Even the ancients noticed some amazing properties of the so-called "golden ratio". For example, the Giza pyramid complex was built on this principle. Also in the facade of the ancient Greek temple of the Parthenon there are "golden" proportions. How is the golden ratio built?
It is necessary
Ruler, pencil
Instructions
Step 1
Proportion (from the Latin word proportio) is the following equality a: b = c: d. The golden ratio is such a division of a segment into parts, in which the length of the entire segment refers to the length of the greater part, just as the length of the greater part refers to the length of the smaller part. The very concept of the golden ratio was introduced by Leonardo da Vinci. He considered the human body to be the most perfect creation of nature. If a human figure is tied with a belt, it turns out that the height of the whole person refers to the distance from the waist to the heels, just as the distance from the waist to the heels refers to the distance from the waist to the crown of the head.
Step 2
If we take, for example, a segment of a straight line AB and divide it by a point C, so that AB: AC = AC: BC, then we get the following equality AB: AC = AC: (AB-AC) or AB (AB-AC) = AC2 or AB2-AB * AC-AC2 = 0. Next, place AC2 outside the brackets AC2 (AB2: AC2 - AB: AC - 1) = 0.
Step 3
If you designate the expression AB: AC with the letter K, you get the quadratic equation K2-K-1 = 0. One of the roots of this quadratic equation will be the number 1, 618. In other words, the "golden ratio" is an irrational number, approximately equal to 1, 618.
Step 4
The Egyptian pyramids were built according to the principle of the golden ratio. There is a square at the base of the pyramids. For example, at the base of the Cheops pyramid lies a square with a side length of 230, 35 meters. The height of this pyramid is 146.71 m. The side face of the Cheops pyramid is an isosceles triangle with a right angle at the apex and angles at the base equal to 45 degrees
Step 5
There are four such side faces of isosceles triangles in total, since the base is a square. The triangle highlighted in red in the figure is called the "Egyptian" sacred triangle. An Egyptian triangle is a triangle with sides 3, 4, 5, or k3, k4, k5, where k belongs to the set of real numbers. In such a pyramid, the side of the base refers to the height as 1,618 - this is the golden ratio
Step 6
So, to build a pyramid in the proportions of the golden section, you need to: 1. Draw a square (the side of the square should be equal to k * 3, where k is a natural number).2. Construct the diagonals of the given square. 3. At the point of intersection of the diagonals, lower the height equal to the side of the square divided by 1, 618.4. Connect the upper point of the height of the pyramid with the four vertices of the base.
