Geo_Book_Answers
Geo_Book_Answers
Geo_Book_Answers
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<strong>Answers</strong> to Exercises<br />
18. The golden ratio is 1+ 5 , or approximately<br />
2<br />
1.618. Here is one possible construction:<br />
A<br />
mB 90°<br />
Construct BC 1<br />
2 AB<br />
AC <br />
2 5 AB<br />
AX AD <br />
2 5 AB 1<br />
2 AB<br />
AX 5 1<br />
<br />
2<br />
AB<br />
AB<br />
2<br />
AX<br />
5 1<br />
1+<br />
2 5<br />
<br />
Therefore, X is the golden cut.<br />
128 ANSWERS TO EXERCISES<br />
D<br />
X<br />
C<br />
B<br />
19a. <strong>Answers</strong> will vary.<br />
19b. Possible answer: The shape is an irregular<br />
curve.<br />
19c. <strong>Answers</strong> will vary. Possible answers: As the<br />
circular track becomes smaller, the curve becomes<br />
more circular; as the track becomes larger, the<br />
curve becomes more pointed near the fixed point.<br />
As the rod becomes shorter, the curve becomes<br />
more pointed near the fixed point; as the rod<br />
becomes longer, the curve becomes more like an<br />
oval. As the fixed point moves closer to the traced<br />
endpoint, the curve becomes more pointed near<br />
the fixed point; as the fixed point moves closer to<br />
the circular track, the curve begins to look like a<br />
crescent moon.
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