Observational Geometry

Cover Observational Geometry
Observational Geometry
William T William Taylor Campbell
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Four lines can be divided into two groups in two ways (see p. 134), I line and 3 lines, or 2 lines and 2 lines. If the lines of each group are parallel, how many points of intersection will there be?
138 OBSERVATIONAL GEOMETRY You will notice that each line of a group cuts each line of the other group in one point; but the lines of the same group cannot cut one another : why ?
2. How many points of intersection will six straight lines make when divided into groups as in the preceding problem ?
...L- li III II 7 -U- 3. Five straight lines ?
4. Eight straight lines ?
5. Nine straight lines ?
6. If the number of lines be 12, and the number of points of intersection be 27, how many lines are there in each group ?
7. Can ii lines and 17 lines each be divided into two groups of paralleMines so as to give 30 points of intersection?
8. What numbers of lines can be divided into groups, each of parallel lines, so as to give 30 points of intersection ?
9. Fifteen lines, when divided in various ways into two groups of parallel lines, give the following numbers of points of intersection, 14, 26, 36, 44, 50, 54, 56 : what do you notice about the successive differences between these numbers ?


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