Tattoo of a triangle - meaning
Symbolic can be not only the shape of the figure, but also its lettering. For example, the triangle can be inverted, empty inside or with a painted center, it can also be combined with other figures and drawings. Therefore, the meaning of the tattoo varies depending on the shape and lettering.
Most often in tattoos there are equilateral figures, because it is this drawing has found a sacred meaning. In astrology, this symbol refers to the element of the earth: it is no coincidence that the Masonic sign is an open eye in a triangle, symbolizing the victory of the spiritual over the material.
In many pagan cults there was a symbolism of trinity - a combination of the three beginnings, for example, the elements, as the Celts or worlds, as the Slavs. In esotericism, the tripartite sign is a symbol of the device of the universe, in which the two basic beginnings are male and female, joining in harmony of perfect interaction.
In alchemy, as in astrology, the tripartite geometrical symbol symbolizes the element of the earth. This symbol is an inverted equilateral triangle with a transverse line at the bottom.
In addition to the figure itself, there are other tattoos with a triangle, which have accompanying images: flowers, animals such as a wolf, various signs and figures. Depending on the sketch, they can be placed on the chest, back or neck.
Tattoo of a rose in a triangle
Popular are tattoo sketches with a rose in a triangle. Such tattoos mean the harmony of nature and science. In addition, such a drawing can have romantic overtones and denote feminine beauty, but more often the sketch symbolizes the submission of nature to reason.
In addition to the rose, the facets can frame other flowers - peonies, daisies, daffodils, depending on personal preferences of the person. Such a tattoo looks great in the rib area, on the forearm, on the back.
Tattoo triangle with a circle
Many are interested in what an isosceles triangle inscribed in a circle means, because this figure occurs very often, both in tattoos and in various esoteric and philosophical movements.
This sign symbolizes harmony in the world's chaos, the desire of the mind to order things, the need to find logic in the disorder.
There is also an inverse image with an inscribed circle. This is a symbol of the taming of the world chaos by the human mind. This sketch is chosen by followers of existentialism in philosophy, as well as lovers of alchemy and science. Alchemical tattoos are most often placed on the neck in the back of the head.
Tattoo of two triangles.
The two figures can join together to form a Star of David, or simply overlap each other. The Star of David or Solomon is an ancient Jewish religious symbol that should not be applied to those who are far from that religion.
Two figures standing side by side or overlapping symbolize the unity of the feminine and the masculine. If the figures touch each other by the tops, making a kind of hourglass, then such a drawing means the lunar cycle and the inexorable run of time, death and birth, the preservation of energy and its eternal cycle.
Tattoo of three triangles
Wrist drawing in the form of triangles, whose number repeats the number of faces and tops, means a triumph of the symbol's main meaning.
Trinity in the absolute, the power of three, including can have a literal meaning - the indestructible union of three people.
Penrose Triangle.
A mathematical figure that exists only as a blueprint, since it cannot be implemented in reality. Like the classical figure the Penrose triangle has faces and vertices, but they are connected not by sharp angles, but by straight lines, thanks to which there is a surreal effect. Such a figure has faces of rectangular beams, so you can clearly see the right angle of the connection.
Such a tattoo means a mathematical mindset, wit and irony of its owner.
A triangle with a line in the middle
A figure that has a cross line in the middle means one of the elements in alchemy and astrology.
Each of the elements is denoted by one of the triangles:
- Earth - an inverted symbol with a line in the middle;
- Water - inverted symbol without a line;
- Air - symbol in upright position with a line in the middle;
- Fire - a symbol in upright position without a line.
Such tattoos are often portrayed on the hand, for example, on the wrist, sometimes the drawings can be paired and applied to both hands.
Black Triangle
A fully painted figure can have several meanings depending on its position.
- The top up - masculinity, strength, stability, activity;
- Top down - femininity, wisdom, passivity.
Also, an all-black symbol can act as part of a composition or a paired drawing.
Color and black triangle tattoo on the arm: real examples of art
Most examples of tattoos with a triangle on the arm are made with colored ink. Especially spectacular on the wrists looks triangle tattoo in watercolor technique. Unusual natal design will suit girls who are not discouraged by life, and try to see everything through a multicolored prism of happiness. If we talk about the black version of the tattoo on the hand, the triangle in this format looks neat, which, in any case, is already considered fashionable.
Meaning of the Valknut symbol
Everyone has heard about the religion of the ancient Scandinavians, who can be considered one of the branches of the Slavs-Aryans - there are legends about Odin, Thor, Loki and many other gods. Naturally, both legends and documentary evidence of the beliefs of the ancient Scandinavians have come down to us from ancient times. One of the key places in the beliefs and symbolism of the Nordic peoples was the symbol Valknut, which was the sign of the head of the Nordic pantheon of gods - Odin. This legendary symbol is often called the Knot of the Dead or the Knot of the Chosen. The main purpose of the symbol is to control the transitions between worlds, moving the souls of the dead from one world to another. Only Valknut knows where the soul needs to go - to the glorious Valhalla or to the lesser known Hell. A person who wears and knows the true meaning of the Valknut has the unique ability to understand the basics of Being and even slightly open the borders between worlds.
Another meaning of the Valknut symbol is the unity of time - present, past and future. This sign unites the triple nature of Odin - with Vili and Ve, with Henir and Lodur, Heimdall and Loki. Figuratively speaking, Valknut is the union of soul, spirit and body. Equally often this symbol is an image of the unification of all the components of human life and the transition from one state to another.
If we talk about the practical meaning of the symbol Valknut, it is very interesting, as the presence of the amulet with three intertwined triangles on it allows you to get the key to the hidden from the uninitiated view of knowledge. The use of this symbol allows its possessor to concentrate his thoughts, switch his attention from one subject to another, improve his logic, comprehend the current situation, and have common sense when making difficult and responsible decisions. Very often, a person wearing a talisman Valknut has wisdom beyond his years, thanks to which he is able to doubt everything, even his beliefs and principles.
Tattoo of two triangles: paired designs for two halves
Men consider the tattoo of a triangle, made in a pair with the other half, a symbol of power, beauty and intelligence. The paired tattoo symbolizes the merging of souls into one and the unity of the relationship. Certain details in paired tattoos indicate that there is a certain unbreakable thread between the lovers that maintains the relationship. Inverted triangle images indicate that both people support each other in everything. In general, all paired images have a certain character, including additional ornaments to the triangle.
Triangle Tattoo Sketches
Stylish triangle tattoos can be done in a variety of techniques, being both monochrome and colored. Geometric symbols can be combined with images of animals, plants, and numbers. For example, it is common to frame three sides with numbers 2 or 3, putting into the drawing their own meaning or based on numerological meanings.
In spite of universality of the symbol for men and women, its value can vary depending on the drawing, its shape and additional elements.
Compositions with other elements
Geometric tattoos are often supplemented with images of animals. Then the associations associated with the selected animal are superimposed on the original meaning of the symbol. The location of the objects in the composition in question may be any. The figure may frame the animal or be part of it. For example, the nose, muzzle or torso. There are also such sketches, in which a triangle is formed due to a particular curvature of the body of the animal. In this case, the body remains proportional and looks as natural as possible.
In sketches for girls, the triangle is braided with flower sprouts, and large buds fill the inner space of the figure. Geometric minimalism is also popular with the fair sex. As an example of this is the composition, consisting of several simple figures, consistently following each other and occasionally intersecting. The concept may be complemented by a mystical or feminine symbol, straight lines, the sign of the zodiac.
The triangle can be a torn off or broken off part of a broken object or wounded animal. To enhance the effect, such images are supplemented with bows, arrows, vectors. An additional element can also be matched to the beast. Thus, a full moon is combined with a wolf, and the sun with a lion.
Relationship of Valknut and the theory of worlds
Scandinavian runic symbols have a very strong magical effect on humans, so handling them is a process,
which should be undertaken by a person who knows not just basic concepts and definitions, but who also has deep knowledge and some connection with other worlds. В
A large enough row of Scandinavian and Slavic amulets Valknut can proudly occupy a place next to Thor's Hammer and Trixel. The three intertwined triangles are groups of worlds - Midgarth, Asgard and Hel.
The first world, Midgarth, is the world where humans have lived since time immemorial; the second, Asgard, is the abode of the Gods, the spiritual world; and Hel, the abode of the dead. Symbol of the union of worlds has a very strong energy, so Valknut often used by magicians and wizards who draw from the amulet endless energy and secret knowledge of the three worlds. It is believed that meditation with Walknut gives the opportunity samotransform, acquire knowledge and rethink the structure of the universe, which is inaccessible to mere mortals.
It is a common opinion in the literature that the symbol of Valknut is not so much Scandinavian as it is more Egyptian-Greek. This is confirmed by the fact that even though it is a symbol of Odin, it is very rare to find Valcnut in his images. Those same skeptics believe that the amulet does not have the proper effectiveness as described, and believe that its power is fictitious.
But it is this rune symbol is a projection of the path of any warrior, so it can often be found alongside images of warriors and forces that have an impact on the path of man, who chose the path of the warrior. With this sign of the warrior emphasizes the likelihood of his fall into either the spirit world or the world of the dead. Quite often a similar meaning of the Valknut symbol is associated with the heart of Hrungir, the only giant who dared to compete with Odin in riding (he was later killed by Thor). If you consider the Valknut from this perspective, it clearly shows the triple union of worlds, and the symbol is more suitable not magician, but a warrior, as it does not help to comprehend Genesis, but to take certain actions to change it.
Individual meaning
The tattoo "triangle" is something special for each person. For example, for girls, this simple looking figure, can mean something important and profound. The triangle represents three cycles in the life of almost any woman. These are virginity, motherhood and old age. Not everyone can think of such a thing. However, such a clarification has been around for a long time, and many people stuff the triangle intentionally for this purpose.
For men, however, the figure means something else. The triangle also symbolizes the "trinity", but in this case it is not the cycle of life, but the qualities. More specifically, wisdom, strength and beauty. By the way, it is very important which area was chosen for the tattoo. It is able to enhance, to emphasize the given meaning. Most often such tattoos can be seen on the wrist, forearm or on the back of the head. These are the most popular variants of execution. But in fact, a person chooses the place himself.
Sometimes the triangles are painted over. Color also means a lot of things. Red symbolizes passion, black symbolizes negativity, green symbolizes safety, and orange symbolizes vitality. The hue can really say a lot about a lot of things, so you should choose it particularly carefully. And by the way, keep in mind that on the skin the selected color always looks 2-3 tones darker. You should be aware of this and pick up the paint with the awareness of this fact.
The area of an arbitrary triangle
Let's use this formula to get the formula for the area of an arbitrary triangle. Let us drop a perpendicular from the vertex of the triangle to the side (see Fig. 3).
Fig. 3. Arbitrary triangle with a perpendicular dropped on the side
Our triangle is divided into two right triangles and , and its area is equal:
We use the distributive law from right to left and take the common factor out of the brackets:
So we obtained that the area of an arbitrary triangle can be calculated as the half-product of the length of the perpendicular dropped from the vertex to the opposite side of the triangle and the length of this side.
But such a formulation is too cumbersome, and the formula is used quite often, so a special name was invented for the perpendicular the height of the triangle
.
The side to which the altitude is drawn is called the ...the base of a triangle...
. The point at which the perpendicular descends is called the is the base of the altitude
. Then
the area of an arbitrary triangle
- is the half product of the altitude by the base:
Sacred Geometry
We often hear the phrase "Sacred Geometry. This is especially important when it comes to exploring tattoos that have shapes and figures within them. The double triangle is a perfect example of sacred geometry. Sacred geometry gives symbolic and sacred meaning to specific shapes. The use of certain geometric proportions can be associated with God and God as the geometer of the world.
Many people love ancient Egypt. Egypt is full of pyramids. Many consider their creation a mystery. This is why the pyramids are a prime example of sacred geometry. Because all pyramids have triangular sides, many people mix the two ideas of a double triangle and pyramids. Two triangles overlapping each other like the ancient Egyptian pyramids is a very creative tattoo. This tattoo shows not only your love for geometric patterns, but also your love for ancient mysterious civilizations.
Peculiarities of Valcnut amulet usage
Valcnut in the runic circle was rarely used as a talisman, but because of its tremendous power, it can change a person's life to ward off bad luck, problems, the evil eye.
But in order for the amulet to bring good luck, its owner will have to endure certain tests, during which will be tested determination, will to win and strength of mind. At the same time, each test will be generously rewarded with good luck. It should be said that Valknut tattoo should not be applied in the heart area, as the energy of the symbol is very strong, and not everyone is able to cope with it.
Obereg is a universal amulet, so it is suitable for everyone. The only recommended restriction is that you should not wear it on children, because their energy protection is very weak. You will be able to use a silver Valknut (one of the strongest metals from the energetic point of view) to reveal your inner strength, get a constant feeding of energy from all three worlds, become stronger in spirit and not to be afraid of problems. Buy Valknut - this means to obtain the patronage not only of Odin himself, but also the entire pantheon of Scandinavian gods.
Remarkable lines and points of the triangle
Earlier we highlighted four important lines in the triangle:
- altitude
- the perpendicular dropped from the vertex to the opposing side; - the median
- the line connecting the vertex of the triangle to the midpoint of the opposing side; - bisector
- the line that divides the angle in half; - midpoint
- perpendicular to the side through its midpoint.
Of course, you can think of and derive properties for many lines in a triangle (for example, the line that divides the angle in relation to ). But the lines we have considered are the most common in solving various practical problems (some of them we have considered today), so they will be the focus of attention in planimetry lessons. They are even called the remarkable lines of a triangle.
. And the points at which these lines intersect are. the orthocenter, the center of gravity, the centers of the incircle and the circumcircle,
- ...are called...
the remarkable points of a triangle.
.
English layout
Alt code | Symbol | Alt-code | Symbol | Alt-code | Symbol | Alt-code | Symbol | Alt-code | Symbol | Alt-code | Symbol | Alt-code | Symbol | Alt-code | Symbol |
0127 | "?" (empty character) | 0144 | ђ | 0160 | <��неразры вный пробел> | 0176 | ° | 0192 | À | 0208 | Ð | 0224 | à | 0240 | ð |
0128 | Ђ | 0145 | ‘ | 0161 | ¡ | 0177 | ± | 0193 | Á | 0209 | Ñ | 0225 | á | 0241 | ñ |
0129 | Ѓ | 0146 | ’ | 0162 | ¢ | 0178 | ² | 0194 | Â | 0210 | Ò | 0226 | â | 0242 | ò |
0130 | ‚ | 0147 | ” | 0163 | £ | 0179 | ³ | 0195 | Ã | 0211 | Ó | 0227 | ã | 0243 | ó |
0131 | ƒ | 0148 | ” | 0164 | ¤ | 0180 | ´ | 0196 | Ä | 0212 | Ô | 0228 | ä | 0244 | ô |
0132 | „ | 0149 | • | 0165 | ¥ | 0181 | µ | 0197 | Å | 0213 | Õ | 0229 | å | 0245 | õ |
0133 | … | 0150 | – | 0166 | ¦ | 0182 | ¶ | 0198 | Æ | 0214 | Ö | 0230 | æ | 0246 | ö |
0134 | † | 0151 | — | 0167 | § | 0183 | · | 0199 | Ç | 0215 | × | 0231 | ç | 0247 | ÷ |
0135 | ‡ | 0152 | ˜ | 0168 | ¨ | 0184 | ¸ | 0200 | È | 0216 | Ø | 0232 | è | 0248 | ø |
0136 | ˆ | 0153 | ™ | 0169 | © | 0185 | ¹ | 0201 | É | 0217 | Ù | 0233 | é | 0249 | ù |
0137 | ‰ | 0154 | š | 0170 | ª | 0186 | º | 0202 | Ê | 0218 | Ú | 0234 | ê | 0250 | ú |
0138 | Š | 0155 | › | 0171 | « | 0187 | » | 0203 | Ë | 0219 | Û | 0235 | ë | 0251 | û |
0139 | ‹ | 0156 | œ | 0172 | ¬ | 0188 | ¼ | 0204 | Ì | 0220 | Ü | 0236 | ì | 0252 | ü |
0140 | Œ | 0157 | ќ | 0173 | н | 0189 | ½ | 0205 | Í | 0221 | Ý | 0237 | í | 0253 | ý |
0142 | Ž | 0158 | ž | 0174 | ® | 0190 | ¾ | 0206 | Î | 0222 | Þ | 0238 | î | 0254 | þ |
0143 | Џ | 0159 | Ÿ | 0175 | ¯ | 0191 | ¿ | 0207 | Ï | 0223 | ß | 0239 | ï | 0255 | ÿ |
The Reuleau triangle in art
Architecture
The form of the Rhölö triangle is also used for architectural purposes. Its two arcs form a characteristic Gothic lancet arch, but it is rarely found in Gothic structures as a whole. The triangle-shaped Rölö windows can be found in the Church of Our Lady of Bruges as well as in the Church of Scotland in Adelaide. As an ornamental element, it is found on the window grilles of the Cistercian abbey in the Swiss commune.
The Rolo triangle is also used in non-Gothic architecture. For example, built in 2006 in Cologne, a 103-meter tower called "" in the section is a figure. Some examples of use
The window of the church of Our Lady of Bruges | The window of St. Salvator's cathedral in Bruges | Notre Dame de Paris window | «» |
Window of the Church of St. Michael in Luxembourg | Window of Notre Dame Church in Bruges | Window of Saints Michael and Gudule Cathedral in Brussels | Window of the Cathedral of St. Bavon in Ghent |
See also the category "Reuleaux triangles in architecture" on Wikimedia Commons
Shape and color
Reuleaux triangle in the correspondences of I. Yitten
According to Johannes Yitten's formulas, in the "ideal" , part of the spectrum of each color stays as such - with a form (geometric figure). The green color is "derivative": result of mixture of transparent blue and light yellow (without inclusion), and as in this model a circle and a right triangle correspond to them, namely the figure named by I. Itten's spherical triangle, the R¨olo triangle, and corresponds to green.
Literature
In Paul Anderson's science fiction story "The Triangular Wheel," the Earth crew made an emergency landing on a planet whose population did not use wheels, as everything round was under religious prohibition. Hundreds of kilometers from the landing site, the previous Earth expedition left a warehouse with spare parts, but it was impossible to move the two-ton nuclear generator needed for the ship from there without any mechanisms. In the end, the Earthlings were able to honor a taboo and move the generator using rollers with a section in the form of a Rhölö triangle.
Popular places to apply
Quite often the Triangle tattoo is found on the hand. Any part of it, from the wrist and ending with the forearm, can become a place of application. For this role fits both the front side, as well as the back side.
Young girls and guys as a place to apply the Triangle tattoo often choose the back of the neck or the space just under it. This option is ideal for tattoos-talismans and mystically colored images. Especially spectacular looks inscribed eye. Well and large-scale tattoos are placed on the collarbones, back.
Variations and generalizations
Rolo polygon
Main article: R¨olo polygon
Reuleau's heptagon built on an irregular stellate heptagon
We can generalize the underlying Reuleau triangle construction idea by using not an equilateral triangle but a star-shaped polygon formed by line segments of equal lengths to create a constant-width curve. If we draw an arc of a circle from each vertex of the star polygon to connect its two vertices, the resulting closed curve of constant width will consist of a finite number of arcs of the same radius. Such curves (as well as the shapes bounded by them) are called polygons of Reulo
.
Right polygons of Reuleaux
The family of Reuleaux polygons of definite width a{{displaystyle a} forms a dense subset everywhere in the set of all curves of constant width a{{displaystyle a} (with the Hausdorff metric). In other words, one can use them to approximate any curve of constant width with any precision.
Among R¨olo polygons, there is a class of curves constructed on the basis of regular star polygons. This class is called regular Reuleaux polygons.
. All the arcs that make up such a polygon have not only the same radius but also the same length. A R¨olo triangle, for example, is a regular polygon. Among all Reuleaux polygons with a fixed number of sides and the same width, regular polygons limit the largest area.
The shape of such polygons is used in coinage: the coins of a number of countries (in particular, and 50 pence Great Britain) are made in the form of a regular heptagon Reuleau. There is a bicycle made by a Chinese officer, the wheels of which have the shape of a regular triangle and pentagon Reuleau.
Three-dimensional analogues
R¨olo's tetrahedron.
The three-dimensional analogue of the Rhölö triangle as an intersection of three circles is a Reulo tetrahedron
- Crossing of four identical spheres which centers are located in the tops of a regular tetrahedron, and the radii are equal to the side of this tetrahedron. However, the R¨¦olo tetrahedron is not a body of constant width: the distance between the midpoints of the opposite curved edges connecting its vertices is 3-22=1,02494...{\displaystyle {\sqrt {3}}-{\frac {\sqrt {2}}{2}}=1{,}02494\ldots } times as much as the edge of the original regular tetrahedron.
Nevertheless, the R¨olo tetrahedron can be modified so that the resulting body turns out to be a body of constant width. To do this, in each of the three pairs of opposite curvilinear edges one edge is "smoothed" in a certain way. The two different bodies obtained in this way (the three edges on which the substitutions occur can be taken either emanating from one vertex or forming a triangle) are called Meissner bodies, or Meissner tetrahedrons. The hypothesis formulated and formulated by Werner Fenchel in 1934 states that it is these bodies that minimize the volume among all bodies of a given constant width, but (as of 2011) this hypothesis is unproven.
Finally, a body of rotation obtained by rotating a Reuleau triangle around one of its second-order symmetry axes is a body of constant width. It has the smallest volume among all constant-width bodies of rotation.
The median perpendicular and the circumcircle of a triangle
Consider a practical problem. Suppose we have three settlements . And we need to place an ambulance station so that it can serve all three settlements (see Fig. 33). It is clear that the station should be located so that the distance from it to each of the three settlements was the same.
Figure 33. It is necessary to locate the ambulance station so that it could serve all three settlements
Let us first solve a simpler problem. Let there be only two settlements - and (segment ). Where should the station be located in this case?
Consider a line that passes through the middle of the segment and is perpendicular to it. This line is called the midpoint perpendicular
(see fig. 34).
Fig. 34. Midpoint perpendicular to a line segment
Consider any point which belongs to the midpoint of . Triangles and are equal by the first sign of equality of triangles (two cathetuses and the angle between them): , because , is the midpoint of , is common, . Thus (see Fig. 35).
Figure 35. Equal triangles and
It is not difficult to prove that any point, for instance, which does not lie on the midpoint perpendicular, will not satisfy the property, i.e. (see (a). Fig. 36).
Figure 36. Point , is the midpoint perpendicular:
Proof
How can we prove that any point that is not on the midpoint perpendicular is not equidistant from the ends of the segment? Again we will use the contrary method.
Suppose a point is not on the midpoint perpendicular to the segment , but it is equidistant from the ends of the segment: (see Fig. 37).
Fig. 37. The point is the midpoint perpendicular to ,
Connect the point with the midpoint of the segment - point . Consider the triangles and .
Fig. 38. Triangles considered and
In them: (by our assumption), , since , is the midpoint of the segment , is common. By the third sign of a triangle (three sides) the triangles and are equal.
But then : they are adjacent (i.e. they form an unfolded angle and their sum is equal to ). So . But then the line is perpendicular to the segment and passes through its middle. Hence it is the midpoint perpendicular to .
We obtain a contradiction (the point should not lie on the midpoint perpendicular.) So the initial assumption is wrong, and if the point does not lie on the midpoint perpendicular, then it will not be equidistant from the ends of the segment.
Let us formulate an equivalent definition of the midpoint perpendicular
- is the geometric place of points (GMT) equidistant from the ends of the segment.
It is clear that the emergency station must be located on the midpoint perpendicular to the segment (ideally, at the point, the middle of the segment, because in this case the distance from it to the points will be the smallest).
More about the content
The triangles are mostly drawn on the wrists, shins and the back of the neck (if we are talking about men), while girls much more often like the simplest figure of three lines. At the same time, they try to apply it on the forearm, scapula, neck, foot, and lower back. Interestingly, among criminals, the triangle is interpreted in two ways: as an expression of life's impasse and utter hopelessness, as well as a regret for the crooked path chosen.
The advantage of geometric shapes is that they are universal, independent of time and fleeting fashion, look beautiful on the skin of any color, on people of all ages and genders. In addition, the triangle is variable: you can make the corners at the base sharper or more obtuse, make the top tucked up or flattened. There's no particular point to it, except that you'll like it.
Even an isosceles triangle is quite possible to flip the top down. And if you write it in a square, you will have a hint at the combination of heavenly and earthly principles. Color choose for yourself, there are no rules.
The area of right triangle
One of the most important characteristics of a geometric figure in the plane is its area. We have already derived the formula for the area of a triangle using the formula for the area of a rectangle. Consider a right triangle with sides and , which form a right angle (see Fig. 1). These sides in a right-angled triangle are called the cathetuses
, and the third side is the the hypotenuse .
.
Figure 1. Rectangular triangle with cathetuses and
Now consider a rectangle with sides and . Draw the diagonal (see Fig. 2).
Fig. 2. Rectangle with sides and a drawn diagonal
It is easy to prove, using the sign of equality of triangles (by two sides and the angle between them), that we have two equal right-angled triangles. Equal triangles have equal areas, so we get:
From whence:
So we have obtained that The area
of any of a right triangle
is equal to the half product of the lengths of its cathetuses.
A painted triangle
The color palette also brings semantic accents to the symbolism. For example, a triangle painted red gives away a passionate and energetic nature. A green triangle indicates that a person needs protection. In this case, the geometric figure acts as a talisman, which gives a sense of security. Cheerful, positive and open-minded people prefer orange triangles. Black triangles symbolize emptiness and darkness. But it can also indicate the seriousness and focus of the owner.
In addition to the standard shading, customers are increasingly choosing sketches with triangles, inside which are tattooed pictures. Girls prefer to tattoo triangles with flowers. Men insert small biomechanical-style fragments into the triangle. People interested in the secret orders will certainly appreciate the tattoo triangle with an eye inscribed in it - the main symbol of the Masonic lodge. These tattoos look very original and offer plenty of room for your own imagination.
Commentary
- There are other variants of the transcription of the surname Reuleaux. For example, I. M. Yaglom and V. G. Boltyansky in their book "Convex Figures" call it a "Reuleaux triangle".
- The reference line passes through one point of the boundary of the figure, not dividing the figure into parts.
- ↑ The center of a Rello triangle is the intersection point of all the medians, bisectors, and altitudes of its right triangle.
- For a R¨olo triangle this circle coincides with one of the three circles which form its boundary.
- This statement follows from a set of two theorems, Didon's classical isoperimetric problem and Barbier's theorem.
- This property is quite characteristic of
figures of constant width. In other words, any figure around which a described square can be "rotated" will be a figure of constant width. - In the original. "We have all heard about left-handed monkey wrenches, fur-lined bathtubs, cast-iron bananas. We have all classed these things with the ridiculous and refused to believe that anything like that could ever happen, and right then along comes a tool that drills square holes!"
- In other words, equal to these arcs.
How to use the jackknife as a talisman
The meaning of the wanknut in everyday life is the pursuit of knowledge.
It is worn to immerse yourself in the mysteries of the world around you and find your own life meaning.
Also, the talisman can develop the wearer's ability to clairvoyance and logical thinking.
At the same time, it optimizes cognitive functions (memory, attention, etc.).
But at the same time, such a talisman is dangerous because it calls on the wearer serious tests.
If a person wearing this sign, will withstand the hardships heaped upon him, he will be granted access to hidden knowledge.
The talisman is used in the form of all kinds of jewelry: bracelet valcnut, pendants, rings, rings, earrings, pendants.
It is also still a common practice to put this sign on the body as a tattoo.
WARNING: Wearing the amulet valknut requires a thoughtful attitude. It is believed that its location at the heart significantly worsens health (that is, the test for the bearer will be on the part of his physical body). Therefore, it is advisable to wear this sign either above or below the location of the heart. This sign is also a danger to military personnel, because previously such a symbol was carried on those warriors who went to his last battle.
Inverted.
An inverted triangle tattoo has recently become popular. This symbol had no special meaning for a long time, but at the moment it is associated with:
- The opposite meaning of the standard triangle. This symbol has come to mean the desire for chaos, non-standard behavior;
- irrationality of thought, rejection of standards, high creativity.
Other marks on clothing tags
Similar universal markings are used, which are identical in all countries and on all continents. They are understandable and can be explained without words, you just need to know the system of symbols.
Washing process on things will show a picture of a bowl of water with temperature mode and washing methods, drying is indicated by a square, dry cleaning by a circle with different letters inside it, and ironing by a schematic picture of an iron.
Washing
The schematic depiction of a trough of water is the symbolism for the washing process.
Inside it, the labels may contain such numbers and drawings:
- 95 - wash and boil. Suitable for cotton, linen and light-colored items.
- 60 or three dots - hot water wash for fabrics that are contraindicated in boiling.
- 40 or two dots - washable in warm water and neutral stain removers for bright cotton and synthetic light garments.
- 30 or one dot - wash only with cold water at gentle mode for wool clothes.
- Hand dipped in water - wash item only by hand.
- Bowl with liquid without markings - washing is possible.
- Crossed out trough - washing is prohibited. Only dry cleaning is possible.
- One line under the bowl - gentle washing, it is not recommended to subject to strong mechanical treatment.
- Two lines horizontally under the bowl of water - gentle mode, cleaning delicate things. A lot of water, minimum mechanical treatment and a quick rinse should be used.
Drying and spinning
The drying pattern is a square shape.
If only a square is depicted, dry things without fear.
If a crossed out square is drawn, drying is not recommended or allowed.
A square figure with a circle in the middle indicates that wringing and drying in a washer or dryer is allowed.
If the circle in the square is crossed out, drying and spinning is prohibited.
A crossed out rope - spinning is not recommended or prohibited, it is better to wash without spinning.
In the square a circle with two dots - drying is possible if you use a medium temperature mode.
If the square represents three vertical lines, dry without wringing.
If the square has one line in the horizontal dimension, this fabric can be dried only horizontally.
The dots inside the circle placed in the square will tell you at what temperature parameters the thing must be dried: three dots - choose a high parameter, two - medium and one - very low.
Dry cleaning .
The symbol for dry cleaning on clothes tags is a circle.
If an empty circle is depicted, dry cleaning of the thing is possible.
If the circle is crossed out with two lines, dry cleaning is forbidden, it can ruin the fabric.
If the circle has a big "A," use all kinds of chemical solvents for cleaning.
The letter "P" in the circle means cleaning is possible with hydrocarbon, chloroethylene or monofluorotrichloromethane.
Ironing
For the sake of accessibility and comprehensibility, a schematic picture in the form of an iron is used to indicate ironing. Whether the picture shows the iron itself or the crossed-out iron on the label determines the ironing temperature and its suitability for the type of fabric.
If there is only one iron on the label, iron without fear.
If there is a picture of a crossed-out iron with intersecting lines, do not iron the garment.
Mug iron - Iron wool garments to 140° C.
An iron with dots will show you the safe level of heat at which you can iron things:
- Three dots on the iron - iron the product at a sufficiently high heat level - up to 200 ° C.
- Iron with two dots - you can iron at a medium temperature level - up to 150 ° C.
- With one - ironing is recommended at a low temperature mode, up to 110 ° C. It is used for synthetic clothing.
If you see an iron symbol with a crossed out pattern indicating steam, it is strictly forbidden to steam the garment.
After deciphering all the symbols, be it the crossed out triangle on the garment or the square with a circle inside, follow the care instructions for your purchase, so you keep its original appearance for a long time without ruining the fabric. Try to throw in one wash, only clothes that are suitable for one mode. Choose a detergent recommended on the label.
Tattoo triangle value in the zone
People who are in prison or have already come out of there tattoos have their own meanings. If for law-abiding citizens triangles mean mostly spiritual moments, the connection of close hearts, the unity of soul, body and mind, then for the prison culture more down-to-earth meanings are used.
A prisoner who tapes himself a triangle demonstrates confusion of spirit, a dead-end situation in life, and regret for what he has done. Choosing additional symbols for combinations with this geometric figure, it is necessary to take into account their meaning in the subculture.