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Approximating the Golden Ratio
Use the formula for
φ
to successively improve an approximation:
φ
0
=
1
φ
1
=
1 + 1/φ
0
φ
2
=
1 + 1/φ
1
φ
3
=
1 + 1/φ
2
.
.
.
It is possible to show that the error of each approximation
x/y
is less than
1/y
2
.
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