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Line segments in the golden ratio
A
golden rectangle
with longer side
a
and shorter side
b
, when placed adjacent to a square with sides of length
a
, will produce a
similar
golden rectangle with longer side
a + b
and shorter side
a
. This illustrates the relationship
a
+
b
a
=
a
b
≡
φ
{\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}\equiv \varphi }
.