The origin of the golden section? Who knows.

History of discovery

Since the Pythagoreans in ancient Greece in the 6th century BC studied the drawing of regular pentagons and regular decagons, modern mathematicians inferred At that time, the Pythagoreans had already touched upon and even mastered the golden section.

In the 4th century BC, the ancient Greek mathematician Eudoxus was the first to systematically study this problem and establish the theory of proportion.

When Euclid wrote "Elements" around 300 BC, he absorbed the research results of Eudoxus and further systematically discussed the golden section, becoming the earliest treatise on the golden section.

After the Middle Ages, the golden section was cloaked in mystery. Several Italian painters, Pacioli, called the middle ratio a sacred ratio and wrote books specifically about it. German astronomer Kepler called the golden section the divine section.

It was not until the 19th century that the name golden section gradually became popular. The golden section has many interesting properties, and its practical applications are also widespread. The most famous example is the golden section method or 0.618 method in optimization, which was first proposed by the American mathematician Kiefer in 1953 and popularized in China in the 1970s.

|..........a..........|

+----------- --+--------+ -

| | | .

| B | A | b

| | | .

+----------- --+--------+ -

|...b...|..a-b...|

Usually Use Greek letters to represent this value.

The wonderful thing about the golden section is that its ratio is the same as its reciprocal. For example: the reciprocal of 1.618 is 0.618, and 1.618:1 is the same as 1:0.618.

The exact value is square root 5+1/2

The golden section number is an irrational number, and the first 1024 digits are:

1.6180339887 4989484820 4586834365 6381177203 0917980576

2862135448 6227052604 6281890244 9707207204 1893911374

8475408807 5386891752 1266338622 2353693179 3180060766

7263544333 8908659593 9582905638 3226613199 2829026788

0675208766 8925017116 9620703222 1043216269 5486262963

1361443814 9758701220 3408058879 5445474924 6185695364

8644492410 4432077134 4947049565 8467885098 7433944221

2544877066 4780915884 6074998871 2400765217 0575179788

3416625624 9407589069 7040002812 1042762177 1117778053

1531714101 1704666599 1466979873 1761356006 7087480710