General rules for any foundation
Select a starting point. The first side of our foundation needs to be tied to some object on our site.
Example. Let's make sure that our foundation (house) is parallel to one of the sides of the fence. Therefore, we stretch the first string equidistant from this side of the fence to the distance we need.
Construction right angle(90⁰). As an example, we will consider a rectangular foundation in which all angles are as close as possible to 90⁰.
There are several ways to do this. We will look at 2 main ones. © www.site
Method 1. Golden triangle rule
To construct a right angle we will use the Pythagorean theorem.
In order not to go deep into geometry, let's try to describe it more simply. So that between two segments a And b to make an angle of 90⁰, you need to add the lengths of these segments and derive the root of this sum. The resulting number will be the length of our diagonal connecting our segments. It is very easy to do the calculation using a calculator.
Usually, when marking the foundation, the dimensions of the sides are taken so that when taken from the root, a whole number is obtained. Example: 3x4x5; 6x8x10.
If you have a tape measure, then in general there will be no problems if you take segments that are different from those in common use. For example: 3x3x4.24; 2x2x2.83; 4x6x7.21
If we made measurements in meters, then the values turn out to be very clear: 4m24cm; 2m83cm; 7m21cm.
Calculator
It is also worth noting that measurements can be made in any length measurement system; the main thing is to use the aspect ratio we know: 3x4x5 meters, 3x4x5 centimeters, etc. That is, even if you don’t have a tool for measuring length, you can take, for example, a staff (the length of the staff does not matter) and measure it with it (3 staff x 4 staff x 5 staff).
Now let's see how to put this into practice.
Instructions for marking a rectangular foundation
Method 1. Rules of the golden triangle (i.e. Pythagoras)
Let's look at the example of building a rectangular foundation with dimensions 6x8m using the golden triangle (so-called Pythagoras).
1. Mark the first side of the foundation. This is the easiest part in constructing our rectangle. The main thing to remember. If we want our foundation (house) to be parallel to one of the sides of the fence or other object on the site or beyond, then we make the first line of our foundation equidistant from the object we have chosen. We described this procedure above. To place the first string, you can use pegs firmly fixed in the ground, but in ideal For this purpose, use cast-offs. We will use it. We will make the distance between cast-offs for this side 14 m: between cast-offs and future corners, 3 m and 8 m under the foundation.
2. Pull the second string as perpendicular to the first as possible. In practice, it is difficult to pull it perfectly perpendicular, so in the figure we also showed it slightly deflected.
3. We fasten both strings at the intersection point. You can fasten it with a staple or tape. The main thing is to be reliable.
4. We begin to form a right angle using the Pythagorean theorem. We will build right triangle with legs 3 by 4 meters and a hypotenuse of 5 meters. To begin with, we measure 4 meters from the intersection of the strings on the first string, and 3 meters on the second. Place marks on the lace using tape (clothespin, etc.).
5. Connect both marks with a tape measure. We fix one end of the tape measure at the 4 meter mark and lead it towards the 3 meter mark on the other string.
6. If we have a right triangle, then both marks should converge at a distance of 5 meters. In our case, the marks did not match. Therefore, in our case, we move the string to the right until the 3 m mark coincides with the 5 m division of the tape measure.
7. As a result, we got a right triangle with an angle of 90⁰ between the two strings.
8. We don’t need any more marks and they can be removed.
9. Let's start building a rectangle. We measure on both strings the lengths of the sides of our foundation to be 6 and 8 meters, respectively. We put marks on the strings.
10. Pull the third string as perpendicular to the first string as possible. We fasten both strings at the 8 m mark.
11. Pull the fourth string as perpendicular to the second string as possible. We fasten both strings at 6 meter marks.
12. We make marks on the third string 6 meters and on the fourth 8 meters.
13. To get a quadrilateral with right angles in our case, it is necessary that both marks on the third and fourth strings coincide. To do this, move both strings until the marks connect.
14. As a result, if everything was measured correctly, then we should get a regular rectangle. Let's check if it turned out by measuring the diagonals.
15. We measure the lengths of the diagonals. If they are the same, as in our case, we have a regular rectangle. The diagonals have the same length and isosceles trapezoid. But we know one angle of 90⁰, and in an isosceles trapezoid there are no such angles.
16. Ready marking of a rectangular foundation using the Pythagorean theorem. © www.site
Method 2. Web
A very simple way to make markings in the form of a rectangle with corners of 90⁰. The most important thing we need is twine that does not stretch, and the accuracy of your measurements using a tape measure.
1. Cut the pieces of twine that we will need to form the markings. IN in this example we are building a foundation with sides 6 by 8 meters. Also, to correctly construct a rectangle, we will need equal diagonals, which for a 6 by 8 meter rectangle will be equal to 10 meters (i.e. Pythagoras is described above). You also need to take a reserve length of string for fastening.
2. We connect our “web” as in the picture. We fasten the sides with diagonals in 4 places in the corners. The diagonals themselves do not need to be fastened at the intersection point.
3. Pull the first string (points 1,2). We will secure it with pegs. The main thing is that the pegs hold firmly in the ground and do not move away when our structure is pulled. This important point need to be taken into account.
4. We tighten corner 3. The main condition is that string 1-3 and diagonal 2-3 do not sag and are as tight as possible. After fixing with a peg at point 3, we have an angle at point 1 of 90⁰.
5. Pull corner 4 and install the peg. We make sure that the twine at points 2-4, 3-4 and diagonal 1-4 do not sag and are as tight as possible.
6. If all conditions are met, then the result should be a rectangle with angles as close as possible to 90⁰.
Marking for the foundation of the house
We make a two-tier cast-off. The lower tier is the level of the pillars.
The upper tier of cast-off is the level of the grillage.
Create a rectangle for the outer contour using the so-called Pythagoras. Then we retreat by an amount equal to the width of the tape and make an internal contour.
The easiest way to mark. We build a rectangle according to the dimensions of the foundation using the Pythagorean theorem to find the right angle. © www.site
From the author
In this article, we looked at how to make markings for the foundation with your own hands by constructing a rectangle with angles of 90⁰. In general, there is nothing complicated about the markup. The cost of the issue is the cost of twine, boards for casting (an economical option - pegs) and the ability to use a tape measure.
A right angle between walls is necessary quite often. For example, to properly install a bathtub, kitchen sink or table. But most people simply do not take this need into account, and then regret it when a centimeter gap appears between the bathtub and the wall. Also, an indirect angle is detected by floor tiles, when the trimming on the sides turns out different. And there are even worse situations. Therefore, take this material seriously.
Builders erecting modern houses, contrary to the opinion of the majority, they do not care about the proximity of the corners in apartments to 90 degrees. All they care about is the amount of work, and often they are not even given any measuring equipment. Just a trowel and a trowel. “Way, Rovshan!”
How to make a right angle between the walls after such a hack? There are two options here: either we plaster on the beacons, or we level the walls with plasterboard. And if in the second case no difficulties should arise - we just twist the profiles along the square, then everything is a little more complicated. By the way, the option “I’ll level everything with tiles” won’t work either. Practice shows that all those who try to make a right angle by smoothly building up a layer of tile adhesive invariably mess up. Moreover, their angle is not straight, and the tiles lie crooked. If you find the strength and courage to plaster on beacons, then you can make a perfect right angle without any problems. On which you can quite calmly lay the tiles “under the comb”.
The first fundamental principle of right angle plastering is to first plaster one wall in the usual way.
Usually the longest. Entirely. It is much easier and faster to build an angle from a finished plane.
What's next? You will need two plastering rules. Preferably the length of the entire wall. Often bathrooms have dimensions around 175x175, so in this case, take two two-room apartments and shorten them with a grinder or a hacksaw.
Let's assume that you have already plastered one wall, ideally. And the adjacent one has dimensions of 175x275 cm. In this case, two beacons will be needed. Let's mark them. Everything is as it should be, at a distance of 30 cm from the walls. But there's one here important nuance. The pair of lower screws must be strictly at the same level. Accordingly, the top pair too. A little later you will find out why. It is also recommended to mark a line on the plastered wall that lies at the same level as the bottom pair of screws.
Next, holes are drilled and dowels and screws are driven into them. What now? Of course, you can’t do anything with a simple half-meter square. The solution lies on the surface - you need a larger square. It is made from two rules. But how to make sure that they form a strictly 90 degree angle? Not on a small square, that makes no sense. Everything is much simpler.
There is the Pythagorean theorem. Which unambiguously establishes the ratio of the sides of a right triangle. The root of the sum of the squares of the legs is equal to the hypotenuse. Remember your school geometry course. What this all means is that if you can build a triangle on the floor whose sides are related in the same way, one of its angles will be exactly 90 degrees. The simplest case is the so-called. Egyptian triangle, whose sides are in a ratio of 3:4:5. It is usually convenient to take 120:160:200 cm in practice.
So, a line is drawn on the floor with a pencil. It is not advisable to use a marker; accuracy is important here. Two points are placed on it: one at the edge, the second at a distance of 120 cm from the first. Then take a piece of the lighthouse, or you can use a tape measure. It will be necessary to set aside 160 cm from the first point, and 200 cm from the second. More precisely, construct fragments of circles specified radii. The intersection point of these figures will be the third vertex of the triangle. All that remains is to connect the vertices. That's it, you have constructed a right triangle with high accuracy. 
The next step is to place two rules on the floor exactly along the lines. Since they will lie with their beveled edges facing outward, this will not be so easy. You'll have to use a square. So, the rules are combined with the lines: 
Now you need to securely fasten them together. This is usually done with self-tapping screws with a press washer or black metal screws. The main thing is to prevent the rules from shifting relative to the lines under the influence of vibration from a screwdriver or drill. It is enough to consolidate the rules at two points:
But, in general, this is not enough. You need to use an additional strip from a Knauf protective corner, for example. We fasten it as shown in the figure: 
Now you have a huge, hard, and most importantly, accurate square. You return to the room where you will have beacons. There is already a line marked along which you will apply the square. Yes, you need to place it strictly in horizontal plane, otherwise there will be an error.
You should have already previously assessed the degree of deviation of the angle from 90 degrees, so you know which screw from the bottom pair to take as a basis. Let's assume that the angle was obtuse, so the screw closest to the already plastered wall is unscrewed to a minimum (7-8 mm). And the far one will already twist around the square. Apply it to the line already finished wall and to the exposed screw of the lower pair on the marked one. Look. Let's say the farthest self-tapping screw does not reach the square by about 4 mm. Unscrew it approximately this distance and again assess the situation with a square. You may have to apply it several times, but, in general, the installation process of the self-tapping screw will take you no more than a couple of minutes. If the angle was initially sharp, install the farthest self-tapping screw first. And the neighbor - along the square.
It is inconvenient to set the top pair of screws with the same square - it is heavy, it is difficult to lift it, it constantly slides off the heads. Therefore, it will be easier to simply set them vertically relative to the bottom pair. Plumb or bubble level. In any case, if your first wall is perfectly aligned, you will get a perfectly right angle both above and below, automatically.
If you need to set a right angle on the opposite wall, then no problem, do everything exactly the same. This may be necessary, for example, if the dimensions of the bathtub are close to the walls. At the same time, cutting the tiles on the floor will work out perfectly. It is recommended not to set up all the beacons in advance and then plaster them. It would be much better, although it would take longer, to mark and plaster each wall one at a time. But you will know for sure that you have not made a mistake anywhere.
Now you know how to make a right angle between walls when plastering. By spending a couple of hours laying out the tiles, you'll save more on your tile installation costs and get a professional quality finish much easier.
Jun 6, 2014 ADMIN
This - oldest geometric problem.
Step by step instructions
1st way. - Using the “golden” or “Egyptian” triangle. The sides of this triangle have the aspect ratio 3:4:5, and the angle is exactly 90 degrees. This quality was widely used by the ancient Egyptians and other ancient cultures.
Ill.1. Construction of the Golden or Egyptian Triangle
- We manufacture three measurements (or rope compasses - a rope on two nails or pegs) with lengths of 3; 4; 5 meters. The ancients often used the method of tying knots with equal distances between them as units of measurement. Unit of length - " nodule».
- We drive a peg at point O and attach the measure “R3 - 3 knots” to it.
- We stretch the rope along the known boundary - towards the proposed point A.
- At the moment of tension on the border line - point A, we drive in a peg.
- Then - again from point O, stretch the measure R4 - along the second border. We don’t drive the peg in yet.
- After this, we stretch the measure R5 - from A to B.
- We drive a peg at the intersection of measurements R2 and R3. – This is the desired point B – third vertex of the golden triangle, with sides 3;4;5 and with a right angle at point O.
2nd method. Using a compass.
The compass may be rope or pedometer. Cm:
Our compass pedometer has a step of 1 meter.
Ill.2. Compass pedometer
Construction - also according to Ill. 1.
- From the reference point - point O - the neighbor's corner, draw a segment of arbitrary length - but larger than the radius of the compass = 1m - in each direction from the center (segment AB).
- We place the leg of the compass at point O.
- We draw a circle with radius (compass step) = 1 m. It is enough to draw short arcs - 10-20 centimeters each, at the intersection with the marked segment (through points A and B). With this action we found equidistant points from the center- A and B. The distance from the center does not matter here. You can simply mark these points with a tape measure.
- Next, you need to draw arcs with centers at points A and B, but with a slightly (arbitrarily) larger radius than R=1m. You can reconfigure our compass to a larger radius if it has an adjustable pitch. But for such a small current task, I wouldn’t want to “pull” it. Or when there is no adjustment. Can be done in half a minute rope compass.
- We place the first nail (or the leg of a compass with a radius greater than 1 m) alternately at points A and B. And draw two arcs with the second nail - in a taut state of the rope - so that they intersect with each other. It is possible at two points: C and D, but one is enough - C. And again, short serifs at the intersection at point C will suffice.
- Draw a straight line (segment) through points C and D.
- All! The resulting segment, or straight line, is exact direction north:). Sorry, - at a right angle.
- The figure shows two cases of boundary discrepancy across a neighbor's property. Ill. 3a shows a case where a neighbor’s fence moves away from the desired direction to its detriment. On 3b - he climbed onto your site. In situation 3a, it is possible to construct two “guide” points: both C and D. In situation 3b, only C.
- Place a peg at corner O, and a temporary peg at point C, and stretch a cord from C to the rear boundary of the site. – So that the cord barely touches peg O. By measuring from point O - in direction D, the length of the side according to the general plan, you will get a reliable rear right corner of the site.
Ill.3. Constructing a right angle - from the neighbor’s angle, using a pedometer and a rope compass
If you have a compass-pedometer, then you can do without rope altogether. In the previous example, we used the rope one to draw arcs of a larger radius than those of the pedometer. More because these arcs must intersect somewhere. In order for the arcs to be drawn with a pedometer with the same radius - 1m with a guarantee of their intersection, it is necessary that points A and B are inside the circle with R = 1m.
- Then measure these equidistant points roulette- V different sides from the center, but always along line AB (neighbor’s fence line). The closer points A and B are to the center, the farther the guide points C and D are from it, and the more accurate the measurements. In the figure, this distance is taken to be about a quarter of the pedometer radius = 260mm.
Ill.4. Constructing a right angle using a compass-pedometer and tape measure
- This scheme of actions is no less relevant when constructing any rectangle, in particular the contour of a rectangular foundation. You will receive it perfect. Its diagonals, of course, need to be checked, but isn't the effort reduced? – Compared to when the diagonals, corners and sides of the foundation contour are moved back and forth until the corners meet..
Actually, we solved a geometric problem on earth. To make your actions more confident on the site, practice on paper - using a regular compass. Which is basically no different.
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When starting the study of geometry, in the very first lesson they tell you that geometry from Greek is translated as earth measurement. And when one day you have to build or repair something, and there is a need to measure the land in literally This word, it turns out, was not taught at school! Because drawing a house plan on paper is one thing, but explaining to an excavator operator where and how much to dig while standing on a grassy wasteland is quite another.
But it is not holy pots that are sculpted; after studying the information further, you will be able to perform pit layout for the future building, and implement connection to the location of the structure existing only on paper, determine heights, draw a horizontal line, while using the simplest tools.
Constructing a right angle on the ground
Let's start with the most important thing - constructing a right angle on the ground. This is not difficult to do, and the only tools you need are a ten-meter tape measure, four pegs and a roll of nylon cord.
We determine the line from which we will build a right angle. For example, this is the wall of a future building. We hammer in two pegs and stretch a cord between them. We take an arbitrary distance between the pegs, but slightly more than four meters.
Peg A will be the top of our corner, and the stretched cord will be one of the sides. We measure from peg A along the cord four meters and hammer peg C.
Now we need helpers. One of them holds the beginning, or zero, of the roulette wheel on peg A, the second - on peg C keeps the mark of 8 meters. You take the tape measure at the 3 m mark and stretch it so that a triangle is formed, one of the legs of which will be a stretched cord, the second leg will be a tape measure segment from zero to three, and the hypotenuse will be a segment from three to eight meters. We try to keep the tape measure closer to the surface of the earth - so that all the segments, if possible, lie in the same plane.
And the segment between zero and three (in the figure blue), and the piece of tape between the three and eight meter marks (red) should be equally well stretched. We drive in peg B exactly in the place where the three meter mark fell. How it all looks can be seen in the figure.
Angle CAB will be equal to 90 degrees, as required. Now, to build any rectangle on the ground, it is enough to plot the length and width on the sides of our angle and build another right angle.
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At school we have been diligently studying geometry for several years in a row. But are we wasting our time? How can geometry help in life? Measure the distance from point to point, calculate the area or volume of an object and that’s all? Of course not. The laws of geometry apply literally at every step. You just need to know how to use them.
