same distance, and starting from any
point, A, in the circumference, mark
off the points B, C, D. Now, with the
centers A and D and the distance
AC, describe arcs at E, and the dis-
tance EO is the side of the square
sought. If, therefore, we mark off F
and G from A with this distance, the
points A, F, D, G will be the four
comers of a perfect square.
- LINES AND SQUARES
Answers 285If you draw 15 lines in the manner A p, C J) E F
shown in the diagram, you will have
formed exactly 100 squares. There are
40 with sides of the length AB, 28 of
the length AC, 18 of the length AD,
10 of the length AE, and 4 squares
with sides of the length AF, making
100 in all. It is possible with 15 straight
lines to form 112 squares, but we were
restricted to 100. With 14 straight
lines you cannot form more than
91 squares.
The general formula is that with n straight lines we can form as many as
(n - 3)(n - l)(n + 1) squares ifn be odd and (n - 2)n(n - 1) ifnbeeven
24 '24'
If there are m straight lines at right angles to n straight lines, m being less
m(m - 1)(3n - m - 1)
than n, then 6 = number of squares.
- MR. GRINDLE'S GARDEN
The rule is this. When the four sides are in arithmetical progression the
greatest area is equal to the square root of their continual product. The
square root of 7 X 8 X 9 X 10 is 70.99, or very nearly 71 square rods. This is
the correct answer.