# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.08

## Topology

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## 2. NODES AND NETWORKS

- (a) Look at figure 23. There are four paths from the point B. One leads to A; where do the others lead?
- (b) How many paths are there from C?
- (c) State the order of each node marked with a letter in figure 23.

### EXERCISE B

- 1. Make a list of the letters which have among
- others: NOTE: PROVIDE EACH STUDENT A COPY of 26
- LETTERS.
- (a) One 3node, (b) two 3nodes, (c) one 4node.
- 2. Why is it impossible to draw a figure with one 1node and no other nodes?
- 3. Which of the letters in question 1 are topological transformations of the letter C?
- 4. Which of the letters in question 1 are equivalent to the letter Y? How many nodes has each of these letters? What kind of nodes are they? NOTE: WE DO NOT COUNT 2NODES SINCE EVERY POINT OF AN ARC IS 2NODE WITH THE EXCEPTION OF ITS ENDS.
- 5. Complete the table for the networks in figure 24. NOTE: PROVIDE EACH STUDENT A COPY OF FIGURE 24 AND ADD 5 MORE DIAGRAMS.

### INVESTIGATION 1

Draw, if possible, figures which have:NETWORK | 1NODE | 3NODES | 4NODES | 5NODES | 6NODES |

1. | — | — | 2 | — | — |

2. | — | 4 | 1 | — | — |

3. | — | — | — | — | 1 |

4. | 4 | — | 1 | — | — |

5. | 1 | 1 | — | — | — |

6. | — | 1 | 1 | 1 | — |

7. | — | 3 | — | — | — |

8. | — | 2 | 1 | — | — |

(b) When is it impossible to draw a figure?

(c) Try to find a rule for deciding whether or not a figure can be drawn.