Information model– a model of an object, presented in the form of information that describes the parameters and variable quantities of the object that are essential for this consideration, the connections between them, the inputs and outputs of the object, and which allows, by feeding the model information about changes in input quantities, to simulate possible states of the object.
Information models cannot be touched or seen; they have no material embodiment, because they are built only on information. An information model is a set of information that characterizes the essential properties and states of an object, process, phenomenon, as well as the relationship with the outside world.
An information model is a formal model of a limited set of facts, concepts, or instructions designed to satisfy a specific requirement.
To build an information model, it is necessary to go through a number of stages presented in Diagram 3. The process carried out from the “object of knowledge” to the “formal construction” is called “formalization”, and the reverse process - “interpretation” - is most often used in knowledge of the world and learning .
Information modeling is based on three postulates:
everything is made up of elements;
elements have properties;
elements are interconnected by relationships.
The object to which these postulates apply can be represented by an information model.
Stages of building an information model.
F Object of knowledge I
O Cognizing subjects N
P Personal presentation T
M Formed thought E
And the “Live” word R
L Written word P
I Scientific text R
Z Formal constructions E
Classifications of information models:
-according to the method of description:
Using formal languages (mathematical language, tables, programming languages, extension of human natural language, etc.);
Graphic (flowcharts, diagrams, graphs, etc.).
-according to the purpose of creation:
Classification (tree-like, family tree, computer directory tree);
Dynamic (as a rule, they are built on the basis of solving differential equations and are used to solve control and forecasting problems).
- by the nature of the modeled object:
Deterministic (definite), for which the laws by which the object changes or develops are known;
Probabilistic (processing of statistical uncertainty and some types of fuzzy information).
Historical origin and methodological significance of the concepts of model and analogy.
The word “model” comes from the Latin word “modulus”, meaning “measure”, “sample”. Its original meaning was associated with the art of building, and in almost all European languages it was used to denote an image or prototype, or a thing similar in some respect to another thing.
Modeling in scientific research began to be used in ancient times and gradually captured new areas of scientific knowledge: technical design, construction and architecture, astronomy, physics, chemistry, biology and, finally, social sciences. The 20th century brought great success and recognition in almost all branches of modern science to the modeling method. However, modeling methodology has long been developed by individual sciences independently of each other. There was no unified system of concepts, no unified terminology. Only gradually the role of modeling as a universal method of scientific knowledge began to be realized.
The term “model” is widely used in various fields of human activity and has many meanings. In this section we will consider only those models that are tools for obtaining knowledge.
Thus, model– a simplified idea of a real object, process or phenomenon. A model is a material or mentally imagined object that, in the process of research, replaces the original object so that its direct study provides new knowledge about the original object.
Under simulation understands the process of constructing, studying and applying models. It is closely related to such categories as abstraction, analogy, hypothesis, etc. The modeling process necessarily includes the construction of abstractions, inferences by analogy, and the construction of scientific hypotheses. Modeling– building models for research and study of objects, processes, phenomena.
Models of objects must reflect something that actually exists. Therefore, object models are often understood as an abstract generalization of real-life objects. For example, models of objects can be copies of architectural structures, the solar system, the structure of parliamentary power in the country, etc. A model can describe phenomena of living and inanimate nature, and not just one, but a whole class of phenomena with common properties. Models of objects or phenomena reflect the properties of the original - its characteristics, parameters.
You can also create process models, e.g. simulate actions on material objects: progress, successive changes of states, stages of development of one object or their system. Examples of this are well known: these are models of economic or environmental processes, the development of the Universe or society, etc.
Methodological basis for modeling.
The modeling theory is based on a systems approach. The systems approach is that the researcher tries to study the behavior of the system as a whole, rather than focusing on its individual parts. This approach is based on the recognition that even if each element or subsystem has optimal design or functional characteristics, the resulting behavior of the system as a whole may be only suboptimal due to the interaction between its individual parts.
The increasing complexity of organizational systems and the need to overcome this complexity have led to the systems approach becoming an increasingly necessary research method.
A certain set of elements of the system under consideration can be represented as its subsystem. It is believed that subsystems include some independently functioning parts of the system. Therefore, to simplify the research procedure, it is initially necessary to correctly identify the subsystems of a complex system, that is, to determine its structure. The structure of a system is a time-stable set of relationships between its components (subsystems). And with a systems approach, an important step is to determine the structure of the system being studied and described.
A system is a whole made up of parts. A system is a set of elements that are in relationships and connections with each other and form a certain integrity and unity.
Computer model.
Computer model– a model implemented by means of a software environment.
When dealing with a computer as a tool, you need to remember that it works with information. Therefore, one should proceed from what information and in what form a computer can perceive and process. A modern computer is capable of working with sound, video, animation, text, diagrams, tables, etc. But to use the entire variety of information, you need both hardware (Hardware) and software (Software). Both are computer modeling tools. Now there is a wide range of programs that allow you to create various types of computer iconic models: word processors, formula editors, spreadsheets, database management systems, professional design systems, as well as various programming environments.
Modern computers provide ample opportunities for modeling various phenomena and processes. In the educational process, a computer should not simply replace a blackboard, a poster, a film and slide projector, or a natural experiment. Such a replacement is advisable only when the use of a computer will provide a significant additional effect compared to the use of other teaching aids.
Computer modeling (CM) is a promising method for enhancing the educational process. It is gaining more and more importance in modern scientific knowledge, and, in addition, is currently becoming a popular didactic tool. Let's consider this direction in more detail.
The subject of CM is the study of processes and phenomena using a computer, which in this case acts as an experimental setup. When using CM to solve problems, the stages of problem formulation, model development, computer (computational) experiment, and analysis of modeling results are distinguished. If the simulation results do not meet the goal, then there is a need to return to previous stages.
Mathematical models.
Mathematical modeling allows you to create a description of the ongoing process using mathematical symbols and dependencies.
Mathematical model is a set of mathematical objects and relationships between them that adequately reflects the properties and behavior of the object under study. The model is considered adequate if it reflects the properties under study with acceptable accuracy. The accuracy is assessed by the degree of agreement between the values of the output parameters predicted during a computational experiment on the model and their true values.
A mathematical model covers a class of undefined (abstract, symbolic) mathematical objects such as numbers or vectors, and the relationships between these objects.
A mathematical relation is a hypothetical rule connecting two or more symbolic objects. Many relationships can be described using mathematical operations that connect one or more objects with another object or set of objects (the result of the operation).
A mathematical model will reproduce suitably selected aspects of a physical situation if a correspondence rule can be established linking specific physical objects and relations with specific mathematical objects and relations. The construction of mathematical models for which there are no analogues in the physical world can also be instructive and/or interesting. The most commonly known mathematical models are systems of integers and real numbers and Euclidean geometry; the defining properties of these models are more or less direct abstractions of physical processes (counting, ordering, comparison, measurement).
The objects and operations of more general mathematical models are often associated with sets of real numbers that can be related to the results of physical measurements.
Numbers, variables, sets, vectors, matrices, etc. act as mathematical objects.
Classification of mathematical models based on the characteristics of the mathematical apparatus used.
4.8 Graphic information models.
A graphical information model is a visual way of representing objects and processes in the form of graphic images. These include: drawings, graphs, diagrams, figurative models, diagrams (maps, graphs, flowcharts).
Graphic (geometric) information models convey the external characteristics of an object - size, shape, color, location. In graphic information models, conventional graphic images (figurative elements) are used to visually display objects. Often graphic models are supplemented with numbers, symbols and texts (sign elements). In this case, they are called mixed models.
Figurative models are visual images of objects recorded on some information medium (paper, photo and film, etc.). These include drawings and photographs.
Scheme- this is a representation of some object in general, main features using symbols. Scheme is a graphical representation of the composition and structure of a complex system. With the help of diagrams, both the appearance of an object and its structure can be represented. A diagram as an information model does not claim to be complete in providing information about an object. With the help of special techniques and graphic symbols, one or more features of the object in question are highlighted more clearly.
In computer science, a special place is occupied by the construction of flowcharts. Block diagrams clearly reflect the algorithm, i.e. sequence of actions when solving a problem. They are built during programming - creating new programs.
Map describes a specific area, which is the object of modeling for it. This is a reduced generalized image of the Earth’s surface on a plane in one or another symbol system .
The map is created with specific purposes to determine:
locations of settlements;
terrain;
highway locations;
measuring distances between real objects on the ground
etc.
Drawing– an exact geometric copy of a real object. Drawing- a conventional graphic image of an object with an exact ratio of its dimensions, obtained by the projection method. The drawing contains images, dimensional numbers, and text. Images give ideas about the geometric shape of the object, numbers - about the size of the object and its parts, inscriptions - about the name, the scale in which the images are made. Drawings are created by designers, designers, they must be very accurate, because... they indicate all the necessary dimensions of the real object. There are a lot of different computer environments for creating design drawings: AutoCAD, Adem, Compass, 3D MAX - for three-dimensional modeling, etc.
Graphs and diagrams are information models that present numerical and statistical data in a visual form.
Schedule- a line that gives a visual representation of the nature of the dependence of one quantity (for example, path) on another (for example, time). Schedule– display and visualization of various processes (natural, economic, social and technical). The graph allows you to track the dynamics of data changes. 
Diagram- a graphic image that gives a visual representation of the relationship between any quantities or several values of one quantity, and the change in their values. The types of charts and methods for constructing them will be discussed in more detail when studying spreadsheets.
Graphs occupy a special place among graphical models.
4.9 Graphs
Graphs are wonderful mathematical objects; with their help you can solve a lot of different, outwardly dissimilar problems. There is a whole section in mathematics - graph theory, which studies graphs, their properties and applications. In computer science, programs are built using graphs. This section discusses only the most basic concepts, properties of graphs and some methods for solving problems.
If the objects of a certain system are represented by points (circles, ovals, rectangles...), and the connections between them - by lines (arcs, arrows...), then we will obtain an information model of the system in question in the form of a graph. Graph is a set of vertices and edges connecting them. The vertices of the graph can be designated by letters, numbers, words...
If the edges of a graph are characterized by some additional information (expressed in numbers), it is called weighted, and the numbers are scales ribs The weight of the edges can correspond, for example, to the distance between objects (cities).
If the edges of a graph indicate direction (represented by arrows), then the graph is called oriented(digraph). Movement in a directed graph is only possible in one direction (along the arrows). In this case, connections between objects - vertices - are considered asymmetrical. In an undirected graph, the connections between objects - vertices - are symmetrical.
Identical but differently drawn graphs are called isomorphic. Isomorphic graphs have the same vertices connected.
Degree A vertex in a graph is called the number of edges leaving it. A vertex with an even degree is called even vertex,A vertex having an odd degree is called odd vertex. In the figure, vertices A, B, D are even. Their degree is 2. The vertices C and E are odd. Their degree is 3.
One of the main theorems of graph theory is connected with the concept of vertex degree - the theorem on the parity of the number of odd vertices.
Theorem : Any graph contains an even number of odd vertices.
To illustrate, consider a problem.
There are 5 telephones in the town of Malenky. Is it possible to connect them with wires so that each phone is connected to exactly 3 others?
Solution: Let's assume that such a connection between telephones is possible. Then imagine a graph in which the vertices represent telephones, and the edges represent the wires connecting them. Let's count how many wires there are in total. Each phone has exactly 3 wires connected, i.e. the degree of each vertex of our graph is 3. To find the number of wires, you need to sum up the degrees of all the vertices of the graph and divide the resulting result by 2 (since each wire has two ends and when summing the degrees, each wire is taken 2 times). (3*5)/2=15/2=7.5
But this number is not an integer, that is, the number of wires will be different. This means that our assumption that each phone can be connected to exactly five others turned out to be incorrect.
Answer. It is impossible to connect phones this way.
There is another important concept related to graphs - the concept of connectivity. The graph is called coherent,
if any two of its vertices can be connected by,
those. continuous sequence of edges. There are a number of problems whose solution is based on the concept of graph connectivity. The graph in the figure below has three connected components (consists of three separate parts).
A vertex that has no edges is called isolated vertex and constitutes a separate connected component. A vertex with only one edge is called terminal or hanging.
A path along the vertices and edges of a graph, in which any edge of the graph occurs at most once, is called chain (1) . A chain whose starting and ending vertices coincide is called cycle (2). Tree (hierarchy) is a graph in which there are no cycles (3), that is, in it it is impossible to go from a certain vertex along several different edges and return to the same vertex. A distinctive feature of a tree is that there is only one path between any two of its vertices.
(1) 
(2) 
(3)
Any hierarchical system can be represented using a tree. A tree has one main vertex, called its root. Each vertex of the tree (except the root) has only one ancestor; the object designated by it is included in one class1 of the highest level. Any vertex of a tree can generate several descendants - vertices corresponding to lower-level classes. This communication principle is called “one-to-many”. Vertices that have no generated vertices are called leaves.
For example, it is convenient to depict relationships between family members using a graph called a family tree or family tree.
A graph with a cycle is called network. If we represent the characters of a certain literary work as vertices of a graph, and the connections existing between them are depicted as edges, then we get a graph called semantic network.
4.10
Using graphs to solve problems
Example 1. In order to write down all three-digit numbers consisting of digits 1 and 2, you can use a graph (tree)
You don’t have to build a tree if you don’t need to write down all possible options, but just need to indicate their number. In this case, you need to reason like this: in the hundreds place there can be any of the numbers 1 and 2, in the tens place there can be the same two options, in the units place there can be the same two options. Therefore, the number of different options: 2 2 2 = 8.
In general, if the number of possible choices at each step of constructing the graph is known, then all these numbers are needed to calculate the total number of options multiply.
Example 2. Let us consider a slightly modified classical crossing problem.
On the bank of the river stands a peasant (K) with a boat, and next to him there is a dog (S), a fox (L) and a goose (G). The peasant must cross himself and transport the dog, fox and goose to the other side. However, in addition to the peasant, either only a dog, or only a fox, or only a goose can be placed in the boat. You cannot leave a dog with a fox or a fox with a goose unattended - the dog is a danger to the fox, and the fox is a danger to the goose. How should a peasant organize a crossing?
D 
To solve this problem, let's create a graph whose vertices will be the initial placement of the characters on the river bank, as well as all sorts of intermediate states achieved from the previous ones in one crossing step. We denote each crossing state vertex by an oval and connect it with edges to the states formed from it. Invalid states according to the conditions of the problem are highlighted with a dotted line; they are excluded from further consideration. The initial and final states of the crossing are highlighted with a thick line.
The graph shows that there are two solutions to this problem. Here is a crossing plan corresponding to one of them:
a peasant transports a fox;
the peasant returns;
a peasant transports a dog;
the peasant returns with the fox;
a peasant transports a goose;
the peasant returns;
a peasant transports a fox.
Player I can remove one match (in this case there will be 4 of them) or 2 at once (in this case there will be 3 of them).
If the player I left 4 matches, player II can leave 3 or 2 matches on its own. If after the first player's turn there are 3 matches left, the second player can win by taking two matches and leaving one.
If after the player II 3 or 2 matches left, then the player I in each of these situations has a chance to win.
Thus, with the right game strategy, the first player will always win. To do this, he must take one match on his first move.
In Fig. 2.8 presents a graph called game tree; it reflects all possible options, including erroneous (losing) moves of players.
Control questions.
What information models are classified as graphic?
Give examples of graphical information models that you are dealing with:
What is a graph? What are the vertices and edges of the graph?Use your own example graph.
Which graph is called directed? Weighted?
What graphs are called isomorphic?
What is the degree of a vertex? Specify the degrees of the vertices in your graph.
Formulatetheorem on the parity of the number of odd vertices.
Which graph is called connected? Draw a graph with two connected components.
Which vertex is called isolated? Hanging? Use your own example – graph.
What is a path? Chain? Cycle?Give examples of circuits and cycles available in your graph.
What is a tree? What systems can trees serve as models? Give an example of such a system.
Create a semantic network based on the Russian folk tale “Kolobok”.
Hearing words such as “modelling”, “model”, a person imagines images from his childhood: models of houses, small cars, airplanes, a globe. It is with the help of such simplified options that the functions and characteristics of genuine objects and objects are reflected. Looking at examples of information models, it is much easier to understand the essence and purpose of the original itself.
Main purpose of modeling
Examples of graphical information models are common in everyday life. It is with their help that one can visualize the complexity of real processes. They are similar to real objects, but have only those characteristics that will be in demand in a certain situation. Examples of information models show that there is no point in giving them absolutely all the characteristics of a real object. After all, the structure will have to be significantly complicated; it will be inconvenient to use.
It is important to understand what the main purpose of creating the model is and in what situation it will be used. Based on these characteristics, the created reduced copy of the real object is endowed with certain parameters. In modern modeling they try to adhere to a clear sequence. It includes the creation of the object itself, setting a goal for creating a smaller copy, and determining its main characteristics.
System analysis
If you analyze examples of information models, you need to focus on verbal, graphic, mathematical, and tabular options. Let's try to identify the most important parameters that are necessary for modeling, and also find the relationship between them. The process concerning the compilation of a set of properties of a real object to form its reduced copy is usually called system analysis.
Presentation option
Examples of information models of various types confirm the importance of finding the optimal form of their representation. It is precisely this that is associated with the formation of a certain image about a real object. Among the main requirements for the project, the leading position belongs to visibility. It is provided by an information graphic model. Let's talk about it in more detail.
It is quite easy to give graphic examples. They can be maps of a certain area of the area, electrical diagrams, various drawings, and graphs. It can be considered interesting that the same value being studied, for example, the average daily air temperature, can be presented in various forms. It can be expressed in the form of a table, a coordinate system, or text. An example of constructing an information model using the same data is used in both general education institutions and higher education.
Application of Simulation
Once a prototype of a real object has been formed, its parameters can be used to get acquainted with the original, predict the behavior of the object under study depending on the conditions, and carry out the necessary calculations. Examples of object information models indicate that it is often more convenient to use mixed options. Where can you find such a symbiosis? Examples of mixed-view information models are common in construction. They make it possible to determine, through preliminary mathematical calculations, the optimal loads on different parts of the building, and to prevent “subsidence” of the foundation.
Vivid examples of mixed-type graphical information models are various geographical maps. They are supplemented with tables, explanatory inscriptions, and topographical special symbols. In addition, in geography they often use diagrams, graphs, and diagrams. The latter are divided into graphs, blocks, maps.
About the classification of models
In order to make it convenient to work with the created models, there is a conditional division of them into blocks:
- by areas of application;
- branches of knowledge;
- time factor;
- type of presentation.
In addition, it is possible to divide according to the type of construction into network, hierarchical, and tabular types. Depending on the type of data presentation, there are various examples of graphic information models of a symbolic or figuratively symbolic type. A real object can be considered using a description of its properties or an analysis of the principle of its operation.
Examples of figurative information model
Let’s say the teacher gave the students an assignment during the lesson: give examples of graphical information models. What needs to be done for this? To begin with, you can select options recorded on paper. They can be considered any geographical maps, drawings, photographs, graphs. There are quite a lot of similar examples in educational institutions. After all, one of the main ways of visual learning is to present the material being studied in graphical and tabular form.
Not only in geography lessons, the teacher offers his students numerous diagrams and maps. A subject such as history is also closely related to drawings, graphs, and various tables. If a history teacher tells his pupil: “Give examples of graphic information models relating to the Battle of Stalingrad,” the child just needs to open the atlas to the right page. With the help of arrows and color accents, the map reflects all the main points regarding this legendary event. In addition to educational institutions, variants of the figurative information model are also found in scientific institutions that specialize in dividing objects according to their external characteristics.
Division of models by time
There are dynamic and static options. They are significantly different. Static information models assume the object being studied in a specific period of time. Examples of them can be found during the construction of a building. Construction involves initial calculations of strength and resistance to static load. There are static options in dentistry. Describing the condition of the patient’s oral cavity during a medical examination, the doctor notes the presence of various defects and the number of fillings.
With the help of the dentist, he will analyze the dynamics of changes in the condition of a person’s teeth over a certain period of time. For example, for the last year or since the previous appointment. Dynamic information models are also encountered when working with characteristics or factors that imply changes over time. Among such parameters we can mention seismic vibrations, temperature jumps, and changes in air humidity.
Verbal Information Models
An example of a student’s information model clearly explains this group. When answering questions proposed by the teacher, the child uses a verbal description of the phenomenon or process. For example, when talking about the rules of behavior for a pedestrian on the road, a student independently models the situation and offers his own way of resolving it. A rhyme that the poet has not yet managed to transfer to a sheet of paper is also included in this category. The verbal information model is descriptive in nature. An example of this is prose in works, text descriptions of certain objects and phenomena.
Iconic models
As another characteristic, one can imagine the display of the characteristics of an object using a formal language. Giving 2 examples of a sign information model, we will focus on texts and diagrams. Both methods of representing an object are used in almost all areas of modern human activity. There is a division of iconic models into structural, special, verbal, logical, and geometric types.
Mathematical forms
The main feature of the mathematical information model is the search for relationships between quantitative characteristics when describing an object. For example, knowing the mass of the body in question, you can use the formula to calculate the speed of its movement over a certain time period. Mathematical information models are divided into types: discrete, static, simulation, continuous, dynamic, logical, algorithmic, multiple, game, probabilistic.
Tabular Information Models
If the properties of an object or model are presented in the form of a list, and the values are in cells, we are talking about a tabular model. It is considered one of the most common ways of transmitting information. Using tables, dynamic and static information characteristics are formed in a variety of application areas. In everyday life, a person is faced with similar options, analyzing the schedule of commuter trains, studying the TV program, and looking at the weather forecast. There are binary tables that represent two characteristics of the process or phenomenon under consideration.
For example, in order to create a speed graph, a table of data is drawn. It contains movement and time parameters. “Object - object” tables involve listing their names in rows and columns. For example, there may be an indication of settlements. The relationship between them will be qualitative characteristics. The tables of the “object - property” option contain information about the event in a row and information about its characteristics in a column. Using such tables, you can determine weather parameters: temperature, wind strength, precipitation for several days. It is convenient to use tabular models in cases where the object in question has few characteristics. If you need to create a diagram of metro lines that has a lot of branches and transitions, you need a network information model. An example of a hierarchical information model is a family tree.
Conclusion
Numerous information models help modern man to organize the characteristics of objects found in nature and technology that he encounters in everyday life. It is with their help that you can get an idea of some real object or phenomenon in order to find the best ways to use it and control it. Without information models of various types, it is problematic for representatives of many professions to work.
Homework check Give various examples of graphical information models. Give various examples of graphical information models. Graphic model of your apartment. What is this: map, diagram, drawing? Graphic model of your apartment. What is this: map, diagram, drawing? What form of graphical model (map, diagram, drawing, graph) is applicable to display processes? Give examples. What form of graphical model (map, diagram, drawing, graph) is applicable to display processes? Give examples.
Dynamic Simulation
Meaningful formulation of the problem During the training of tennis players, machines are used to throw the ball at a certain place on the court. It is necessary to set the machine the required speed and angle of throwing the ball to hit an area of a certain size located at a known distance.
Qualitative descriptive model: the ball is small compared to the Earth, so it can be considered a material point; the ball is small compared to the Earth, so it can be considered a material point; the change in the height of the ball is small, therefore the acceleration of gravity can be considered a constant value g = 9.8 m/s 2 and the movement along the Y axis can be considered uniformly accelerated; the change in the height of the ball is small, therefore the acceleration of gravity can be considered a constant value g = 9.8 m/s 2 and the movement along the Y axis can be considered uniformly accelerated; the speed of throwing the body is low, therefore air resistance can be neglected and the movement along the X axis can be considered uniform. the speed of throwing the body is low, therefore air resistance can be neglected and the movement along the X axis can be considered uniform.
Mathematical model x = v0 cosα t y = v0 sinα t – g t 2 /2 v0 sinα t – g t 2 /2 = 0 t (v0 sinα – g t/2) = 0 v0 sinα – g t/2 = 0 t = (2 v0 sinα)/g x = (v0 cosα 2 v0 sinα)/g = (v0 2 sin2α)/g S x S+ L – “hit” If x is S+L, then this means “overfly”.
Computer model in Pascal language Computer model in Pascal language program s1; uses graph; (connecting a graphics module) uses graph; (graphics module connection) var g, V0, A, t: real; var g, V0, A, t: real; gr, gm, S, L, x, i, y: integer; gr, gm, S, L, x, i, y: integer;
Computer model in Turbo Pascal language Computer model in Turbo Pascal language begin g:=9.8; g:=9.8; readln(v0, a, S, L); gr:=detect; initgraph(gr,gm,""); (call the GRAPH procedure) line(0,200,600,200);(draw the x-axis) line(0,0,0,600);(draw the y-axis) setcolor(3);(set the blue color) line(S*10,200,(S+L) *10,200); (draw a platform)
Computer model in Turbo Pascal language Computer model in Turbo Pascal language x:=round(v0*v0*sin(2*a*3.14/180)/g); if x S+L then outtextxy(500,100,"perelet") else outtextxy(500,100,"popal"); (record the flight result) readln;closegraph;end.
