The five-pointed star is a wonderful graphic, and many countries in the world have five-pointed stars on their flags. Just like our motherland, China, there are 5 big five-pointed stars and 5 small five-pointed stars on the national flag, 50 on the American flag, 1 on the North Korean flag, etc. In children's paintings, we can often see that the stars in the paintings are drawn into five-pointed stars, so we can see five-pointed stars almost wherever we go.

The five-pointed star is a figure surrounded by 10 sides, with 5 angles. The sum of the internal angles is 180 degrees, which is radiative. It is precisely because of the shape of the five-pointed star that it gives people authority, justice, and Fair impression.

The wonderful thing about the five-pointed star lies in mathematics. Everyone knows the famous golden section, its value is √5-1÷2, which is approximately equal to 0.618. A line segment is divided into two parts of different lengths. The ratio of the short part to the long part is equal to the ratio of the long part to the original line segment. This ratio is the golden section. And this famous value is hidden on the five-pointed star. Looking at the picture, there are three points A, B, and C on the five-pointed star. BC:AB=AB:AC. This ratio is exactly equal to the golden section point.

Drawing a five-pointed star accurately is impossible with bare hands. In some paintings, the imprecise five-pointed star gives people a relaxed feeling, but in the national flag, national emblem, and trademark, the five-pointed star must be completely accurate, and the ratio of any line segment of the five-pointed star must be equal to the golden section. This requires the help of tools. In fact, it is difficult to draw with freehand, but it is easy to draw with the help of tools. You only need an unmarked ruler and a compass to draw, using the ruler and compass drawing method. The five-pointed star drawn using the following method is absolutely accurate.

1. Draw a certain point O on the white paper. With O as the center and an appropriate length as the radius, draw a circle O.

2. Make a diameter AZ, and then make a diameter XY perpendicular to it.

3. Draw the midpoint M of OY.

4. With M as the center and MA as the radius, draw arc ⌒AN and radius AX to intersect at N.

5. With A as the center of the circle and AN as the radius, continuously intercept equal arcs on the circle so that the chords AB=BC=CD=DE=AN.

6. Connect AD, AC, EB, EC, BD to get a five-pointed star.