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Historical origin

Daily use

Intrinsic meaning

manufacturing method

Mathematical geometry

catalogue

1 summary

2 Basic information

3 Historical origin

4 Daily use

5 Intrinsic meaning

6 production method

7 mathematical geometry

A five-pointed star is a star-shaped figure with five sharp corners and drawn by five straight lines. The English word "five-pointed star" comes from Greek, and its original meaning is probably "five straight lines" or "five elements". The meaning of "five-pointed star" in Chinese is obvious, which refers to a star with five corners. However, the Chinese "five-pointed star" does not necessarily refer to the "standard" five-pointed star. The Chinese "five-pointed star" sometimes refers to all the stars with five angles.

Basic information

Chinese name

five-pointed star

Foreign name

pentagram

spell

five-pointed star

source

Two Rivers Civilization in Babylon, Cuba

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A star-shaped figure with five sharp corners drawn by five straight lines.

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Historical origin

The five-pointed star was first discovered in Mesopotamian literature, which can be traced back to around 3000 BC. In Sumerian, the five-pointed star is a hieroglyphic used as "UB", which means "corner, corner, hiding place, small room, hole, trap", which means something very similar to pentemychos (see the usage of Pythagoras theory below). In labat (Sumerian hieroglyphic Dictionary), it stands for the number 306, which is represented as two upward corners. In Babylonian literature, the side of the five-pointed star may indicate directions: front, back, left, right and "up". These directions also have astrological significance, representing five planets: Jupiter, Mercury, Mars, Saturn and "Ishtar" Venus (representing the upper position).

The earliest use of the five-pointed star was found in the literature of civilization in the two river basins of Babylon, Cuba, indicating something very similar to pentemychos. Representing five planets: Jupiter, Mercury, Mars, Saturn and Venus (representing the upper position).

Daily use

The national flag patterns of many countries include a five-pointed star: Ethiopian, Moroccan, Vietnamese, North Korea, China people, the United States and so on. Many times, the middle of the pentagram is filled, and the boundary between the pentagram and five isosceles triangles is removed.

Intrinsic meaning

The five-pointed star means "victory". It is used as the rank symbol of officers (especially senior officers) by the armies of many countries. It is also often used on flags.

The pentagram has always been closely related to Venus and its worship. Among the possible reasons for this relationship, the most credible is the observation of prehistoric astronomers. Seen from the earth, Venus's orbit around the sun repeats every eight years. Its five intersections just draw a nearly perfect five-pointed star.

In ancient Greece and Babylon, the five-pointed star also had special symbolic significance. The pentagram is a symbol of magic, not a symbol of non-Jews. In the early Christian church, the five-pointed star was also used to represent the five wounds of Jesus, and later it represented pagans and satanists.

The five-pointed star is a special figure in magic. When used in magic, it is usually called a "five-pointed star". Using a positive five-pointed star as a magic circle is white magic, and using an inverted five-pointed star is a symbol of black magic.

In China with oriental civilization, the five elements of Yin and Yang are connected by a five-pointed star. In Japan, the five-pointed star is regarded as the seal of platycodon Abe Zhaohui.

manufacturing method

It is impossible to draw a five-pointed star accurately with bare hands. In some paintings, the inaccurate 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 proportion 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 by hand, and it is easy to draw with tools. You can draw with a ruler and compasses without scales, and you can draw with a ruler. The five-pointed star drawn by the following method is absolutely accurate.

1, circle O. radius OA;

2. The intersection point A is the vertical segment AB of OA, so AB =1/2oa;

3. Add OB and intercept BC = AB on OB.

4. With OC as the radius and A as the starting point, cut equal arcs on the circle O in turn and connect them into a regular decagon.

5. Connect them into regular pentagons at intervals in turn.

6. Connect the diagonals of regular pentagons to get a five-pointed star.

There is another method, because the line segment of the five-pointed star follows the golden ratio, so we can make the five-pointed star by making the golden ratio.

1: make a line segment ab;

2: Make the middle vertical line of the line segment, and the intersecting line segment is at C;

3: Cut CD=AB on one side of the middle vertical line and connect AD;

4: Cut AE = AC on AD

5. Cut CF=DE and DG = de on CD.

6: Draw an arc with C and D as the center and CG or DF as the radius respectively;

7: Draw an arc with F and G as the center and FG length as the radius respectively, and intersect the two arcs in 6 at H and I;

8: DH, CI, FH and GI are connected and extended, and the extension lines of DH and CI intersect at point J;

9: So, the pentagon FHJIG is a regular pentagon, and you can see the five-pointed star.

Mathematical geometry

A pentagram is a polygon with the least number of sides. The simplest drawing method is to draw a regular Pentagon first, connect all the corners with straight lines, and erase the original Pentagon. You can also extend the sides of the original pentagon until they intersect, thus getting a big pentagram.

Golden ratio,

Satisfy:

Play an important role in regular five-pointed stars and five-pointed stars. Each side is divided into several small segments. If you divide the length of the longer line segment in a pair of line segments by the length of the shorter line segment, you will get φ.

One side of the big Pentagon is as long as a blue line segment, and a diagonal of the same small pentagram is as long as a green line segment.

If a line segment has a length (line), then there are two similar regular pentagons in the graph. What a "line segment" is, so are lines, and their intersections may also change. For example, on the national flag of Morocco, the green five-pointed star has a black outline and does not "cross" the intersecting lines. This is different from the five-pointed star on the Ethiopian flag. The five-pointed star is completely yellow and has no outline.

The total degree of the five angles of a five-pointed star is always 180 degrees.

This article is written by Hu, Associate Professor of Nanjing University of Science and Technology.

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