Divide a line segment into two segments A and B with different lengths, so that the ratio of the long segment (that is, a+b) is equal to the ratio of the short segment B to the long segment A, and the formula is A: (A+B) = B: A, where the value of b/a is the golden ratio.

The algorithm is as follows:

Because a: (a+b) = b: a.

So aa=b(a+b) is bb+ab-aa = 0- 1.

Let b:a=n, then b=na,

Replace b in the formula 1 with b=na to get nnaa+naa-aa-=0.

That is, aa(nn+n- 1)=0, where aa is not less than zero, then nn+n- 1=0.

According to the root formula, n=(√5+ 1)/2 or n=(√5- 1)/2.

Because n = b: a

That is, the golden ratio b:a=(√5- 1)/2.

Call it a day when you're done!

I hope it helps you!