There is 1 line segment AB with the length of 1 and point C (AC >: CB), so that AC: CB = AB: AC, then point C is the golden section of AB.

Let AC=x, then BC= 1-x, and substitute the definition AC: CB = AB: AC, we can get:

x:( 1-x)= 1:x

Namely;

The square of x +x- 1=0.

Solve quadratic equation, x 1= (radical number 5- 1)/2? X2=(- radical number 5- 1)/2

Where x2 is a negative value.

So AC= (radical number 5- 1)/2? About 0.6 18

Extended data;

Application example

The golden section has strict proportionality, artistry, harmony and rich aesthetic value, which can arouse people's aesthetic feeling and is considered as the most ideal proportion in architecture and art?

The painters found that the painting with the ratio of 0.6 18: 1 was the most beautiful, and the golden section was used in Leonardo da Vinci's works Vitruvian Man, Mona Lisa and The Last Supper. Nowadays, the average length of women below the waist only accounts for 0.58 of their height.

Therefore, the famous ancient Greek statue of Venus with a broken arm and the statue of Apollo, the sun god, deliberately lengthened their legs, so that their ratio to their height was 0.6 18. Architects especially prefer the number 0.6 18. Whether it is the pyramids in ancient Egypt, Notre Dame de Paris, the Eiffel Tower in France in the past century, or the Parthenon in Athens, Greece, there are footprints of the golden section.

Reference source; Baidu encyclopedia-golden section