Since the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons in the 6th century BC, modern mathematicians have come to the conclusion that Pythagoras school had touched and even mastered the golden section at that time.
In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion.
When Euclid wrote The Elements of Geometry around 300 BC, he absorbed eudoxus's research results and further systematically discussed the golden section, which became the earliest treatise on the golden section.
After the Middle Ages, the golden section was cloaked in mystery. Several Italians, pacioli, called the ratio between China and the destination sacred and wrote books on it. German astronomer Kepler called the golden section sacred.
It was not until the19th century that the name golden section gradually became popular. The golden section number has many interesting properties and is widely used by human beings. The most famous example is the golden section method or 0.6 18 method in optimization, which was first proposed by American mathematician Kiefer in 1953 and popularized in China in 1970s.
|..........a...........|
+ - + - + -
| | | .
| | | .
| B | A | b
| | | .
| | | .
| | | .
+ - + - + -
|......b......|..a-b...|
This value is usually expressed in Greek letters.
The wonder of the golden section is that its proportion is the same as its reciprocal. For example, the reciprocal of 1.6 18 is 0.6 18, while1.618 is the same as 1:0.6 18.
The exact value is the root number 5+ 1/2.
The golden section number is irrational, and the first 1024 bits are:
1.6 180339887 4989484820 4586834365 638 1 177203 09 17980576
2862 135448 6227052604 628 1890244 9707207204 18939 1 1374
8475408807 538689 1752 1266338622 2353693 179 3 180060766
7263544333 8908659593 9582905638 32266 13 199 2829026788
0675208766 89250 17 1 16 9620703222 10432 16269 5486262963
136 14438 14 975870 1220 3408058879 5445474924 6 185695364
86444924 10 4432077 134 4947049565 8467885098 743394422 1
2544877066 47809 15884 607499887 1 24007652 17 0575 179788
34 16625624 9407589069 70400028 12 1042762 177 1 1 17778053
153 17 14 10 1 1704666599 1466979873 176 1356006 70874807 10
13 17952368 942752 1948 4353056783 0022878569 9782977834
7845878228 9 1 10976250 0302696 156 1700250464 3382437764
86 1028383 1 2683303724 292675263 1 1653392473 167 1 1 12 1 15
88 186385 13 3 162038400 5222 16579 1 2866752946 549068 1 13 1
7 159934323 5973494985 0904094762 1322298 10 1 726 1070596
1 164562990 98 16290555 2085247903 52406020 17 2799747 175
3427775927 786256 1943 20827505 13 12 18 156285 5 122248093
947 1234 145 1702237358 05772786 16 0086883829 5230459264
78780 17889 92 19902707 7690389532 1968 1986 15 1437803 149
974 1 106926 0886742962 2675756052 3 172777520 3536 139362
1076738937 6455606060 5922 ...