Diamond image. Rhombus as a geometric figure. The diagonals of a rhombus are the bisectors of its angles
A rhombus is a parallelogram in which all sides are equal.
The diamond drawing is carried out on the basis of GOST 2.109-73 - a unified system of design documentation (ESKD).
You can download this simple drawing for free to use for any purpose. For example, for placement on a nameplate or sticker.
How to draw a drawing:
You can draw a drawing either on a sheet of paper or using specialized programs. No special engineering knowledge is required to complete simple sketch drawings.
A sketch drawing is a drawing made “by hand”, observing the approximate proportions of the depicted object and containing sufficient data for the manufacture of the product.
The design drawing with all the technological data for manufacturing can only be completed by a qualified engineer.
To designate in the drawing, you must perform the following operations:
1. Draw an image;
2. Add dimensions (see example);
3. Specify for production (read more about technical requirements below in the article).
It is most convenient to draw on a computer. Subsequently, the drawing can be printed on paper using a printer or plotter. There are many specialized programs for drawing on a computer. Both paid and free.
Drawing example:
This image shows how simple and quickly drawing can be done using computer programs.
List of programs for drawing on a computer:
1. KOMPAS-3D;
2. AutoCAD;
3. NanoCAD;
4. FreeCAD;
5. QCAD.
Having studied the principles of drawing in one of the programs, it is not difficult to switch to working in another program. Drawing methods in any program are not fundamentally different from each other. We can say that they are identical and differ from each other only in convenience and the presence of additional functions.
Technical requirements:
For the drawing, it is necessary to indicate dimensions sufficient for manufacturing, maximum deviations and roughness.
The technical requirements for the drawing should indicate:
1) Manufacturing and control method, if they are the only ones that guarantee the required quality of the product;
2) Indicate a specific technological method that guarantees that certain technical requirements for the product are met.
A little theory:
A drawing is a projection image of a product or its element, one of the types of design documents containing data for the production and operation of the product.
A drawing is not a drawing. The drawing is made according to the dimensions and scale of the real product (structure) or part of the product. Therefore, to carry out drawing work, the work of an engineer with sufficient experience in producing drawing work is necessary (however, to beautifully display a product for booklets, it is quite possible that you will need the services of an artist who has an artistic view of the product or part of it).
A drawing is a constructive image with necessary and sufficient information about dimensions, manufacturing method and operation. You can download the drawing presented on this page for free.
A drawing is an artistic image on a plane created by means of graphics (brush, pencil or specialized program).
A drawing can be either an independent document or part of a product (structure) and technical requirements related to surfaces processed together. Instructions for joint processing are placed on all drawings involved in the joint processing of products.
For more information on drawings, technical requirements for design and indication of manufacturing methods, see GOST 2.109-73. See the list of standards for the development of design documentation.
Information for ordering drawings:
In our design organization, you can create any product (both parts and assemblies), which will include a drawing of a diamond as an element of the design documentation of the product as a whole. Our design engineers will develop documentation in the shortest possible time in strict accordance with your technical specifications.
Sometimes there is a need to do a basic task, but it turns out that we do not know how to do it. For example - how to draw a rhombus. In fact, everything is very simple.
In this article you will learn how to draw a rhombus correctly and what kind of geometric figure it is.
What is a rhombus?
A rhombus is a type of parallelogram, the peculiarity of which is that the opposite sides of this figure are parallel to each other, and in a rhombus they are also equal to each other. The definition of a rhombus to the general form of a parallelogram is indicated by the fact that opposite angles are equal.
How to draw a rhombus
There are several ways to draw a figure like a rhombus. In this article we will look at two simple methods.
For the first method, we will need: a pen or pencil, an eraser, a checkered sheet from a school notebook, a ruler or any similar straight object, if the exact dimensions of the rhombus are not important.
- So, first, let's draw a point at one of the intersections of the cell lines. It is better, of course, to place the point not too close to the edges. We decide on the size of the figure.
- Next, from the middle point, count the required number of cells to the left (or right) and place another point. On the opposite side, through the same number of cells, draw a third point. Now we do the same in the up and down directions. The sequence does not matter, the main thing here is to count the same distance from the midpoint to the left and right and separately up and down. That is, if four cells are counted to the right, and six cells up, respectively, four cells to the left, six cells down.
- We connect all the points together with a ruler or any other suitable object, except for the middle one. The middle point can be erased with an eraser if you used a pencil. The rhombus is ready.
The second method is similar to the first, but we will draw on clean paper without cells. For this we need: a pencil and/or pen, an eraser, a blank sheet of paper, a ruler and a square (or any object with a right angle).
- We decide on the sizes. Draw a point.
- Take a ruler and place a point at the required distance from the midpoint on the left side. We connect them with a pencil so that the line passes through the middle point. We perform similar actions in the opposite direction.
- We also draw a point at the top and bottom, but use a square so that the line between the top and bottom points is perpendicular to the line between the left and right.
- Let's connect all the dots. Use an eraser to erase the lines in the middle of the figure.
Lesson Objectives
Continue to introduce students to such a geometric figure as a rhombus;
To consolidate knowledge about concepts such as rhombus and square, and also learn to determine their difference;
To refresh students' knowledge about the properties and characteristics of a rhombus;
Continue to improve students' knowledge of geometric shapes through problem solving.
Arouse interest in geometry lessons.
Lesson Objectives
Repeat, generalize and consolidate the acquired knowledge about such a geometric figure as a rhombus;
Continue to develop skills in constructing geometric figures;
Improve rhombus construction skills using drawing tools;
Continue to consolidate students’ knowledge using practical assignments;
Continue to develop attention, perseverance and desire for the cognitive process.
Lesson Plan
1. Disclosure of the main topic of the lesson, definition of the geometric figure “Rhombus”.
2. Familiarization with the properties and characteristics of a rhombus.
3. Theorems and their proof.
4. How to draw a rhombus. Ways to depict a rhombus.
5. How to find the area of a rhombus?
6. Repetition of the material covered.
7. Interesting facts.
8. Homework.
Definition of a rhombus as a geometric figure
A rhombus is a parallelogram in which all sides are equal. If a rhombus has right angles, then it is called a square.
The term “Rhombus” itself, translated from Greek, means “tambourine”. Of course, in our understanding, the tambourine, as a musical instrument, has a round shape. But now the tambourines are made round, but in ancient times it had a square or diamond shape.
Let's look at the basic definitions of a rhombus and try to understand what this geometric figure is.
A rhombus is an equilateral parallelogram that has equal sides but unequal angles.
Unlike a square, a rhombus is an equilateral oblique angle.
As always, we receive many definitions of this or that geometric figure, but this does not mean that every student should sit down and “memorize” these very definitions. The difference in definitions is how broadly they describe our geometric figure. The most important thing is to understand what the definition is talking about and the ability to imagine the figure. If you adhere to these two rules, then you yourself will be able to write or add a couple of definitions.
Properties of a rhombus
2. Its second property is that all diagonals of a rhombus intersect at right angles. At the point of intersection, the diagonals of the rhombus are divided in half.
3. The bisectors of the angles of a rhombus are its diagonals.
4. To find the sum of the squares of the diagonals of a rhombus, you need to multiply the square of its side by four.
5. Opposite sides of a rhombus are equal;
6. The sum of the angles of a rhombus that are adjacent to one side is 180 degrees.
Signs of a diamond
A parallelogram is a rhombus if it meets the following conditions:
1. Firstly, all its sides are equal to each other;
2. Secondly, the diagonals of a rhombus intersect at right angles.
3. Thirdly, if the diagonals of its angles are bisectors.
4. Fourthly, if its two adjacent sides are equal to each other.
5. Fifthly, if at least one of the diagonals is a bisector of a parallelogram.
Theorems and their proof
Now let's take a closer look at the properties and characteristics of a rhombus, proving the theorems:
Theorem 1
Theorem 2
It follows that:
1. A rhombus has two axes of symmetry - diagonals AC and BD.
2. Its diagonals are mutually perpendicular.
3. And also are the bisectors of its angles.
Area of a rhombus
The area of a rhombus is equal to half the product of its diagonals. But since a rhombus is essentially a parallelogram, its area can be found by multiplying its sides by its height.
Formulas for the area of a rhombus:
Where: a – is the side of the rhombus
D – its large diagonal is indicated
d – designated smaller diagonal
α is an acute angle
β – is an obtuse angle
The area of any geometric figure is the part of the surface that is limited by the closed contour of this figure. And the area of a rhombus is expressed by the number of square units it contains.
How to draw a rhombus
To draw a rhombus, we will use the properties of the diagonals of a rhombus. We already know that the diagonals of our geometric figure are mutually perpendicular and bisected at the point of intersection. Therefore, the easiest way to start constructing a rhombus is to construct its diagonals.
First way
And so, first of all, we select a point from which we lay out segments of the same length to the left and right, and identical segments of a different length up and down.
Now all we have to do is connect the ends of these segments, and as a result we will get a rhombus.
Second way
A rhombus can also be drawn without using diagonals. In this case, you only need to determine the ends of the diagonals and then connect the points with segments.
Third way
And finally, the third method, drawing a rhombus can be done using a ruler. Since you and I know that a rhombus has equal sides, we first need to draw its lower part. Then you need to set aside an equal segment from it. And since the third side is parallel to the first, connecting the ends of the first and third segments, we get a rhombus.
Repetition
You have already become acquainted with such a geometric figure as a rhombus and understand that the square is its special case.
1. Therefore, let's remember the definition, what is a square? Give your own definition of a square.
2. What properties does a square have? Name them.
3. What is the difference between a rhombus and a square, if the square is its special case?
4. What figure is called a quadrilateral, and does a rhombus belong to this geometric figure?
5. What types of quadrilaterals have you already studied? Name them.
6. What differences exist between them?
It's interesting to know
Did you know that if we take a rectangle and connect the midpoints of its sides with segments, we will end up with a rhombus.
But if, on the contrary, we take a rhombus and try to connect its midpoints with segments, then we will get a geometric figure like a rectangle.
If you take a parallelogram with equal heights, then such a parallelogram is a rhombus.
Did you know that the name of the card suit of tambourines, which has a rhombic shape, appeared back in the days when the tambourine was far from round in shape, but in the form of a rhombus or square.
For the first time the word "rhombus" was used in his vocabulary by Gerron and Pope of Alexandria.
Homework
1. Do you think a rhombus is a parallelogram that has at least one right angle?
2. Is it true that every parallelogram is a rhombus?
3. If the diagonals of a parallelogram are 5 cm and 7 cm, can this parallelogram be a rhombus?
4. If the diagonals of a parallelogram are equal, then can it be a rhombus?
5. What is the special property of a rhombus that its diagonals have, besides the fact that they are divided in half by the point of intersection?
6. Think about where a geometric figure such as a rhombus is used in everyday life?
Rhombus- one of the simplest geometric figures. We encounter a rhombus so often in geometric problems that the words “fantasy” and “rhombus” seem to us to be incompatible concepts. Meanwhile, the amazing, as they say, is nearby... in Britain. But first, let's remember what a “rhombus” is, its signs and properties.
The term “rhombus” translated from ancient Greek means “tambourine”. And this is no coincidence. Here's the thing. Everyone has seen a tambourine at least once in their life. And everyone knows that it is round. But a long time ago, tambourines were made in the shape of a square or rhombus. Moreover, the name of the suit of diamonds is also associated with this fact.
From geometry we imagine what a rhombus looks like. This is a quadrangle, which is depicted as a tilted square. But under no circumstances should a rhombus and a square be confused. It would be more correct to say that a rhombus is a special case of a parallelogram. The only difference is that all sides of a rhombus are equal. To quickly and correctly solve geometry problems, you need to remember the properties of a rhombus. By the way, a rhombus has all the properties of a parallelogram. So:
Properties of a rhombus:
- opposite sides are equal;
- opposite angles are equal;
- the diagonals of a rhombus intersect under a straight line and are divided in half at the intersection point;
- the sum of angles adjacent to one side is 180°;
- the sum of the squares of the diagonals is equal to the sum of the squares of all sides;
- the diagonals are the bisectors of its angles.
Signs of a diamond:
- if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus;
- If the diagonal of a parallelogram is the bisector of its angle, then the parallelogram is a rhombus.
And one more important point, without knowledge of which it is not possible to successfully solve the problem - formulas. Below are formulas for finding the area of any rhombus, which are used depending on the known data: height, diagonal, side, radius of the inscribed circle. The following formulas use the following conventions: a – side of the rhombus, h a – height drawn to side a, A– the angle between the sides, d 1 d 2 – the diagonals of the rhombus.
Basic formulas:
S = a 2 sin A
S = 1/2 (d 1 d 2)
S = 4r 2 / sin a
There is another formula that is not used so often, but is useful:
d 1 2 + d 2 2 = 4a 2 or the sum of the squares of the diagonals is equal to the square of the side multiplied by 4.
Now it's time to go back to the very beginning. What's so surprising 
maybe in this figure? It turns out that in the 19th century a rhombus was found during archaeological excavations. Yes, not simple, but golden, and in the most literal sense of the word! This find from the British Bash Mound was found in the Wilsford area, not far from the famous Stonehenge. The mysterious diamond is a polished plate on which unusual patterns are engraved. Its size is 15.2 x 17.8 cm (rhombus with only a small caveat). In addition to the edging, the plate has three smaller diamond-shaped patterns that are supposedly nested within each other. At the same time, a rhombic mesh is engraved in the center of the latter. Along the edges of the diamond is a chevron pattern - nine symbols on each side of the diamond. There are thirty-six such triangles in total.
Of course, this product is very expensive, but it is also obvious that the creation of such a diamond had a specific purpose. But for a long time scientists could not figure out which one.
One of the more plausible and accepted versions concerns Stonehenge itself. It is known that the structures of Stonehenge were built gradually over several centuries. It is believed that construction began around 3000 BC. It should be taken into account that gold in Britain became known already somewhere from 2800 BC. From this we can make the assumption that the golden diamond could well have been a priest’s instrument. In particular, the visor. This hypothesis was brought to the attention of modern scientists by Professor A. Tom, a famous researcher of Stonehenge, in the last quarter of the twentieth century.
Not everyone can imagine that ancient builders could accurately determine the angles on the ground. However, the English researcher D. Furlong proposed a method that, in his opinion, the ancient Egyptians could have used. Furlong believed that our ancestors used predetermined aspect ratios in right triangles. After all, it has long been known that the Egyptians widely used a triangle with sides of three, four and five dimensional units. Apparently, the ancient inhabitants of the British Isles knew many similar techniques.
Well, even if we imagine that the people who built Stonehenge were excellent surveyors, how could a golden diamond help them with this? It is unlikely that any modern surveyor will be able to answer this question. Most likely, the fact that Furlong was a surveyor by profession enabled him to solve this riddle. After careful study, the researcher came to the conclusion that the polished gold diamond with markings is excellent for use as a reflector of sunlight, in other words, a special measuring mirror.
It was proven that to quickly determine the azimuth on the ground with fairly small errors, it was necessary to use two similar mirrors. The scheme was as follows: one priest, for example, stood on the top of one hill, and the other in the adjacent valley. It was also necessary to first establish the distance between the priests. This can be done in simple steps. Although they usually used a measuring stick, since the results were more reliable. Two diamond-shaped metal mirrors provide a right angle. And then it’s easy to measure almost any required angles. D. Furlong even gave a table of such pairs of integers, which allows you to set any angle with an error of one degree. Most likely, this was the method used by the priests of the Stonehenge era. Of course, to confirm this hypothesis it would be necessary to find a second, paired golden diamond, but, apparently, this is not worth it. After all, the evidence is already quite obvious. In addition to calculating azimuths on the ground, another ability of the amazing golden diamond was discovered. This amazing little thing allows you to calculate the moments of the winter and summer solstices, the spring and autumn equinoxes. This was an indispensable quality for the life of the ancient Egyptians, who then worshiped primarily the Sun.
It is likely that the imposing appearance of the diamond was not only an indispensable tool for the priests, but was also a spectacular decoration for its owner. Generally speaking, the vast majority of seemingly expensive jewelry found today are, as we learn later, measuring instruments.
So, people have always been attracted to the unknown. And, judging by the fact that so much remains mysterious and unproven in our world, people will continue to try to find clues to antiquity for a long time. And this is very cool! After all, we can learn a lot from our ancestors. To do this you need to know a lot, be able to and study. But it is impossible to become such a highly qualified specialist without basic knowledge. After all, every great archaeologist and discoverer once went to school!
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08.08.2014
Relief patterns with knitting needles ‒ this is an alternation when knitting front and back loops, while the fabric turns out to be three-dimensional due to the combination of convex and concave sections, and also quite dense (without gaps), so such patterns are especially expressive. There are a great variety of relief patterns, they differ in small or large repeat. These patterns are ideal for plain cotton, cotton rayon, silk and linen blends. If the yarn is thick, then the pattern looks especially prominent, and if it is thin, then the result will be an exquisite, noble structure. Relief patterns are quite easy to knit, so they are recommended for beginners, because... help them gain skill and experience. Confident knitters also do not ignore embossed patterns, because they are convenient for combining with openwork and give it a special elegance. To prevent the charm of relief patterns from disappearing, you should not iron or steam them, just moisten them and let them dry flat.
We offer you a large collection of simple relief patterns with rhombuses and rhombuses
for knitting with samples, diagrams, descriptions and symbols.
Choose and create with pleasure!
Attention! Pattern diagrams are shown as they look from the front side.
Abbreviations:
n. - loop;
persons - facial;
purl - purl;
chrome - edge;
cross. - crossed.
Pattern 81 "Pomegranate"(for 6 loops and 6 rows)
Pattern 80 "Simple relief"(for 14 loops and 12 rows)
Pattern 79 "Structural ornament"(for 11 loops and 30 rows)
Pattern 78 "Coffee beans"(for 18 loops and 36 rows)
Pattern 77 "Diamond cells"(for 6 loops and 16 rows)
Pattern 76 "Expressive rhombuses"(for 16 loops and 18 rows)
Pattern 75 "Charm"(for 18 loops and 24 rows)
Pattern 74 "Giza Plateau"(for 16 loops and 36 rows)
Pattern 73 "Rhombuses with insert"(for 18 loops and 22 rows)
Pattern 72 "Curly rhombuses"(for 22 loops and 32 rows)
Pattern 71 "Simple rhombuses"(for 10 loops and 20 rows)
Pattern 70 "Pastila"(for 12 loops and 12 rows)
Pattern 69 "Parquet"(for 8 loops and 16 rows)
Pattern 68 "Elongated rhombuses"(for 8 loops and 10 rows)
The pattern is double-sided, looks the same on the front and back sides.
For the sample, cast on the number of loops that are a multiple of 8 + 2 chrome.
1 row
2nd row: 1 chrome; * 3 p.; 4 persons; 1 purl**; repeat from * to **; 1 chrome
3rd row: 1 chrome; * 2 persons; 4 purl; 2 persons**; repeat from * to **; 1 chrome
4 row: 1 chrome; * 1 purl; 4 persons; 3 p.**; repeat from * to **; 1 chrome
5 row
6 row: 1 chrome; * 4 purl; 4 persons**; repeat from * to **; 1 chrome
7 row: 1 chrome; * 1 person; 4 purl; 3 persons**; repeat from * to **; 1 chrome
8 row: 1 chrome; * P2; 4 persons; 2 purl**; repeat from * to **; 1 chrome
9 row: 1 chrome; * 3 persons; 4 purl; 1 person**; repeat from * to **; 1 chrome
10 row: 1 chrome; * 4 persons; 4 purl**; repeat from * to **; 1 chrome
Repeat from the 1st to the 10th row.
Pattern 67 "Graphic rhombuses"(for 28 loops and 16 rows)
Pattern 66 "Rhombuses from triangles"(for 14 loops and 14 rows)
Pattern 65 "Diamonds from triangles"(for 8 loops and 16 rows)
Pattern 64 "Strike through diamonds"(for 14 loops and 32 rows)
Pattern 63 "Noble structure"(for 14 loops and 30 rows)
Pattern 62 "Beautiful relief"(for 12 loops and 32 rows)
Pattern 61 "Unusual structure"(for 10 loops and 20 rows)
Pattern 60 "Chain of diamonds"(for 8 loops and 20 rows)
Pattern 59 "Exquisite structure"(for 16 loops and 32 rows)
Pattern 58 "Moths"(for 12 stitches and 24 rows)
Pattern 57 "Moths"(for 10 stitches and 20 rows)
Pattern 56 "Rombita"(for 28 loops and 28 rows)
Pattern 55 "Tenderness"(for 22 loops and 36 rows)
Pattern 54 "Finishing rhombus"(for 17 loops and 30 rows)
Pattern 53 "Cones" reverse side of the "Candles" pattern (for 12 loops and 32 rows)
Pattern 52 "Candles" reverse side of the "Pine cones" pattern (for 12 loops and 32 rows)
Pattern 51 "Bunches"(for 8 loops and 28 rows)
Pattern 50 "Diamond"(for 14 sts and 28 rows)
Pattern 49 "Diamond"(for 10 stitches and 24 rows)
Pattern 48 "Rhombuses in a zigzag"(for 16 loops and 20 rows)
Pattern 47 "Bows in rhombuses"(for 20 loops and 18 rows)
Pattern 46 "Original relief"(for 26 loops and 34 rows)
Pattern 45 "Crossroads"(for 12 loops and 24 rows)
Pattern 44 "Brocade"(for 20 loops and 14 rows)
Pattern 43 "Diamond mosaic"(for 12 loops and 28 rows)
Pattern 42 "Chess of rhombuses"(for 14 loops and 28 rows)
Pattern 41 "Combined structure"(for 16 loops and 32 rows)
Pattern 40 "Beaded diamonds"(for 12 loops and 32 rows)
Pattern 39 "Structural rhombuses"(for 12 loops and 18 rows)
Pattern 37 "Pearl diamonds on the front surface"(for 10 loops and 10 rows)
Pattern 36 "Grape paradise"(for 10 loops and 24 rows)
Pattern 35 "Pearl rhombuses"(for 10 loops and 20 rows)
Pattern 34 "Strips of pearl rhombuses"(for 10 loops and 16 rows)
Pattern 33 "Traditional rhombuses"(for 20 loops and 24 rows)
Pattern 32 "Triangles" reverse side of the Mirage pattern (for 16 loops and 32 rows)
Pattern 31 "Mirage" reverse side of the "Triangles" pattern (for 16 loops and 32 rows)
Pattern 30 "Rhombuses with stripes"(for 18 loops and 36 rows)
Pattern 29 "Vertical of rhombuses and bows"(for 22 loops and 18 rows)
Pattern 28 "Horizontal of rhombuses and bows"(for 22 loops and 20 rows)
Pattern 27 "Stained glass"(for 14 loops and 14 rows)
Pattern 26 "Kaleidoscope"(for 12 loops and 12 rows)
Pattern 25 "Relief rhombuses"(for 15 loops and 30 rows)
Pattern 24 "Rep diamonds"(for 6 loops and 12 rows)
Pattern 23 "Linear rhombuses"(for 12 loops and 12 rows)
Pattern 22 "Chain-link mesh"(for 8 loops and 16 rows)
Pattern 21 "Mesh"(for 8 loops and 14 rows)
Pattern 20 "Armor mesh"(for 14 loops and 28 rows)
