A gold clock with seven different colored circles in it
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the golden ratio（Ogonhi、hero: golden ratio）What is、It is a ratio expressed by the following value：
1
:
1
+
5
2
.
{\displaystyle 1:{\frac {1+{\sqrt {5}}}{2}}\
,.
}
golden rectangle（The ratio of length and width is the golden ratio（ 1: 1
.
618…）a rectangle that is）If we cut off the largest square from、be similar to the original rectangle
。
The red line is a golden spiral、The green line connects the quadrants within the square
.。
Yellow represents overlapping areas
。
The mathematical properties described below are、This property is only possessed by this value that is not a rational number
.
、Rational approximations are basically meaningless
.。
「make the design beautiful」Regarding theories that are often seen in the public such as「use」See section
。
Expanding to a decimal is 1 : 1
.
6180339887
...
Or 0
.
6180339887
...
: will have a value such as 1
。
The golden ratio is one of the precious metal ratios
.
（1st precious metal ratio）
。
Geometrically、a : If b is the golden ratio、
a : b = b : (a + b)
Since the equation holds
,
、The remaining rectangle after cutting off the largest square from a rectangle with golden ratio aspect ratio is、After all
,
it is a golden ratio rectangle
.
、It has the property of being similar to the original rectangle
.。
The ratio of one side of a regular pentagon to the diagonal is equal to the golden ratio
。
sequence a
,
b
,
a + b is、form a geometric progression
。
Therefore、（Middle term b and final term a + in the sense of the ratio of b）middle end ratio（Chuumatsuhi）Also called
。
Divide the line segment into two、The ratio of the length of the short part to the long part is、Because it is the ratio when it is made equal to the ratio of the long part to the whole length、Outside-Chinese ratio（Gaichuhi、hero: extreme and mean ratio）Also called
。
Golden ratio division or golden section is the division of length etc
.
by the golden ratio
.
（hero: golden section or english: golden cut）That
。
1 in the golden ratio
+
5
2
{\frac {1+{\sqrt {5}}}{2}}
the golden number（Ogonsu、hero: golden number）That
。
often the Greek letter φ（phi）It is expressed as、T（Tau）may also be used
。
golden number is、Quadratic equation x2 − x − 1 = is the correct answer to 0：
�
=
1
+
5
2
=
1
.
6180339887 ⋯{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1
.
6180339887\cdots }
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