Converting a triangle to a star - methods, formulas and examples

became a symbol of Jewish identity. No wonder it is placed on the Israeli flag. However, the magical power of the six-pointed figure is recognized not only in the Holy Land. For many peoples, a hexagram that harmoniously fits into a circle was considered a talisman against demons. Across cultures, the Star of David has been a sign of wisdom and freedom, life and hope. Archaeologists find an image of a six-pointed star in Pompeii and Crete, among the Gibeonians and Etruscans. It was in use among the ancient Slavs and Egyptians, Celts and Indians.

See also:

• Charms against damage and the evil eye: 5 strong amulets
• 5 powerful amulets for good luck and wealth

History of the Star of David symbol

Why is the symbol called the “Star of David”?
One of the legends tells the following story. Before the battle with his enemy Nimrod, the young king David prepared for himself a shield, to the back of which two triangles were attached. At the height of the battle, the triangles merged into one figure. The young man won the battle, and since then the symbol of the victor has been known as Magen David (“shield of David”). The star-shaped six-pointed figure was known to Jews back in Antiquity. But then it was used not as a religious attribute, but as a decorative element of religious buildings. Sometimes the Star of David was used as a trade mark. The earliest archaeological find associated with this symbol dates back to the 6th century BC. A certain Joshua ben Asaiah, a resident of the city of Sidon, used the Star of David on his seal.

For the first time, the hexagram appears as a sacred sign in the 11th century on one of the pages of the manuscript of the Hebrew Bible - Tanakh. Then, during the early Middle Ages, the six-pointed star acquired the meaning of a talisman and was used by Christians, Muslims and Jews as a talisman against demonic forces and fires.

In the middle of the 14th century. Emperor Charles IV allowed the Prague Jews to use the Star of David as a symbol on their battle standard. However, Czech historian Alexander Putik believes that this is nothing more than a legend and provides other information. According to Putik, the Prague Jewish community first appeared with the Star of David on its flag in 1490 at public celebrations for the coronation of Ladislaus II as King of Hungary. It was then that the authorities first officially recognized this symbol of the Jewish people.

In the 18th century, the hexagram acquired even more important meaning. The Age of Enlightenment inspired new hopes for Jews to gain full citizenship in the newly formed states. Thus Magen David became the spokesman for the ethnic aspirations of the Jews. In 1897, the world Zionist community adopted the sacred hexagram as the emblem of their organization.

The history of the six-pointed star in the middle of the 20th century. marked with tragedy. During the Holocaust, Jews in France, Holland, Belgium, Croatia, Slovakia and Romania were severely persecuted and forced to wear a yellow six-pointed star. Those who refused this humiliation faced severe punishment.

After World War II, the yellow star of shame became the blue star of honor. Now it flies on the Israeli flag as a symbol of protection and security for every Jew.

For what?

When we began to study electronics, resistors were connected either in series or in parallel, and we learned to replace such combinations with their equivalent resistances, often with the goal of reducing the entire network of resistances to a single equivalent resistance visible from the power supply. After this came circuits (Figure 1) that contained resistors that were neither series nor parallel, but could still be eliminated by carefully identifying and cutting the circuit pieces in the correct order. Note that R1 is not in parallel or series with either R2 or R3, but by combining R2 in series with R4, and combining R3 in series with R5, we can then combine these two equivalent resistances in parallel and finally combining the result in series with R1, obtain the impedance seen by the power supply, which, using Ohm's law, will help obtain the total current of the power supply.

Picture 1

But now we come to the circuits (Figure 2), where there are no pairs of resistors that are connected in series or in parallel, it seems that we have reached a dead end. One way to analyze this circuit is to use Kirchhoff's voltage law (second law) and Kirchhoff's current law (first law) to obtain algebraic equations that we can solve for voltages and currents. While this approach will always work (for this and most other types of circuits), it can be quite cumbersome. We might live with this as the cost of being able to analyze these more complex circuits, but sometimes we can avoid paying this bill by modifying or "transforming" parts of the circuit to turn it into something we can reduce using only the serial/parallel rules associations.

Figure 2

For simplicity, we will only consider DC circuits with resistors, but these principles apply to any AC or DC linear system. Also, to keep the discussion focused on conversions, we will only find the total current supplied by the voltage source, which means we are aiming to reduce the entire network of resistors into a single equivalent resistance.

Let's look at these two schemes in a little more detail (Figure 3). We can see that the only difference between them is what is inside the dotted circles. In each case, the circuit in the circle has three contacts that cross the circle to interact with the rest of the circuit. In the left circuit (Figure 3(a)), resistors are connected to the contacts in a delta configuration (in English literature, a delta configuration, named after the capital Greek letter Δ). And in the right circuit, the resistors are connected in a “star” configuration (in English literature, the “wye” configuration, named after the capital English letter Y, although in the circuit it is upside down).

Figure 3

Now imagine that the resistors inside the dotted circle in the left circuit are placed in a black box, this box is removed from the circuit and replaced with another black box that causes the circuit to behave exactly the same. Next, imagine that when you open this new box it contains three resistors arranged as in the right circuit. Whoever came up with the second black box very carefully chose the resistor values ​​so that the two blocks would be indistinguishable from the rest of the circuit: we know how to analyze the right-hand circuit, and we now know that when we do this, the results can be applied to left diagram because they are equivalent. This is why you need to perform the triangle→star and star→delta transformations.

Who can wear the Star of David?

Many people firmly believe that the six-pointed Magen David is a Jewish symbol, and representatives of other religions have no right to wear it.
However, an amulet with the Star of David can become a talisman for both Jews and Christians. The sacred hexagram protects a person regardless of what faith he adheres to. If you are often attacked by ill-wishers, you should use the Star of David as a talisman. A silver pendant with the image of this symbol will not only protect the owner from negativity, but will also share with him a charge of positive energy. If you want to enjoy life in harmony with others and discover your deepest talents, wear an amulet with a gold Star of David.

You can buy the Star of David in the form of a pendant or bracelet made of silver or gold from us. See the catalog at the link.

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Special case: symmetrical circuits

If the resistances in each leg of a delta or star connected circuit are equal, the circuit is considered “symmetrical”. It means that

\[R_∆ = R_{AB} = R_{BC} = R_{AC}\]

\[R_Y = R_A = R_B = R_C\]

Combining this condition with the relation from the previous section immediately leads to the transformation equation for the symmetry case.

\[2R_Y = \frac{R_∆(2R_∆)}{3R_∆}\]

\[R_Y = \frac{R_∆}{3}\]

\[R_∆ = 3R_Y\]

This is a much more significant result than it might seem at first glance, and the reason is quite simple - when engineers design delta or star circuits, they often try to make the circuits symmetrical. Although, of course, this is not always possible, and therefore we should be able to deal with the general case when the circuit is not symmetrical.

The meaning of the symbol in Judaism

Among Jews there are several explanations for the symbolism of Magen David.
Historian Uri Ofer believes that the six-pointed figure is an image of a white lily, which is identified in the minds of Jews with the Israeli people themselves. The German thinker F. Rosenzweig put forward an original interpretation of the hexagram. In his opinion, the Star of David symbolizes the relationship between the universe, God and people.

The Jews have adopted the custom of placing the Star of David in the tent in which a Jew should stay during the autumn holiday of Sukkot. The six points of the sacred star symbolize the legendary biblical characters who visit this temporary home - Jacob, Isaac, Joseph, Aaron, Abraham and Moses.

Most Jews perceive the six-pointed star as a sign of mercy. It is not surprising that the symbol of the emergency medical service, organized in 1930 in the capital of Israel, became a red hexagram on a white background.

Facts, position and map

With an area of ​​132 square degrees, the Triangulum constellation ranks 78th in size. Covers the first quadrant in the northern hemisphere (NQ1). It can be found in latitudes from +90° to -60°. Adjacent to Andromeda, Aries, Perseus and Pisces.

Contains a star with a planet and a Messier object (Messier 33). The brightest star is Beta Trianguli, whose apparent magnitude reaches 3.00. No meteor showers were detected. The constellation is part of the Perseus group along with Andromeda, Cassiopeia, Cepheus, Cetus, Lizard, Pegasus, Perseus and Auriga. Consider the diagram of the Triangulum constellation on a star map.

Star of David in Kabbalah

Adherents of Kabbalistic beliefs who lived in the Middle Ages attributed magical powers to the Star of David.
Inside this symbol they placed 9 sefirot (spheres), and the hexagram itself was placed on amulets. According to Kabbalah, the Star of David includes the following symbolism: Heaven and Earth

Traditionally, the Star of David consists of two triangles facing in different directions. One Kabbalistic interpretation states that the upward-facing triangle signifies God and His place in heaven as the Creator of the Universe, while the downward-facing triangle symbolizes the earth and humanity. The overlap of these two principles shows that the spiritual and materialistic go hand in hand.

Unity of the pillars of faith

In Kabbalah, the three sides of the triangle are believed to stand for the fundamental aspects of Judaism—God, the Torah, and the People of Israel. Each of the two figures in the Magen David symbolizes this unity. The ascending triangle demonstrates the emotional side of the relationship, and the descending triangle demonstrates the physical side.

The Omnipresence of God

One Kabbalistic interpretation of the Star of David points to the symbolic meaning of its six faces. These are the six directions where God's presence can be felt: North, South, East, West, Above and Below, while the center of the Star indicates the center of the Universe - the place of God's existence. An interesting detail: the phrase “Magen David” in Hebrew contains exactly six letters.

Unity of the nation

Since the magical hexagram has six sides, it has twelve edges. Kabbalah interprets this as a symbol of the twelve tribes of Israel, which currently form the unified nation of the state of Israel.

General case of triangle→star transformation

For the delta/star conversion, we are given a known delta-connected circuit and we want to find the values ​​for the equivalent star-connected circuit - so we try to find {RA, RB, RC} for the given {RAB, RBC, RAC}.

We'll start by rewriting our basic relationships from the original form in a slightly more compact form by defining a new quantity, RΔS, which is equal to the sum of the resistances of all the resistors in the delta-connected circuit.

\[R_{ΔS}=R_{AB}+R_{BC}+R_{AC}\]

We then rearrange our relation to obtain the form of a linear algebraic equation with unknowns {RA, RB, RC}.

\[(0)R_A+(R_{ΔS})R_B+(R_{ΔS})R_C=R_{AB}R_{BC}+R_{BC}R_{AC}\]

Since we have three unknowns, we need two more equations. They are obtained from the equivalent resistances visible when considering the other two pairs of contacts. Doing this (or using symmetry) we get

\[(R_{ΔS})R_A+(0)R_B+(R_{ΔS})R_C=R_{AB}R_{AC}+R_{BC}R_{AC}\]

\[(R_{ΔS})R_A+(R_{ΔS})R_B+(0)R_C=R_{AB}R_{AC}+R_{AB}R_{BC}\]

Adding these two equations together and subtracting our first equation gives us

\[2(R_{ΔS})R_A=2R_{AB}R_{AC}\]

\[R_A= {R_{AB}R_{AC} \over R_{ΔS}}\]

We can solve the system equation for the other two unknown resistances (or use symmetry) to get

\[R_B= {R_{AB}R_{BC} \over R_{ΔS}}\]

\[R_C= {R_{AC}R_{BC} \over R_{ΔS}}\]

These relationships can be summarized very compactly. The resistance connected to each node in an equivalent wye-connected circuit is equal to the product of the resistances connected to the corresponding node in a delta-connected circuit divided by the sum of the resistances of all resistors in the delta. This is usually expressed by a formula such as

\[R_N= {R_{N1}R_{N2} \over R_{ΔS}}\]

Where

• RN – resistor connected to pin N in a star circuit;
• RN1 and RN2 are resistors connected to pin N in a delta circuit

Six-pointed star in Christianity

The Christian interpretation of Magen David differs from the Jewish interpretation.
In Orthodoxy, the hexagram is perceived as a symbol of the six days during which the creation of the world took place. Many Orthodox Christians consider the Star of David to be a symbol that unites the Old and New Testaments. On the tops of the crosses of Christian churches you can sometimes see a hexagram symbol, and there is nothing strange about this. From sacred Orthodox texts we learn that Jesus Christ compared himself to the morning star, which was supposed to dispel the darkness of death and sin. In addition, for Christians, the Star of Bethlehem is of particular significance, showing the way to the birthplace of the Savior.

General case of star→delta transformation

For the star-delta conversion, we are given a known star-connected circuit and we want to find the values ​​for the equivalent delta-connected circuit. Hence, we try to find {RAB, RBC, RAC} for given {RA, RB, RC}.

This is not as simple as the delta-wye conversion because the unknown resistances are multiplied together, making the resulting equations nonlinear. Fortunately, we can get around this inconvenience by considering the ratios of the resistors in each circuit. For example, taking the ratio of RA to RB we get

\[{R_A \over R_B} = { R_{AB}R_{AC} \over R_{AB}R_{BC} } = {R_{AC} \over R_{BC} }\]

In other words, the ratio of the resistances of the resistors connected to any two terminals in a star circuit is equal to the ratio of the resistances of the resistors connecting the same two terminals to the third terminal in a delta circuit. Therefore, the other two relations will be as follows

\[{R_B \over R_C} = {R_{AB} \over R_{AC} }\]

\[{R_A \over R_C} = {R_{AB} \over R_{BC} }\]

Armed with this, we could return to our basic relations and work with them further, but it is easier to use one of the relations from the general case of the triangle→star transformation as a starting point.

\[R_A= {R_{AB}R_{AC} \over R_{AB} + R_{BC}+R_{AC} }\]

\[R_{AB}R_{AC} = R_A (R_{AB} + R_{BC}+R_{AC})\]

\[R_{AB} = R_A \left( {R_{AB} + R_{BC}+R_{AC} \over R_{AC} } \right)\]

\[R_{AB} = R_A \left( {R_{AB} \over R_{AC}} + {R_{BC} \over R_{AC} } + 1 \right)\]

\[R_{AB} = R_A \left( {R_{B} \over R_{C}} + {R_{B} \over R_{A} } + 1 \right)\]

\[R_{AB} = R_A + R_B + {R_AR_B \over R_C } \]

The other two expressions are obtained similarly (or according to symmetry):

\[R_{BC} = R_B + R_C + {R_B R_C \over R_A } \]

\[R_{AC} = R_A + R_C + {R_A R_C \over R_B } \]

These expressions can be generalized very compactly. The resistance connected between each pair of nodes in a delta-connected equivalent circuit is equal to the sum of the resistances of the two resistors connected to the corresponding nodes in a star-connected circuit, plus the product of the resistances of those two resistors divided by the resistance of the third resistor.

A common way to express this is to place the right-hand side under the common denominator, and then note that the numerator in each expression is the sum of the products of each pair of resistances in the star-connected circuit, and the denominator is the resistance connected to the third terminal.

\[R_{AB}={R_P \over R_C}\]

\[R_P = R_A R_B + R_B R_C + R_A R_C\]

Star of David in Islam

During the Middle Ages, the hexagon was popular not only among Jews, but also among Muslims.
Adherents of Islam called the six-fingered star “Khatam Suleiman” (“Seal of Solomon”). The Quran mentions the name Solomon (son of David) at least sixteen times because this biblical king of the United Kingdom of Israel and Judah was one of the revered prophets who lived before Muhammad. According to legend, the hexagram that adorned the ring of the wisest of rulers gave him power over the genies, the ability to see the future and understand the language of animals. The six-pointed star was especially common among the followers of the teachings of the Hanafi madhhab, as well as among the Turkish beyliks of Anatolia (Isfendiyarids and Karamanids). A seal depicting a hexagram was often used by the Ottomans when arranging mosques, on coins, and even on the personal banners of pashas (for example, naval commander Hayreddin Barbarossa). The Star of David adorned the swords of Ottoman soldiers. It was also placed on the tombs of early Islamic figures in Medina.

Now the sacred symbol is actively used in many esoteric practices of the Arab East. And a ritual black stone is built into one of the walls of the Mecca Kaaba, which is traditionally covered with a vestment with the image of a hexagram.

Manifestations in religion

Secret symbolism is closely related to religion and the occult. Due to the interpenetration of religions, the same symbol can have different interpretations. The Seal of Solomon is a fairly common sign, and therefore has its manifestation in many religions and religious movements. Moreover, sometimes it acquires completely opposite meanings.

Star of Judaism

According to one version, the symbol first appeared thanks to David, who is considered the liberator of the Jewish state. It is said that David's army used shields in the shape of a six-pointed star during their campaigns. Michael Laitman (an Israeli Kabbalist), in defense of this version, says that this form in itself is convenient for several reasons: the ends of the star protect the head and legs, and the double middle (one triangle superimposed on the other) protected the chest well.

Christianity

This is the shape of the star that marked the birth of Jesus.
The image of a star is also mentioned among Christians. It was she who marked the birth of Christ and served as a signpost for the Magi, who, following her, brought their gifts to the newborn. And although the Gospel of Matthew clearly speaks of the appearance of the star itself, the number of its rays remains in question. Nevertheless, the Bethlehem symbol is often depicted with 6 corners, since Jesus is the son of David. Previously, Christianity gave preference to 6 angles, in which this number symbolized 6 days spent on the creation of the world.

Symbol of 2 triangles in Hinduism

Although very few people associate the hexagonal symbol with India, it was the culture that first used it in its religion. In Hinduism, this version of execution is considered a manifestation of the connection between Shiva (upper triangle) and Kali (lower triangle), which means the unity of the masculine and feminine principles and at the same time - the struggle of spiritual and carnal principles.

Magic and symbol of the Star of David

Performers of magical rituals usually call the six-pointed star a hexagram.
In magic, it is customary to associate the hexagon (symbol of the macrocosm) with the pentagram (embodiment of the microcosm). By changing his inner world, the magician has the power to influence the world around him. The Star of David symbol is interpreted in magic as follows. The sacred figure consists of two triangles. One of them - “broad-shouldered” - rests on the tip of the corner; the other - “pointed” - is located at an upward angle. Each triangle contains triple symbolism:

• upper: masculinity, fire, spirituality;
• lower: femininity, water, material world.

The connection of these two triangles symbolizes the balance of antagonistic forces.
The hexagram is also interpreted as a symbol of the astral (“stellar”) plane of existence, in which energy, rather than matter, plays a key role. Therefore, the symbol of a six-pointed star is often used in planetary magic. Seven planets can be placed in the six corners of the hexagram and in its center.

Depending on the order in which the magician draws the sacred hexagon, he is able to call on the power of a specific celestial body to realize his plans. In planetary magic, planets have the following abilities:

• Saturn limits the enemy's forces and causes damage;
• Jupiter gives power to the magician or another person;
• Mars helps to defeat an opponent;
• The Sun is used to balance a specific area of ​​life;
• Venus awakens love;
• Mercury helps to convince an opponent or earn money;
• The Moon develops magical abilities or intuition.

By drawing a hexagram in a certain way, the magician can either take advantage of the listed properties of the planets, or get rid of their influence if they interfere with the implementation of his plans.
Since the hexagram combines several symbols and balances them, it has extremely strong protective functions. Therefore, the magician often puts this particular symbol on the Book of Shadows, in which he writes down his knowledge and secrets.

Basic relationships

To determine the equations relating resistors in a delta-connected circuit to resistors in a wye-connected circuit, we need nothing more than our trusty series/parallel formulas (and a little algebra). The idea is to equalize the equivalent resistances between the corresponding pairs of contacts with the remaining contact disconnected (Figure 4)

Figure 4

Doing this for the equivalent resistance between BC pins gives:

\[R_B + R_C = \frac{R_{BC} \left( R_{AB} + R_{AC} \right) }{R_{AB} + R_{BC} + R_{AC}}\]

If we repeat this process for each other pair of contacts in turn, we end up with two more similar equations, and either one will give us the information we need (provided we recognize the symmetry involved).

Star of David Tattoo

In 1950, a collection of tattoos that were popular at the time was published in France. Among them was the hexagonal Star of David. The authors of the book argued that it should be done by sailors going on long voyages. Such a tattoo was supposed to play the role of an amulet and guarantee the safe return of the sailors to their home port.

Nowadays, the Star of David is usually “stuffed” on different parts of the body:

• on the forearm: if a man gets a tattoo of this symbol on his forearm, this speaks of his courage, strength and endurance;
• on the shoulder blade: here the image of the sacred hexagram symbolizes the desire to fly and the irresistible desire to achieve the goal;
• on the ring finger: in this place, a tattoo with the Star of David means loyalty or commitment to some idea;
• a six-pointed star on the wrist is a symbol of achievements that are very dear to a person;
• The hexagram on the chest is usually painted by basketball players as a sign of sports solidarity.

For those who want to emphasize their bright individuality, a tattoo with Magen David in 3D format is ideal. The higher the professionalism of the master, the more realistic and convincing such a pattern will look on the skin.

Interpretation of the meaning of the star of England

Scientists put forward several other versions about the meaning of the symbol:

1. In Slavic mythology, there were 3 dimensions: Prav, Nav and Yav, where the gods lived, the souls of the dead and living people, respectively. Three triangles symbolized 3 worlds, and their merging represented harmony between dimensions.
2. In Christianity, a person consists of 3 parts: soul, body and spirit, which are associated with the 3 triangles of the star. The circle around the symbol is conscience, and the emptiness behind it is the Universe.
3. The three components of the amulet are personifications of the elements: Water, Fire and Earth, and the circle symbolizes Air.

For men

For men, the amulet gives confidence, courage, strengthens the sense of justice, and shows the right path. If you carry a pendant with you, you can achieve success at work and improve relationships with the opposite sex.

For women

The talisman protects women from dangers, helps them get through difficult times and protects them from accidents. The symbol replenishes vitality and protects against conflicts and bad people.

Due to its powerful energy, it is not recommended to wear the amulet every day - it is better to put it on before some important event or during a period of fatigue to recharge your energy.

The phenomenal popularity of the ancient symbol

The mystical six-pointed one can be found in the most unexpected places. Here is a far from complete list of them, which can cause culture shock among those uninitiated in the topic:

• family coats of arms of many Russian nobles and Austrian bankers-rich Rothschilds;
• coats of arms of Croatia and Bukovina, Kolomna and Krasnodar, Poltava and Ternopil, Zagreb and Rakvere, Herbstedt and Hamburg;
• the flags of Burgundy and Northern Ireland (not to mention the Israeli one);
• personal flag of the leader of the Cossacks Bogdan Khmelnytsky;
• Russian popular prints of the 18th-19th centuries;
• Delhi tomb of Humayun, ruler of the Mongol Empire;
• Florence Church of the Holy Cross;
• Moscow Cathedral of Christ the Savior;
• Ahmed ibn Tulun Mosque in Cairo;
• Tashkent Museum of Applied Arts;
• Moroccan coins and Scottish pounds;
• Christmas decorations common among residents of Northern Europe;
• The “Star of David” emoticon that has taken root on the Internet.

It is obvious that in terms of its prevalence, the Star of David is a grand symbol, known in world culture for at least 25 centuries.

Varieties of the star of England

The sign placed in the center gives the talisman additional power and abilities.

Sword point down

The most common sign is the sword in the star of England. It can be pointed downwards, which means wisdom and knowledge, or upwards - protection from evil spirits.

The talisman is recommended to be worn by male representatives. It endows its owner with masculinity, determination, bravery and intelligence, helps to tame temperament and find harmony.

The amulet is also suitable for those people whose work involves risk: military personnel, firefighters, security guards.

Women can wear the symbol if they are stressed, attacked by colleagues, and often enter into conflicts and disputes. The talisman will also help mothers raising children alone and those who lack self-confidence.

Amulet with a sword point down for courageous men.

fern color

The Slavs associate ferns with wealth. According to legend, this flower can only be found on the night of Ivan Kupala, and the one who does this will never need money.

A star with a fern helps the owner solve financial difficulties, gives purposefulness and responsibility. The amulet also fulfills dreams, attracts good luck and fortune, and protects against evil spirits.

Amulet Star of England with fern to solve financial problems.

Perunitsa

This variety is complemented by lightning - a symbol of Perun, the main god in Slavic mythology. Perunitsa is capable of destroying the darkness surrounding a person and bringing light and secret meaning into his life.

The talisman protects against any danger and negativity, gossip, damage and the evil eye.

Its owner becomes stronger, more confident, and more easily overcomes difficulties and obstacles along the way. The amulet is considered a source of energy, so it should be worn by those who are very tired at work or are prone to frequent depression.

Perunitsa is recommended for both men and women. For the former, it will strengthen leadership qualities, and for the latter, it will help maintain attractiveness and improve health.

The Perunitsa talisman gives its owner strength.

How to use the amulet

An amulet purchased in a store needs to be cleaned and activated. If this is not done, then due to the imprints of someone else’s energy, the talisman will not work.

Cleaning and activation

To clean the symbol you will need:

• spring water;
• rock salt.

How to clear extraneous energy:

1. Pour water into a container, add a little salt and mix thoroughly until it dissolves.
2. Place the product inside for 24 hours. Then pour the water into the toilet or under an old tree.

If the talisman cannot be wetted, then clean it without using liquid:

1. Salt is poured into a cup and the symbol is immersed there for 2 days.
2. The procedure is repeated twice.

If the amulet is made with your own hands, then it does not need to be cleansed.

After cleaning, the amulet is activated using 4 elements:

1. They carry candles over the flame 3-4 times, asking the fire for protection.
2. Then the product is placed in a pot of soil with a request to charge the product with force.
3. Rinse under running water, mentally turning to this element.
4. Leave to dry in the fresh air.

Activation is performed in clear, sunny weather. When the star of England dries, it is put on and left in place for 24 hours. At this time, the energy of the amulet will merge with the life force of the owner, so the process cannot be interrupted.

Wearing Features

The talisman can be worn as a decoration or used in magical rituals to increase the power of the latter. If a bad streak has come in life, you should ask the amulet for help.

To prevent the amulet from losing its properties, it is regularly cleaned of negative energy. This is especially true for silver items - if they turn black, this means that the amulet took a blow from the enemy. A broken or cracked talisman must be buried in the ground or thrown into the river - it has exhausted itself and will no longer be able to work.

If the amulet turns black, it means a negative influence was directed at you.

Interesting objects that are part of the constellation

The Triangulum Galaxy is a spiral galaxy and acts as one of the distant objects that can be easily found with the naked eye. The visual magnitude indicator is 5.72 units, and the normal distance is up to 3070 light years. The object is the third largest in the third group after the Milky Way, and its diameter can span 5,000 years and 40 billion stars.

Within the galaxy there are 54 clusters (globular). One can easily detect a black hole, the origin of which was marked by gravitational collapse. It was found in 2007, and its mass is 15.7 solar masses. William Herschel made many discoveries regarding this object, and he included it in his personally developed catalog of nebulae.

Along with this, the Triangle constellation contains several more objects that have received alphanumeric designations.

NGC 604

This is an emission-type nebula, which is located northeast of the central core. The distance is 1,500 years, and the apparent value is 14 units. The element was found as a result of the works of W. Herschel.

NGC 595

This is one of the common areas with a distance of 3,000,000 light years. It was discovered to science in 1864 (October 1).

NGC 634

This is a spiral galaxy with an apparent magnitude of 14 units. Its remoteness is 250 million years. The discoverer was E. Stefan.

NGC 925

Another group of spiral-type luminaries, equipped with a jumper and a visual magnitude of 10.7 units.

NGC 672, IC 1727

Objects interact with each other and are separated by 88,000 years.

NGC 784

Another common category is the spiral type, equipped with a jumper. The visible indicator is 12.23 units, and the distance is 16 million years.

NGC 953

This galaxy is elliptical in nature and has an apparent magnitude of 14.5. It was found by G. Louis in 1865.

Thus, the group of luminaries under consideration plays an important role and can be seen with the naked eye. It contains many space objects that continue to be studied by modern specialists.

Equivalent circuit sections with series and parallel connections

Let us denote the complex resistance of a circuit section consisting of two series-connected elements by The complex conductivity of a given circuit section is equal to the active and reactive conductivity:

If two elements with conductivities g and b calculated using these formulas are connected in parallel, then the total complex conductivity will be equal to Y and, accordingly, the complex resistance will be equal to Z,

Such two circuits with serial and parallel connections, having the same resistance at the terminals, are called equivalent.

Due to the fact that the reactance x, included in the calculation formulas, generally depends on frequency, the equivalence condition for these circuits is satisfied only at the frequency for which x is calculated.

Let, for example, be given a circuit with a series connection of resistance and inductance (Fig. 4-7, a). Let's transform it into a circuit with parallel connection of elements (Fig. 4-7, b).

Active and reactive conductivity of the original circuit:

From the condition of circuit equivalence it follows that the parameters of the new circuit will be:

Having calculated using these formulas, we obtain a circuit diagram equivalent to the original one at a given frequency. At other frequency values, the parameters will have different values, therefore, the equivalence of the circuits will be violated.

For example, at a sufficiently high frequency: If the initial circuit is Fig. 4-7, b and the given parameters are then the parameters of the equivalent circuit (Fig. 4-7, a) are determined from the expressions:

From the resulting expressions it is clear that the numerical values ​​of the equivalent circuit depend on the frequency.

The equivalence conditions for circuits with series and parallel connection of resistance and capacitance have the form: At a sufficiently high frequency and then

Stars forming the constellation Triangulum

Beta Triangulum

The most noticeable to an observer is Beta Trianguli, as its apparent magnitude is 3.0m. This star, located 124 sv. years from our planet, can be found under its own name Deltotum. Beta Trianguli is a white giant that belongs to the spectral class A5III.

Alpha Triangulum

Another bright star, but fainter than the previous one, is Alpha Trianguli. It is a spectroscopic binary with a mean apparent magnitude of 3.42m and is often called Mothallah, meaning "vertex of the triangle". This luminary shares a distance of 63 light with the Earth. years. The spectral class of this star is ambiguous: Alpha is a representative of the F5III-F6IV class.

Gamma Triangle

The outermost star in terms of brightness in the trio is considered to be Gamma Triangulum. The star is a white dwarf of spectral class A1Vnn. The apparent magnitude of the gamma is 4.03m. The distance from Earth to this star is 128 light years. years.

Triangle in Triangle

The most curious deep space object in the Triangulum is a galaxy located approximately 3 million light years away. years from our planet. It has the same name as the constellation in which it is located, and in astronomical atlases it is designated as Messier 33 or NGC 598. Being a member of the Local Group of galaxies, it occupies the third largest position in it, with a diameter of about 50 thousand light. years. The apparent magnitude of the Triangulum Galaxy is 5.7m, thanks to which it can be observed even through binoculars.

Selection depending on voltage

Now in industry, domestically produced asynchronous three-phase electric motors, designed for a rated voltage of 220/380 V, are more applicable (127/220 V units are rarely used anymore).

The “triangle” connection diagram is the only correct one for connecting foreign electric motors with a rated voltage of 400-690 V to Russian power grids.

Connecting a three-phase motor of any power is carried out according to a certain rule: low-power units are connected in a “delta” configuration, and high-power units are connected only in a “star” configuration.

This way the electric motor will last a long time and work without failures.

The “star” method is used when connecting three-phase asynchronous motors with a rated voltage of 127/220 V to single-phase networks.

History of the Triangulum constellation

Since the constellation Triangulum is quite ancient, its appearance on the celestial sphere is not without a mythological history.

The area was originally called Sicily. According to legend, the goddess Ceres turned to Jupiter with a request to place the island of Sicily in the sky. As a result, she wanted to immortalize him for all time.

The constellation Triangulum is also known by other names. For example, in Ancient Greece it was called Deltoton. This name was given in honor of the letter of the Greek alphabet, which the area was similar in shape to.