Curricular Resources > 1980 Volume VII > Unit 8 (80.07.08) > Section 4

Problem Solving

CONTENTS OF CURRICULUM UNIT 80.07.08

Unit Guide

Topology

Bhim Sain Kaeley

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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	—	—

(a) Make up some more examples of your own.

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

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