Pentagram

Pentagram (Greek πεντάγραμμος pentágrammos, with five lines ') is, among other term for a form of the five-pointed star ( five star), which arises when the diagonals of a regular pentagon ( pentagon) are tightened. Spreads are also the names pentagram, pentacle and pentalpha, since it can be formed by five alphas into each other standing ( " A"). Since the pentagram has five points, there are two basic types of alignment: a lace top ( then show two peaks down and two to the side ), or with a top down ( then show two peaks upwards and two to the side ). The latter is also referred to as "reversed " or " inverted " pentagram.

• 2.1 antiquity
• 2.2 Heraldry
• 2.3 In the sacral
• 2.4 Freemason Symbol
• 2.5 Numismatics
• 2.6 pentacle
• 2.7 Religion and occultism

Mathematical

Construction

From five evenly, so at intervals of 72 °, distributed on a circle of points can be made using two tendons in five axes symmetrical figures create (design the points, see construction of a regular pentagon with compass and ruler ):

• The five tendons between adjacent points form a regular pentagon ( pentagon) with angles of 108 °.
• The five tendons between non-adjacent points together form the pentagram with acute angles of 36 °.

Geometric properties

The inner portions of the tendons of the pentagram again form a regular pentagon. Relative to the outer, it is rotated by 36 °. The prongs of the pentagram are isosceles triangles. The angle between the base and legs of these triangles be 72 °.

The inner pentagon, together with two non- neighboring points form an isosceles triangle with a blunt tip, the already mentioned 108 -degree angle.

If you draw in the inner pentagon again a pentagram, thus forming the tendon with parts of the tendons of the outer pentagram also isosceles triangles with blunt tip of 108 °. Their bisectors are parallel to those of the prongs triangles, which in turn form the symmetry axes of all pentagrams and pentagons.

Physical pentagram, pentagon and inner pentagram same center. Each chord of the inner pentagram parallel to a center point situated outside the chord of the outer pentagram.

All angles between the edges of the pentagram and the enclosing pentagon therefore be 36 °, 72 ° or 108 °. The five axes of symmetry have the edge angles of 18 °, 54 ° and 90 °.

Denoting with and the radius radius the distance of two adjacent peaks with, the result is the chord length of the pentagram to

Or

Golden section

All tendons and sinews through intersections limited parts of a pentagram together with the outer and inner pentagon have only four different lengths. Of these, the following are all mutually to each other in the ratio of the golden section, ie the ratios:

For it is the case for the first ratio:

( CC'd triangle is isosceles, since it is a proportional reduction of the isosceles triangle BB ' D. )

Due to the radiation law applies:

Consider the ratio

Then and therefore corresponds to the definition of the golden ratio.

Area

Calculation of the area of ​​a pentagram with the side ( side of the pentagon in the pentagram ):

Or ... in numbers:

If, instead of the side length of the inner pentagon of the outer pentagon is known, the following formula is applicable:

In numbers:

History and cultural significance

Antiquity

The pentagram was the symbol of Venus, both the planet and the goddess. It was found on a pitcher from the Mesopotamian Djemdet - Nasr period, ie around 3000 BC, when Sumerian ideogram of the goddess Inanna / Ishtar.

Pythagoras knew it as a symbol of health. He was very interested, the mathematical aspect of the golden section. Since you can draw it in a train and re-entering at the end to the beginning, it was also considered a sign of the cycle of life. Abraxas, God of the Gnostics, was also symbolized by a pentagram because it combines five elemental forces in themselves.

Heraldry

Also in heraldry, for example, on coats of arms and flags, the pentagram is used as a common figure.

In the sacral

The pentagram with his golden section coined some church. Pentacles can still be seen today in many rose windows of Gothic church building. On the east side of the tower of the Market Church Hanover is also seen a pentagram. A Christian interpretation of the five corners are the five wounds of Jesus Christ.

Freemason Symbol

Of the Dombauhütten the pentagram came to the Freemasons and was the parent symbol on their work carpets. Its five peaks indicate the virtues of prudence, justice, strength, temperance, and of diligence.

More symbolic interpretations of the five corners of the pentagram are the spirit and the four elements of fire, water, earth and air; or ether, and the four directions north, south, west and east.

The Blazing Star is a Masonic pentagram, surrounded by a halo and central the letter G contains (same meaning).

Numismatics

As a symbol on coins the pentagram is detectable since the early Middle Ages on Merovingian coins. Also on the coins and banknotes French Morocco to find it in many cases. Examples:

10 Francs, 1943

50 Centimes, 1945

1 Franc, date unknown

Pentacle

The pentagram, especially when it is enclosed by a circle is also used as a symbol of amulets and called pentacle. The word " pentacle " but can also generally amulets for magical incantation call, even if another icon is on.

Religion and Occultism

In medieval and post-medieval period, the pentagram was considered a ban sign against evil and as magic and defensive character against demons. The name pentagram is firstly explained by the fact that the character was viewed as a protective sign against night Spukgeister that Druden. There was also the belief that Druden even leave a birdlike footprint which is similar to the pentagram in about.

In Goethe's Faust I (v. 1395 f ) the characters prevents the devil Mephistopheles from leaving Faust's study:

Since the French occultist Eliphas Levi in particular is the "reverse " brought pentagram / ​​pentacle with Satanism and the occult in conjunction. In Lévis Dogme et rituel de la haute magic from the mid-19th century, it is referred to as a "sign of the goat of the Sabbath ", said prongs each represent the horns, ears and beard of the goat. Conversely, standing on two peaks pentagram became identified with Jesus Christ, where Jesus' Hebrew name was יהושוע ( Yeshua ) the Tetragrammaton יהוה (YHWH ), starting reproduced with יהשוה and called Pentagrammaton.

It relied on numerous later occultists. Surrounded with a goat head in the distorted Hebrew characters ( LVYThN לִוְיָתָן ), inverted pentagram, it appeared in 1961 on the cover of Maurice Bessy Histoire en 1000 images de la magic; Anton Szandor LaVey took this under the name Sigil of Baphomet as a sign of the Church of Satan founded in 1966. LaVey used the Sigil of Baphomet for the cover of the record The Satanic Mass (1968) and The Satanic Bible (1969).

In the 1980s, the inverted pentagram in the metal scene, especially in the Black and Death Metal as a symbol of evil or Satanism became popular, the Sigil of Baphomet appeared for example on records as Jamras The Second Coming (1972 ) and Venom's Welcome to Hell (1982). The pentacle ( pentagram circle) is also in the neo-paganism, especially in the new religious movement of Wicca, an important symbol.