C is the golden section point of line AB, find the value of AC / BC

C is the golden section point of line AB, find the value of AC / BC

AC/BC=BC/AB=BC/(AC+BC)
It is concluded that BC * BC = AC * AC + BC * AC
Divide both sides by ac * BC at the same time, and get AC / BC + 1-bc / AC = 0
Let AC / BC be x, and multiply both sides of the equation by X at the same time to get x * x + X-1 = 0
The final answer is (√ 5-1) / 2

What is the formula of golden section?

In the process of segmentation, it is called golden section when the length is about 0.618 of the whole length. This segmentation point is called golden section. It divides a line segment into two parts, so that the ratio of one part to the whole length is equal to the ratio of the other part to this part. The ratio is an irrational number, which is expressed as √ 5-1 / 2 by fraction, The approximate value of the first three digits is 0.618. Because the shape designed according to this proportion is very beautiful, it is called golden section, also known as the ratio of middle to outer. This is a very interesting number. We use 0.618 to approximate it. Through simple calculation, we can find that: 1 / 0.618 = 1.618 (1-0.618) / 0.618 = 0.618

The closer the ratio of the lower body (the length from the sole of the foot to the navel) to the height is to 0.618, the more beautiful it is. Unfortunately, even the slender Ballerina can not achieve such perfection. A lady, with a height of 1.68m and a lower body of 1.02M, should choose___ Cm (take two significant figures) high heels look more beautiful

Suppose that the height of her high-heeled shoes is xcm, then 102 + X168 + x = 0.618, the solution is: X ≈ 4.8cm. It is found that x ≈ 4.8 is the solution of the original equation, so the answer is: 4.8

The closer the ratio of the lower body (the length from the sole of the foot to the navel) to the height is to 0.618, the more beautiful it is. Unfortunately, even the slender Ballerina can not achieve such perfection. A lady, with a height of 1.68m and a lower body of 1.02M, should choose___ Cm (take two significant figures) high heels look more beautiful

Suppose that the height of her high-heeled shoes is xcm, then 102 + X168 + x = 0.618, the solution is: X ≈ 4.8cm. It is found that x ≈ 4.8 is the solution of the original equation, so the answer is: 4.8