The golden section, also known as Huang Jinlv, means that there is a certain mathematical proportional relationship between the parts of things, that is, the whole is divided into two parts, and the ratio of the larger part to the smaller part is equal to the ratio of the whole to the larger part, and its ratio is 1: 0.6 18 or10/. The above ratio is the ratio that can most arouse people's aesthetic feeling, so it is called the golden section.

Golden section triangle

All triangles that appear after the diagonal of a regular pentagon is full are golden section triangles. ? The golden section triangle has a particularity. All triangles can generate triangles similar to themselves with four congruent triangles, but the golden section triangle is the only triangle that can generate triangles similar to itself with five congruent triangles instead of four congruent triangles. Because the vertex angle of the five-pointed star is 36 degrees, it can also be concluded that the golden section value is 2Sin 18.

As shown in the figure:

Prove: ∫BD= 1/2ab, ∴AB=2BD, so that BD = 1,?

Then AB=2, from Pythagorean theorem:

AD^2=AB^2+BD^2

=2^2+ 1^2=5,∴ad=√5,∵bd=de= 1,ac=ae，

∴ac=ad-de=√5- 1,∵ac=√5- 1,ab=2

∴AC:AB=(√5- 1)/2。