 Answers
7. V+F-E=2 so
V+6-9=2
V-3=2
(add 3 to both sides)
V-3+3=2+3
V=5
8. V+F-E=2 so
V+11-17=2
V-6=2
(add 6 to both sides)
V-6+6=2+6
V=8
9. V+F-E=2 so
V+14-24=2
V-10=2
(add 10 to both sides)
V-10+10=2+103
V=12