"The woman is created for a man, not a man for a woman" - such a postulate ...
Publication date 12.04.2013 14:30
Geometry is ancient science. The word "geometry" means "Amerlemerie" ("Mettero" - to measure "Geo" - Earth), translated from Greek. This is explained by the fact that initially geometry served for various measuring work performed during construction. Gradually, the geometry turned out to be new rules and laws that were subsequently mandatory. This science arose as a result of human practical actions, and during its origin, it served exclusively for practical human needs.
How to measure the height of the tree
There are many ways that allow you to find out the exact height of the tree, without climbing his top and not without cutting it.
The most vintage and easy way is the method of the ancient Greek sage of Falez. In the sixth centuries BC, he first managed to measure height egyptian pyramid. He accurately chose the time when the length of his own shadow was equal to his growth, and determined that the length of the shadow of the pyramid would also be equal to its height. In addition to the length of the shadows, Fales needed to know two geometric triangle properties:
1. The angles at the base of an equilibrium triangle are equal as the parties lying against equal corners of the triangle.
2. The sum of the angles of any triangle of the wound with two direct corners.
Having these knowledge, Fales rightly decided that if his own shadow was equal to his growth, then the base, end, middle and top of the pyramid shadow form an equally chaired triangle.
This method can be applied far from always, since the sun is low above the horizon, and the shadows are accurately displaying items only at noon of the summer period.
It is worth it, however, note that this method is easy to change so that you can use any shadow, whatever length it is. You need to measure your own shadow, or shadow, for example, a pole, and from this data to calculate the necessary height using the proportion:
what does the following mean: the height of the tree exceeds your height at the same time, what time is the shadow of the tree longer than your shadow. All of these data is obtained from the geometric similarity of the ABC and A1B1C1 triangle.
Geometry - very useful science And it is used in many industries. One of the famous figures is a parallelogram. Discover
The height of the tree is defined as the vertical distance between the highest point of the crown and the surface of the Earth. It differs from the length of the tree, which is the length of the barrel from the surface of the Earth to the top of the tree (Fig. 1). Measurements should be carried out with an accuracy of 0.1 m if possible, although this level of accuracy cannot be achieved for large trees.
It is recommended to mark the place (for example, the distance from the tree and azimuth) from which the measurement is carried out to carry out all subsequent measurements from the same position. The same measurement points can be seen in nature on Earth. Although it is believed that overlooking conditions may vary after 10-20 years (growth of teenager, crown development ...), this procedure is one of the ways to limit measurement errors.
Fig.1: Height and Tree length.
Tip: In some cases (for example, rubbing peripheral shoots, shoots off) the tip is considered the highest "live" kidney of the crown. Although winter is not so easy to see the top of the tree during the measurements of the height of deciduous species, but it
it will make it possible to distinguish the vertex from dry dead branches, which in the spring are usually laid out.
Tip: For tilted trees, it is recommended to measure the height of the perpendicular from
the highest point of the crown to the ground in the direction of the tree tilt.
Tip: In the case when planting is located on the slope (\u003e 6 °), it is recommended to measure
the height of the tree at the level of the tree (the same height above sea level) or higher.
2 way
Measurement is carried out together. One person becomes close to the tree, and the other, with a good eye meter, going down at a certain distance to cover, all the tree from Komle to the top, "puts out" to the eye, how many people of this growth "fit" along the entire length of the trunk. At the same time, rationally, each time to postpone the distance twice as much as the previous one, i.e. To mentally postpone first the height of two "men", then add two more to them, then - more than four, then eight, etc. (i.e., according to Scheme 1 - 2 - 4 - 8 - 16). From the point of view of the human character, it is easier and more accurate. Knowing the height of the "man" can be counted the height of the tree.
3 way
Tree height measurement with shadow
On a sunny day, you can use the shadow dropped by them to determine the height of the tree. Measuring your shadow or shadow of some pole, you can calculate the desired height from the proportion of AV: AB \u003d Sun: BC
since the height of the tree is at the same time more than your own height (or hest height), how many times the shadow of the tree is longer than your shadow (or shadow of the pole). This implies, of course, from the geometric similarity of the triangles of the ABC and ABC (for two corners).
The most accurate of indirect ways is used in sunny weather. The shadow from the standing person is precisely measured, whose height is known. Next, the shadow is measured from the tree studied. In a dense forest, when the shadow of a tree or another and, especially, its peaks are difficult to find, can be recommended as follows. To move away from the tree so that the view of a person (head), the top of the tree and the sun lay on the same line, after which they find the shadow on Earth from his own head - it will be a shadow from the top of the tree. It remains only to measure the distance between this point and the base of the tree and determine the height of the tree by proportion: the length of the human shadow / its height is the length of the shadow of the tree / its height.
II.4. 3. Method of determining the age of wood
The accurate age of centuries-old trees is very difficult to determine. Therefore, for such trees, it is customary to talk about the dimensions of the circle and the diameter of their barrel. The dependence of the circumference of the barrel from age is as very relative and depends on those natural conditionsin which the tree grows.
The age of age-old wood is determined by the simple formula:
L \u003d k · c,
where L is the age of the tree
k - coefficient
c - Length of the Table Table (girth) circumference at an altitude of 1.3 meters from the surface of the Earth. For pine coefficient - from 0.7 to 1.5 on dry rocky soil.
Size: px.
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Transcript.
1 1 Regional competition of educational and research and design work Pupils "Applied Mathematics Questions" Geometry How to determine the height of the tree, without faster it and not climbing the top of Belonogov Stas, the gymnasium named after M.Ipinayeva, 8 CL. Anisimova A.A., Mathematics Teacher
2 2 Content Introduction 3 Geometric Problem Statement 4 Description of Experiments 5 Conclusion 12 List of Used Sources and Literature 13 Appendix (photo report) 14
3 3 Introduction to modern world We define the values \u200b\u200bof different quantities (length, mass, temperature, etc.) with various tools and instruments. So in his professional activity Builders, architects, forest rigs, military to determine the height of the object use special complex and expensive devices of altimeters. I had a question: Is it possible to determine the height of the pillar or tree without a high-volume meter? Such a skill is needed by many people in the forest: tourists, hunters, forestry. This skill is taught scouts. Jacob Isidovich Perelman, the author of many popular books in mathematics, "Doctor of Engineering", in the war in Leningrad was the Lecturer-instructor for the preparation of military intelligence officers. He developed several topics relating, mainly, the ability to focus on any terrain and in any weather, without taking this technical means, tools and devices, and relying only on what was "at hand". One of those sounded like this: "How to measure the height of the tree, buildings, towers." Work goal Determine the height of the tree different ways Without special devices. Tasks: 1) consider various methods determining the height of the selected tree; 2) carry out the appropriate measurements and calculations; 3) Establish the results in the form of instructions.
4 4 Geometric setting of the task Geometric setting of the problem: Determine the length of the segment of AB, where and the base of the tree, in its vertex. The length of the segment is determined by either the measurement or the use of geometric methods, for example, associated with the similarity of triangles. Measure the segment means to compare it with a single segment or a segment having a known length. Two segments are called equal, if they coincide when applied. The material associated with the similarity of the figures is considered in grade 8. I use these facts without strict justification. In such figures, the corresponding sizes in the division give the same number. For example, two triangles with respectively equal angles are similar, and the relations of their respective sides are equal. Work formula: H h L L where h The height of the tree, h is the height of the known object, L and L of the values \u200b\u200bassociated with the tree and the object, their meaning will be explained in each experiment. Hence the h l h l
5 5 Description of experiments To fulfill the task, several ways were proposed (their short conditional names are given): 1) statistical evaluation; 2) air ball; 3) photo; 4) shadow; 5) mirror; 6) triangle with an angle of 45 degrees; 7) Pencil. The first and second way is the measurement, because A comparison with a single segment and segments are used. In other ways, the likeness is used. The sources of our methods were the literature and websites of an online scientific position, some methods of measurement we invented themselves. Independent contribution to work, we consider the design of the description of the methods in the form of instructions. Statistical assessment The essence: Suggest as much of the number of people to estimate the height of the tree to the eye, setting next to the tree a vertically meter line. Calculate H as the average arithmetic data obtained. During the experiment, 10 people from the 6th grade determined the height of the tree on the eye. Equipment: meter line. Work move: 1) set a ruler next to the tree vertically; 2) Suggest a person to determine the height of the tree on the eyes; 3) write the resulting value in the table;
6 4) To obtain an average value of the amount of measurement, divided by the number of measurements. Result: 6.2 6.8 6.8 11.5 6.5 6.7 12 7, height 8.46 m 6 Balloon Essence: Compare the height of the tree with a length of a suitable thread. Equipment: air ball filled with helium; Long light rope (thread); Roulette or TP meter. Progress of work: 1) Tail to the ball a long thread and etching it gradually until the ball rises to the tops. 2) Make a mark on the thread (for example, nodule). 3) Return the ball, measure the length of the released part of the thread. Result: 10.5 m Photo Essence: The height of the tree is so many times the height of the line, how many times the length of the image of the tree in the photo is larger than the length of the line of the line. Equipment: camera, metering line, comrade or you yourself as a ruler. Work move: 1) To put a vertically meter ruler next to the tree; 2) take a picture, making sure that the camera is installed in such a way that the film is in the vertical plane;
7 3) Determine the height of the wood H along the finished photo by the formula: H \u003d L / L, where L and L dimensions, respectively, the tree and the line in the photo, H \u003d 1. 23.2 The result: H 11, 05m 2.1. Same Using a known growth person as a human line (for example). Then the formula will be viewed: H \u003d H * L / L, where H and L dimensions, respectively, the tree and the "line" in the photo, l the true dimensions of the "line" (the growth of a friend or yours). 7 Shadow Essence: This is the easiest and most ancient way, with the help of which the Greek sage Falez in the sixth centuries BC determined the height of the pyramid in Egypt. He took advantage of her shadow. We did in the same way. I measured your growth, the length of their shadow and the length of the shadow of the tree. The height of the tree is at the same time more than the growth of a person, how many times the shadow of the tree is larger than the shade of man. Because Tree and man are located perpendicular to the earth, i.e. At an angle of 90 degrees, and the rays of the sun fall on the ground at the same angles, such triangles are formed proportional to the side. Operating formula: H \u003d H * L / L Here L Length of the shade of a tree, l The length of the shade of a person, H height of a person.
8 8 Equipment and work is clear from the picture. Remarks: a) instead of you can put a stick, etc.; b) specified in the picture mutual arrangement Objects not necessarily observe. It is clear that measurements should be carried out at the same time, because The sun does not stand still, and the length of the shade changes. 1.62 17.6 Result: H 10, 89m. 2.62 Mirror Essence: The method is based on the law of reflection of light. ACB angle equal to the corner ECD. Consequently, the ACB triangle is similar to the ECD triangle, and their parties are proportional. Consequently, the basic formula is true. Working formula: H \u003d H * L / L
9 9 Equipment: Flat Mirror, Roulette. Work move: 1) put the mirror on the ground; 2) find such a position to see in the mirror reflection of the top of the tree; 3) measure the distances L, L and H; 4) calculate H; 5) repeat the measurement 5 times when different values L; 6) Calculate H as the average arithmetic values. Result: 1.62 8.68 H 10, 82m 1.3 by version of this method is the determination of the height of the subject on the puddle. This method described on the "St. Petersburg Hunter" website can be successfully used after the rain when many puddle appears on Earth. Measurement is made in this way: find the nudge from the measured items and become about it so that it is placed between you and the subject. After that, they find a point from which the vertex of the subject is visible in the water. The measured object, for example, the tree will be at the same time above you, how much the distance from it to the puddle is larger than the distance from the puddle to you.
10 10 triangle with an angle of 45 degrees ... Building an equally rectangular triangleOne of whose cathets is a tree. Working formula: H \u003d H * L / L Here H and L side of a rectangular triangle with an angle of 45 degrees. Because They are equal, then H \u003d L. Equipment: Any rectangular triangle (paper, plastic, wooden) with an angle of 45 degrees, that is, an isosceles. Working: 1) Holding a triangle vertically, move away from the tree to such a distance, at which, looking along the hypotenuse, see the top of the tree. The height of the tree from the eye level to the top is equal to the distance from the tree to man; 2) measure the distance from the place of measurement to the tree; 3) add your growth to the resulting number (to the eye level). Result: L \u003d 10.5 m; H \u003d 10.5 + 1.38 \u003d 11.88 m Pencil formula and explanation is the same as the previous method. Equipment: pencil (or handle, or any wand), assistant, roulette. Work move: 1) Stand from the tree to such a distance to see it entirely from the base to the top. Next to the trunk to install the helper.
11 11 2) Pull out a hand with a pencil, clamped in a fist. Sooch one eye and bring the tip of the griffel to the top of the tree. Now move nail thumb So that it is under the base of the trunk. 3) Rotate a fist for 90 degrees so that the pencil is located in parallel to the Earth. At the same time, your nail must still remain at the bottom point of the barrel. 4) shout to your assistant so that he will move away from the tree. When it reaches the point to which the point of the pencil indicates, to file a signal so that it stops. 5) Measure the distance from the barrel to the place where the assistant was frozen. It will be equal to the height of the tree. This follows from our basic ratio result: H \u003d 11.6 m. This method of measuring the tree is used by scouts.
12 12 Conclusion We looked at several ways to determine the height of the tree with the help of submitted means without special instruments and tools. All these methods are based either on the definition of the concept of length of the segment and measurement, or on the properties of such figures. Experiments were conducted by B. adverse conditions: uneven, uncomfortable terrain, a lot of snow, frost, no experience and skill. The results of various experiments differed. Fashion / Experiment Name Result Statistical Evaluation 8.46 Air Ball 10.5 Photo 11.05 Shadow 10,89 Mirror 10,82 Triangle with angle, 88 Pencil 11.6 If you do not consider the result of determining the height "on the eye" as the most unreliable , then the difference between the greatest and the smallest values Heights is about 1.5 meters. Therefore, we can assume that the height of the tree is about 11 meters. More exact value It can give measurement with the help of a forester altimeter. After studying the concept of relative and absolute errors, we assume repeat experiments with a measurement of an object with a known height and estimate the accuracy of the methods applied. Those who want to try to determine the height of the inaccessible object can take advantage of our instructions. We consider the pencil method to be the most affordable way. It requires minimum equipment and only one dimension.
13 13 List of used sources and literature 1. Ya.I. Pernelman. Entertaining geometry. M.: AST, L. S. Atanasyan and others. Geometry: Tutorial for 7-9 CL. general educational institutions. M.: Enlightenment, Website "Peter Hunter" 4. "Central Site Scout Site of Russia"
14 16
Preparing for the Name-Rubical Test: Advisor for Applicants Basic Test Edition Second, Recycled and Augmented Bishkek 2004 UDC 378 BBC 74.58 g74 Authors of sections: Mathematics: M. Zelman,
Nizhny Novgorod State University im.N.I.Lobachevsky National Research University Educational and Scientific and Innovative Complex "New Multifunctional Materials and Nanology"
Federal Agency for Education State educational institution Higher vocational education "Ryazan state University name S.A. Yesenin »Front Laboratory
Laboratory work 1.1 1) The simplest dimensions and processing of their results The purpose of the work: familiarization with the methods of measuring the linear dimensions of the bodies and their masses, as well as with the methods of processing experimental
Ministry of Transport of the Russian Federation Federal Agency railway transport Samara State Academy of Ratings of the Department of Physics and Ecological Heat Physics of Physical Measurement
Kazan State University Department of General Physics Processing and presentation of measurement results Guidelines Kazan-1999 1. Measurement and its metrological characteristics are based on
1 educational literature on humanitarian and social disciplines for higher education and secondary specials educational institutions Preparing and published with the assistance of the institute " Open Society"(Soros Foundation) in
Ministry of Education Russian Federation Ural State University and M Gorky prepared by departments of general physics and physics magnetic phenomena Brief results on the processing of results
The purpose of the work is often in practice it is necessary to investigate how the change in one variable x effect affects another value of y for example, as the amount of cement X affects the strength of concrete y.
Ministry of Education and Science of the Russian Federation State Educational Institution of Higher Professional Education "Nizhny Novgorod State University. N.I. Lobachevsky "
Ministry of Education and Science of the Russian Federation Federal Agency for Education Perm State Technical University Department of Theoretical Mechanics Theoretical Mechanics Teaching manual
Grade 7.1. Record several times in a row number 013 so that the resulting number is divided by 9. Explain the answer. Answer: for example, 013013013. Decision. We give several ways to justify. The first way.
Measurement of physical quantities. Uncertainty measurement, measurement errors. Measurement of physical dimensions is called a comparison of this physical value with the size of the same genus adopted
O.P. Sharova Scene Tasks in Mathematics Teaching Summary The article systematizes terminology related to the plot tasks, and the possibilities of using the main methods for solving the plot are revealed.
E. G. Gotman Stereometric tasks and methods of their decision Moscow Publisher MCNMO, 006 UDC 514.11 BBK.151.0 g7 G7 Gotman E. G. Stereometric tasks and methods for their solution. M.: MCSNMO, 006. 160 C.: IL.
Lecture 6. Basic rules for the size of the size in the drawings. All drawings are performed on a specific scale and on each of them there is a linear or transverse scale, which you can always determine the true size of a particular element or an object as a whole. But this method of determining dimensions does not provide sufficient accuracy of measurements, besides, it strongly depends on the scale size. For significant decrease Images The measurement accuracy falls so much that it is possible to judge the sizes only approximately. Therefore, the drawings are always affixed by the rules established by GOST. The dimensional numbers, in this case, accurately determine the value of the subject and its parts depicted on the drawing, regardless of the scale of the selected scale. Examples of machine-building and architectural studio drawing are shown in Fig. 1 and 2. Sizes in the drawing should be so much so that no object element remains without size and so that no size is repeated. Dimensions in drawings are affixed using remote and dimensional lines and dimensional numbers. Dimensional lines are usually carried out in parallel to the line of a straight line, the size of which must be put up, or parallel to the axes of projections (i.e., horizontally or vertically), if, for example, are affixed dimensions object. Fig. 1. In general, the size of the size is quite complex and time-consuming technical and creative process, and each new drawing requires its special approach to solving these tasks. The remote lines are directed towards the object to the measured elements and, as a rule, perpendicular to the dimensional lines. At the points of intersection of remote and dimensional lines can be supplied. 1 (a) Machine-building drawing b) architectural and construction drawing
At the beginning of the lesson of mathematics, after passing the topic "Similar triangles", our teacher Alsu Mailen asked the question "How to measure the height of the subject, to the top of which you can't get? In their professional activities, builders, architects, forest rigs, military to determine the height of the object use special complex and expensive devices - altimeters. And how to determine the height of the pillar or tree without a high-volume? After all, such a skill is needed by many people in the forest: tourists, hunters, forestry. How can I use the properties of such triangles? Today we will learn to determine the height without a high-volume. The object of measurements will be a fir, which grows on the school's territory just before the windows of our class. " We went outside and tried to determine the height with the help of astrolabe. Also, she noticed that there are a lot of measurement methods, they can be carried out without such devices as astrolabe, with priests. One of the ways, with the help of a special pole, is proposed in our textbook "Geometry 7-9". We are interested, began to search in books and on the Internet various measurement methods. With what kind of fool's tools can this be done? Is it possible to do this in the forest, without any measuring instrument? The result of searches and measurements we set out in our work.
- Main part
purpose of work - Determine the height of the tree, without firing it and not falling on it, in different ways, without special devices.
Tasks:
1. Consider various ways to determine the height of the selected tree;
2. Conduct the appropriate measurements and calculations;
3. Make an assessment of the method, identify positive and negative sides, difficulties in using this method, assess accuracy
4. Place the results in the form of instructions.
The sources of our methods were literature and websites of the Internet of a popular science character, some methods of measurement we invented themselves. The result of our searches was the following methods 1) Static evaluation;
2) air ball;
3) comparison with the subject of a known length;
4) photo;
5) shadow;
6) mirror;
7) puddle;
8) triangle with an angle of 45 degrees;
9) homemade simplest device - "Altimeter"
10) pencil;
11) measurement of the height of the tree with the help of a pole (1 option);
12) altimeter of two planks;
13) method of using corners;
14) Measuring the height of the tree with the help of the corners does not approach it;
15) Leskewer altimeter;
16) Measuring the height of the tree with the help of a pole (2 option).
For convenience, research method and our result obtained in this way, we offer together.
- Static evaluation
Essence: Suggest as many people as possible to evaluate the height of the tree to the eye, setting a vertically meter ruler next to the tree. Calculate H as the average arithmetic data obtained. During the experiment, 13 people from the 8th grade determined the height of the tree on the eyes.
Equipment: meter line.
Progress:
- install the meter ruler next to the tree vertically;
- suggest a person to determine the height of the tree tree;
- write the resulting value to the table;
- to obtain an average value of the measurement amount, divided by the number of measurements.
Result:
10,5 | 9,45 | 10,75 |
Height - 9.56 m
Our method estimate:
In our opinion, this method is the most unreliable, but simple, only a member ruler needs, does not require any complex computing.
- Balloon
Essence: Compare tree height with a suitable thread long.
Equipment: air ball filled with helium; Long light rope (thread); roulette.
Progress:
- bind a long thread to the ball and etching it gradually until the ball rises to the top of the tree;
- make a mark on a thread (for example, nodule);
- return the ball, measure the length of the released part of the thread.
Result: 10.8 m
Our method estimate:
The method is quite accurate. The main difficulty of this method is needed windless weather, since at the slightest wind, the ball flies not straight up, and to the side. We had to repeat this experiment within 3 days.
- Comparison with the subject of a known length
Essence: compare the height of the tree with the length of the object of the known length
Equipment: the method does not require any equipment, but it is necessary that the object of the known length is located nearby
Progress: They estimated the length of our fir by comparing with the pillar of the power line. The height of the pillar was found out from local electricians, it is equal to 10 meters from the surface of the Earth. Our Christmas tree is about 1 m above the column. (The pillar height can be found on the Internet. The pillar height depends on the cipher of the support and the rack).
Result: 11 m
Our method estimate:
The method is quite accurate. The main difficulty of this method is to find a subject of a well-known length. We were lucky that there was a pillar next to the Christmas tree.
- The photo
Essence: The height of the tree is so many times the height of the person (ruler), how many times the length of the tree image on the photo is larger than the image of the person (line).
Equipment: Camera, ruler
or comrade for photographing.
Progress:
- next to the tree put a comrade or
vertically meter line;
- take a picture by making sure the preliminary
but that the camera is installed so that the film is in the vertical plane;
- determine the height of the tree H on the finished photo by the formula:
H \u003d L / L, where L and L are the dimensions of the wood and the line in the photo, H \u003d 1.
- The same, using a person's known growth as a human line (for example). Then the formula will look at:
H \u003d H * L / L, where H and L are the dimensions of the wood and the "line" in the photo, L is the true dimensions of the "line" (a comrade or yours).
Result : H \u003d 0.014 m, L \u003d 0.085 m, L \u003d 1.57 m, H \u003d 9.53m
Our method estimate:
D. to this method, you need a camera, a printer for receiving a photo, comrade for photographing or metering line. To obtain an accurate result, all measurements must be performed very accurately.
- Shadow
Essence : This is the easiest and most ancient way, with which the Greek sage Falez in the sixth centuries BC determined the height of the pyramid in Egypt. He took advantage of her shadow. We did in the same way. I measured your growth, the length of their shadow and the length of the shadow of the tree. The height of the tree is at the same time more than the growth of a person, how many times the shadow of the tree is larger than the shade of man. Because Tree and man are located perpendicular to the earth, i.e. At an angle of 90 degrees, and the rays of the sun fall on the ground at the same angles, such triangles are formed, which are proportional to.
Working formula: H \u003d H * L / L
Here L is the length of the shadow of the tree, L is the length of the shade of man,
h is the height of a person.
Equipment and work - Clear from the picture.
Result : h \u003d 1.57 m, L \u003d 4.2 m, L \u003d 26.8 m, H \u003d 10 m
Our method estimate:
The method is quite reliable, but you need sunny weather, measurements need to be carried out at the same time, because The sun does not stand still, and the length of the shade changes.
- Mirror
Essence : The method is based on the law of reflection of light.
The ACB angle is equal to ECD angle. Consequently, the ACB triangle is similar
eCD triangle, and their parties are proportional. Consequently, the basic formula is true.
Working formula: H \u003d H * L / L
Equipment : Flat mirror, roulette.
Progress :
1) put the mirror on the ground;
2) find such a position to see in the mirror reflection of the top of the tree;
3) measure the distances L, L and H;
Result : h \u003d 1.47 m, L \u003d 1.30 m, L \u003d 8.4 m, H \u003d 9.5 m
Our method estimate:
The method is quite reliable, but we need a mirror and roulette.
- Puddle
Measurement with a puddle is an alternative measurement option with a mirror. This method described on the "St. Petersburg Hunter" website can be successfully used after the rain when many puddle appears on Earth. Measurement is made in this way: find the nudge from the measured items and become about it so that it is placed between you and the subject. After that, they find a point from which the vertex of the subject is visible in the water. The measured object, for example, the tree will be at the same time above you, how much the distance from it to the puddle is larger than the distance from the puddle to you.
Our method estimate: The method is quite reliable, but it can be carried out only in the summer and only after the rain.
Essence : Building an equally visual rectangular triangle, one of whose cathets is a tree. H- human growth to eye level
Working formula: AC \u003d Sun, H \u003d AC + H
Here, the AC and Sun - the sides of the rectangular triangle with an angle of 45 degrees. Because They are equal, then H \u003d AC + H
Equipment: any rectangular triangle (paper, plastic, wooden) with an angle of 45 degrees, that is, an anoseced one.
Progress :
1) holding a triangle vertically, move away from the tree to such a distance, with
which, looking along the hypotenuse, see the top of the tree. The height of the tree from the eye level to the top is equal to the distance from the tree to man;
2) measure the distance from the place of measurement to the tree;
3) add your growth to the resulting number (to the eye level).
Result: ac \u003d 8.2 m; H. \u003d 1.47 m H \u003d 8.2 + 1.47 \u003d 9.67 m
Our method estimate:
The method is quite reliable.Equipment is simple, does not require calculations.
- Homemade simplest device - "altimeter"
Measurement with homemade device - "High resistant" is an option for measuring with a triangle with an angle of 45 degrees. You need any plate (you can use a bark of a tree if it has a flat side) and 3 pins. On this plate, three points are planned - the vertices of an equally sized rectangular triangle, and pins stick into them. If there is no drawing ruler at hand, for construction direct corner, and no circula, for deposit equal side, You can use a sheet of paper: overload a sheet of paper, then across the first folding again so that both parts of the first fold coincide - there is a straight angle. With the help of the same sheet, you can measure equal distances.
Result: ac \u003d 9.4 m; H. \u003d 1.47 m H \u003d 9.4 + 1.47 \u003d 10.87 m
Our method estimate:
The method is quite reliable.Does not require O. bars, does not require computing. You can use in the forest. If there is no roulette, then the distance to the base of the tree can be measured by steps.
- Pencil
Formula and explanation is the same as the previous method.
Equipment : Pencil (or pen, or any wand), assistant, roulette.
Progress:
1) Stand from the tree to such a distance to see it entirely - from the base to the top. Next to the trunk to install the helper.
2) stretch your hand with a pencil, clamped in a fist. Sooch one eye and bring the tip of the griffel to the top of the tree. Now move the nail of the thumb so that it is under the base of the trunk.
3) turn a fist for 90 degrees so that the pencil is located
parallel land. At the same time, your nail must still remain at the bottom point of the barrel.
4) shout to your assistant so that he will move away from the tree. When it reaches the point to which the point of the pencil indicates, to file a signal so that it stops.
5) Measure the distance from the barrel to the place where the assistant was frozen. It will
equal to the height of the tree. This follows from our basic ratio
Result: H \u003d 9.5 m
Our method estimate:
The method is quite reliable.No need equipment and calculation. This method of measuring wood use scouts.
Essence : This is another measurement option with a triangle with an angle of 45 degrees. Otherwise, this method is calledJulvernovsky, since he described by Jules Verne in the novel "Mysterious Island".
Equipment: Six, clothing that you are not afraid to stain
Progress: It is necessary to stick this fooled to the ground so that the protruding part was equal to your growth. Then you need to lie on the ground so that, having resting my legs to the pole, you saw the top of the tree on one straight line with the top point of the pole. T. K. The resulting triangle will be equally chaped and rectangular, then l \u003d h.
Result: L \u003d H \u003d 10.7 m
Our method estimate:
The method is quite reliable.Does not require equipment and calculations.
But there are still ways that we did not use, but found their descriptions.
- Altimeter of two slats
- Method of using corners.
This method can be used in high schools, where students know trigonometric functions Corners. To measure the angle, you can use a device made from the transport and attached to it by a special method of a plumb (see Figure). Measurement order: First we will go to the well-known distance from the tree. Then send the device to the top of the tree on the sight line from above and measure the angle that shows the plumb. In this casea. It is necessary to recalculate (subtract out of 90 ° shown angle). It is clear that the height of the tree will be equal to the distance from the tree to the person to multiply on the tangent of the anglea. Well, plus a human growth.
- Measuring the height of the tree with the help of the corners does not approach it
- Hispiems of forest products.
Very convenient, if for any reason it is impossible to approach the tree
- Tree height measurement with a pole (2 option)
(The case from the history of the Great Patriotic War).
This is how one day it was on one of the fronts of the Great Patriotic War. The division of Lieutenant Ivanyuk was ordered to build a bridge over the mountain river. On the opposite coast there were fascists. For the exploration of the place of construction of the bridge, the lieutenant allocated a reconnaissance group led by a senior sergeant Popov. In the nearest forest massif, they measured the diameter and height of the most typical trees and calculated the number of trees that could be used to build. The height of the trees measured with the help of the pace (pole) as shown in the figure.
This method is as follows.
Stripping the sixth above its growth, stuck it in the ground it is hurt at some distance from the measured tree. Go from the pole back to continue DD to the place A, from which, looking at the top of the tree, you will see on the same line with her the top point B of the pole. Then, without changing the position of the head, see the direction of the horizontal direct speaker, noticing the points C and C, in which the ray of sight meets the pole and trunk. Ask the assistant to make marks in these places, and observation is over. It remains only on the basis of the similarity of the triangles ABS and ABC to calculate the aircraft from the proportion
Sun: BS \u003d AC: AS, from where
Sun \u003d Sun (AC / AC).
Distances bc. The speakers and speakers are easy to measure directly. To the obtained value of the Sun, you need to add a Cd distance (which is also measured directly) to find out the desired height of the tree.
- Conclusion
We reviewed several ways to determine the height of the tree with
the help of remedies without special instruments and tools. All these methods are based either on the definition of the concept of length of the segment and measurement, or on the properties of such figures. Experiments were carried out in adverse conditions: uneven, uncomfortable terrain, a lot of snow, frost, lack of experience and skill. The results of various experiments differed.9.5 M.
Triangle with an angle of 45 degrees
9.67 M.
Homemade simplest device - "altimeter
10.87 M.
Pencil
9.5 M.
Measuring the height of the tree with the help of a pole (1 option)
10.7 M.
If you do not consider the result of determining the height of the "on the eye" and the comparison with the subject of a known value, as the most unreliable, then the difference between the greatest and the smallest height values \u200b\u200bis about 0.84 meters. Therefore, we can assume that the height of the tree is about 10 meters. A more accurate value can be measured using a grain height.
After studying the concept of relative and absolute errors, we
we assume repeat the experiments with the measurement of the object with the known
height and estimate the accuracy of the methods applied. Those who want to try to determine the height of the inaccessible object can take advantage of our instructions. We consider the pencil method to be the most affordable way. It requires minimum equipment and only one dimension.
- List of used sources and literature
1. Ya.I. Pernelman. Entertaining geometry. - M.: AST, 2005.
2. L. S. Atanasyan and others. Geometry: Tutorial for 7-9 CB. General education
institutions. - M.: Enlightenment, 2010.
3. http://piterhunt.ru/pages/nk-os/5/15.htm Site "St. Petersburg Hunter"
Subject: "Determine the height of the tree, without climbing on it"
Method 1. "On the eye"
Equipment: measured tree; All participants in the experiment (3 students + head); meter line.
Experimental performance:
1) set a ruler next to the tree vertically.
2) offered all participants to determine the height of the tree tree
3) identified the average arithmetic height of the tree.
Result: 9.32 m
Method 2. "Air Ball"
Equipment: measured tree; air ball filled with helium; Long light thread; human; roulette.
Experimental performance:
1) Tied a long thread to the ball and produced it gradually until the ball rises to the top of the tree.
2) Made a nodule on the thread.
3) returned the ball, measured the length of the released part of the thread.
Result: 10.3 m
Method 3. "Shadow Length"
Equipment: measured tree; human; roulette; The sun.
Experimental performance:
1) measured their growth, the length of its shadow and the length of the shadow of the tree. The height of the tree is at the same time more than the growth of a person, how many times the shadow of the tree is larger than the shade of man. Since the tree and man are perpendicular to the Earth, that is, at an angle of 90 degrees, and the rays of the sun fall on the ground at the same angles, then such triangles are approached proportional to.
2) by the formula: H \u003d HL / L
(L. - the length of the shadow of the tree, l. - the length of the shade of man, h. - The height of the person) was calculated the height of the tree.
Result: 10.49 m
Method 4. "Puddle"
Equipment: measured tree; a puddle formed after the rain or pillow water to the ground (then water is added to the equipment in the container); human; roulette.
Experimental performance:
1) Found a puddle.
2) I got up near her so that it was placed between us and the tree.
3) Found a point from which the vertex of the tree is visible in the water. Wood ( N.) will be at the same time higher than us ( h.), how much is the distance from him to the puddle ( L.) more than the distance from the puddles to us ( l.).
4) by the formula: H \u003d HL / L They calculated the height of the tree.
Result: 10.53 m
Method 5. "Six"
Equipment: measured tree; Long pole or straight stick; human; roulette.
Experimental performance:
1) stuck the pole stepping into the ground so that the protruding part was equal to our growth.
2) lay on the ground so that, resting his legs in the pole, we saw the top of the tree on one straight line with the top point of the pole. As a triangle ABC - equiced and rectangular, then angle a \u003d 450 and, therefore, AB \u003d Sun,i.e. the desired height of the tree.
Result: 10.8 m
Method 6. "Triangle with an angle of 45 degrees"
Equipment: measured tree; Triangle with an angle of 45 degrees; human; roulette.
Experimental performance:
1) holding a triangle vertically, moved from the tree to such a distance, with
which, looking along the hypotenuse, we could see the top of the tree. The height of the tree from the eye level to the top (BC) is equal to the distance from the tree to the person (AC)
2) measured the distance speakers.
3) added its growth to the resulting number (to the eye level).
Result: 11.6 m
Output: The results of various experiments were different, which was expected.
All data listed in the table:
Name of experiment | Result, M. |
"Approximately" | |
"Balloon" | |
"Shadow Length" | |
"Triangle with an angle of 45 ° " |
It can be concluded that the height of the tree will be about 10.5 m
The most simple I. available methods We consider the "air ball" and "triangle". Some require special weather conditionsBut we were lucky, because one day was the sun, another day of rain.
