This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1899 Excerpt: ...6. Seven points? 7. Eight points? 8. Nine points? From the above results a rule can be formed: To find the number of ways in which a group of points can be divided into two groups, divide by 2 the number of points if it be an even number, or one less than the number of points if it be an odd number. 9. Calculate the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1899 Excerpt: ...6. Seven points? 7. Eight points? 8. Nine points? From the above results a rule can be formed: To find the number of ways in which a group of points can be divided into two groups, divide by 2 the number of points if it be an even number, or one less than the number of points if it be an odd number. 9. Calculate the number of ways in which 30 points can be divided into two groups. 10. Calculate the same for 35 points. 11. For 48 points. 12. For 27 points. In these problems you will notice that you do not raise the question which of the two groups contains any particular point. Thus with three points a, b, and c, the groups a--be, b--ac, and c--ab, all come under the head of one division. 4. To draw the greatest possible number of straight lines between points. 1. Between two points how many straight lines can be drawn? Let a and b be the points. Between a and b one straight line can be drawn, and only one. The straight line from a to b is the same as that from b to a. 2. Among three points how many straight lines can be drawn? Let a, b, and c be the points. Between a and b one straight line can be drawn; then the third point c can be connected with each of the other two points; therefore three straight lines can be drawn among three points. 3. According to the preceding problem, three is the greatest number of straight lines which can be drawn among three points: can you place three points so that not so many as three straight lines can be drawn among them? 4. What is the greatest number of straight lines which can be drawn among four points? Draw a diagram for three points and then proceed as in the second question. 5. Find the greatest number of straight lines for five points, drawing a diagram. 6. Do the same, with six points. You will notice that in a g...
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