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Various examples of graphic information models. Checking homework Give various examples of graphic information models

models

A variety of graphic models is large enough. Consider some of them.

Graphs

Claphs are a visual means of mapping the composition and structure of systems. Consider an example. There is a verbal description of some terrain.

The area consists of five villages: Dedkino, Republican, Babkino, Koshkino and Myshkino. The roads are laid between: Dedkino and Babkino, Dedkino and Koshkino, Babkino and Myskino, Babkino and Koshkino, Koshkino and Repkahn.

Such a description is quite difficult to imagine this terrain. It is much easier that the same information is perceived by the scheme. This is not a terrain map. Here, directions on the sides of the world are not supplied, is not complied with the scale. This scheme reflects only the fact of the existence of five settlements and road links between them. Such a scheme that displays the elemental composition of the system and the structure of the links is called the graph.

Composite parts of the graph are vertices and ribs. The vertex figure shows the circles - these are the elements of the system, and the ribs are depicted with lines - these are connections (relationships) between the elements. Looking at this graph, it is easy to understand the structure of the road system in a given area.

The constructed graph allows, for example, answer the question: through which villages you need to go to get from Repkane to Myshkino? It can be seen that there are two possible paths: 1) P - K - B - M and 2) R-K - D - M. Is it possible to conclude from here that the 1st way is shorter than 2)? No you can not. This graph does not contain quantitative characteristics. This is not a map where scale is observed and it is possible to measure the distance.

The graph shown in the following figure contains quantitative characteristics. The numbers near the ribs indicate the lengths of the roads in kilometers. This is an example of a weighted graph. A weighted graph may contain quantitative characteristics of not only connections, but also vertices. For example, in the vertices may indicate the population of each village. According to a weighted graph, it turns out that the second path is longer than the first.
Such graphs also call the network. The network is characterized by the possibility of many different ways of movement through the ribs between some vertices pairs. Networks are also characterized by the presence of closed paths that are called cycles. In this case, there is a cycle: K-D-B-K

On the considered schemes, each edge indicates the presence of a road link between two points. But the road connection acts the same in both directions: if on the way you can drive from b to m, then it can also drive from M to b (we assume that there is a bilateral movement). Such columns are non-oriented, and their connections are called symmetric.

A qualitatively different example of a graph is depicted in the following figure.

This example relates to medicine. It is known that different people have blood in a group. There are four blood groups. It turns out that when blood transfusion from one person to another, not all groups are compatible. Count shows possible options Blood transfusion. Blood groups are the vertices of the graph with the corresponding numbers, and the arrows indicate the possibility of transfusion of one blood group to man with another group of blood. For example, it can be seen from this graph that the blood of the first group can be transferred to any person, and a person with the first group of blood perceives only the blood of his group. It can be seen that a person with an IV blood group can be overflowed any, but its own blood can be transferred only to the same group.

The links between the vertices of this graph are asymmetric and therefore are depicted by directional lines with arrows. Such lines are called arcs (unlike edges of non-oriented graphs). Count with such properties is called oriented. The line emerging and incoming in the same vertex is called loop. In this example, there are four loops.

Tree - Count Hierarchical Structure

A very common type of systems are systems with a hierarchical structure. The hierarchical structure naturally occurs when objects or some of their properties are in relation to coented (attachments, inheritance). As a rule, the hierarchical structure has systems administrative management, between the elements of which the attitudes of the subordination (director of the plant - the heads of workshops are the heads of the plots - brigadiers - workers). The hierarchical structure also has systems, between the elements of which there are the relationship of one to others.

The graph of the hierarchical structure is called a tree. The main property of the tree is that there is a single path between any two vertices. Trees do not contain cycles and loops.

The Tree of the Administrative Structure of the Russian Federation

Look at the graph reflecting the hierarchical administrative structure of our state: the Russian Federation is divided into seven administrative districts; The counties are divided into regions (areas and national republics), which includes cities and others settlements. Such a graph is called a tree.

The tree has one main vertex, which is called the root of the tree. This vertex is depicted at the top; From her there are branches of a tree. From the root begins a countdown of tree levels. The vertices directly related to the root form the first level. They are connections to the tops of the second level, etc. Each vertex of the tree (except the root) has one source vertex at the previous level and can have many generated vertices at the next level. This principle of communication is called "one to many". The vertices that are not generated are called leaves (on our column are vertices denoting cities).

Graphic modeling Research results.

The common goal of scientific graphics can be formulated like this: make an invisible and abstract "visible." The last word is enclosed in quotes, because This visibility is often very conditional. You can see the temperature distribution inside the heterogeneously heated body of a complex shape without introducing hundreds of microdackers into it, i.e. Essentially its destruction? - Yes, it is possible if there is an appropriate mathematical model and, which is very important, an agreement on the perception of certain conventions in the figure. Can see distribution of metal ores underground without excavations? FROM surface Trojection Alien Planet According to the results of the radar? Yes, you can, with the help of computer graphics and the preceding mathematical processing.

Moreover, you can "see" and the fact that, strictly speaking, generally badly corresponds to the word "see." So, the science of chemistry at the junction and physicists - quantum chemistry - gives us the opportunity to "see" the structure of the molecule. These images are the top of the abstraction and conventions, as in the atomic world, our usual concepts about particles (nuclei, electrons, etc.) are fundamentally not applicable. However, a multicolor "image" of the molecule on the computer screen for those who understand the whole of its conditionality, brings more benefits than thousands of numbers that are computing results.

Isolastic.

Standard receiving processing of the results of a computing experiment is to build lines (surfaces), called insulated (isopuries), along which some function has a constant value. This is a very common receiving visualization of the characteristics of a certain scalar field in the approximation of a solid medium: isotherms - line of equal temperature; Isobaras - line of equal pressure; Insulature of the environmental population on the ground, etc.

Conditional colors, conditional contrast

This technique of modern scientific graphics is a conditional coloring. It finds widest use in the most different applications Science and is a set of techniques at the most convenient visualization of computer modeling results.

In various studies of temperature fields, the problem of a visual representation of the results, for example, temperatures on meteorological maps. To do this, you can draw isotherms on the background of the map of the area. But you can achieve even greater clarity, given that most people tend to take red color as "hot", blue - as cold. The transition to the spectrum from red to blue reflects the intermediate values \u200b\u200bof temperatures. When searching for minerals by aerial photography with airplanes or space satellites, computers are building conditional color images density distributions under the surface of the Earth, etc.

Images in conditional colors and contrasts - the most powerful reception of scientific graphics.

  • Do not be confused Studying graphic information modeling with the study of processing technologies graphic information
  • Construction of simple graphic models in the form of graphs and hierarchical structures is appropriate in the basic computer science.
  • The implementation of models of scientific graphics through programming is the material of increased difficulty, the practical work of which is relevant in the profile computer science.

The task :

    • Make a scheme of key concepts;
  • Pick up practical tasks With solutions for basic and profile informatics courses.

Objectives:

  • General education:
  • teach to build models of studied objects using charts;
  • master the methods for visualizing numeric data;
  • fastening concepts and skills to work with a spreadsheet Microsoft Excel.;
  • generalization and consolidation of material on the topic: "Basics of a cell doctrine"

Developing:

  • develop formalization skills when solving information problems using electronic processor tools;
  • develop the ability to analyze and summarize the material studied.

Raising:

  • computer perception as a tool for processing information objects;
  • to form students an idea of \u200b\u200bthe harmful effects of the external environmental factors on the livelihoods of the body.

EQUIPMENT:

Tables, doubts, cards with tasks, computers, software - Excel, Educational Presentation "Cell"<Приложение1> , Presentation "Model"< Приложение2> , Geographic map of Europe, a poultry brain model, a human skeleton model, a microscope.

DURING THE CLASSES

I. Class

II. Opening Word (Computer Science Teacher)

Currently, the most vivid discoveries occur at the junction of science. New sciences arise: bioengineering, bionics, bioinformatics. This is a vivid example of the integration of sciences. Today, at the lesson, we comphect material computer science and biology on the topics "Models", "Building diagrams and graphs in this Excel", "Basics of a cell doctrine" using computer technologies.

III. Actualization of knowledge

COMPUTER SCIENCE

The response is accepted on the topic "Modeling"

Demonstration of the presentation "Model"

Questions on the topic "Models":

What is the model?

What properties of real objects reproduce the following
Models:

  • apple duling;
  • scarecrow birds;
  • the skeleton of man in the Biology Cabinet.

What is the information model?

Explain the difference between the aircraft's technical model and the aircraft information model - the drawing.

Give various examples of graphic information models.

What is the form of a graphic model (map, scheme, drawing, graph) Applicable to display processes?

IV. Work in notebook

The teacher demonstrates various models According to biology.

Record in the notebook in the 1st column of material models, in the 2nd - informational,

in the 2nd patch mark graphic models.

V. Explanation of the new material("Computer modelling")

Modeling is a method of knowledge consisting of creating and examining models.

In almost all sciences about nature, living and inanimate, about society, the construction and use of models is a powerful instrument of knowledge. Real objects and processes are so multifaceted and difficult that the best way to study is often the construction of a model that displays only some line of reality and therefore many times easier than this reality, and the study of this model. The centuries-old experience in the development of science proved in practice the fruitfulness of this approach.

In modeling there are two different ways. The model can be a similar copy of the object made from another material, on another scale, with the lack of a number of parts. For example, this is a toy boat, a plane, a house of cubes and many other full-scale models. The model may, however, show reality with a more abstract - verbal description in free form, a description formalized by some rules, mathematical ratios, etc.

Modeling objectives:

  • the model is needed in order to understand how a specific object is arranged (or how it stems), what is its structure, basic properties, laws of development and interaction with the outside world (understanding);
  • the model is needed in order to learn how to control the object (or process) and determine best ways management for specified purposes and criteria (management);
  • the model is needed in order to predict the direct and indirect consequences of the implementation of the specified methods and forms of impact on the object (prediction).

These goals can be combined in one model, and reach the apart.

Throughout its history, humanity used various methods and tools for creating information models. These methods were constantly improved. So, first information models Created in the form of rock paintings, at present, information models are usually built and are investigated using modern computer technology.

The main stages of development and research of models on the computer:

Using a computer to study information models of various objects and systems allows you to study their changes, depending on the value of certain parameters. The process of developing models and their research on a computer can be divided into several main steps.

At the first stage of the study of the object or process, usually built descriptive information model.Such a model allocates significant, in terms of goals

the studies conducted, object parameters, and non-essential parameters neglected.

At the second stage it is created formalized modelthat is, the descriptive information model is recorded using a formal language. In such a model, with the help of formulas, equations, inequalities, etc., the formal relationships between the initial and end values \u200b\u200bof the properties of objects are recorded, and restrictions on the valid values \u200b\u200bof these properties are superimposed.

However, it is not always possible to find formulas that clearly express the desired values \u200b\u200bthrough the source data. In such cases, approximate mathematical methods are used to obtain results with a given accuracy.

At the third stage, the formalized information model is necessary to convert to computer modelthat is, express it on a computer-understandable language. There are two fundamentally different ways to build a computer model:

  • building a problem solving algorithm and its encoding in one of the programming languages;
  • building a computer model using
    One of the applications (spreadsheets, DBMS, etc.).

In the process of creating a computer model, it is useful to develop a convenient graphical interface that will allow you to visualize the formal model, as well as implement an interactive person's interactive dialogue with a computer at the model research step.

The fourth stage of the research of the information model is to hold computer experiment.If the computer model exists in the form of a program in one of the programming languages, it must be run to execute and get results.

If the computer model is examined in an application, for example, in spreadsheets, you can sort or search for data, build a chart or schedule and so on.

The fifth stage consists in analysis of the results obtained and the adjustment of the model under study.In case of the difference in the results obtained in the study of the information model, with the measured parameters of real objects, it can be concluded that errors or inaccuracies were made at the previous stages of the model. For example, when building a descriptive high-quality model.

Before building an information model, a system analysis of the modeling object is performed.

A task system analysis - Select the essential parts, properties, links of the simulated system, to determine its structure.

BIOLOGY

VI . introduction teacher biology

Biology is exploring the diversity of life forms. There is a huge variety of organisms on Earth. Discerning a number of essential signs among themselves, they have a common property - cellular structure.

VII . Individual task on cards (at the board 4 people)

Card number 1.

What is the structure of the cell?

Write on the board, from what basic, the main parts consists of a cell.

Card number 2.

Write on the board organides cells - special cellular organs located in the cytoplasm, and in which the basic life processes flow.

Card number 3.

Using magnetic manual, assemble an animal cell model.

Card number 4.

What is the exponential (scientific format) of the presentation of numbers used in electronic tables?

Submit numbers in scientific format.

VIII. Actualization of Knowledge (conversation with class)

Show presentation "Cage"

Questions and tasks on the topic "Cell":

  1. What kind of building has animal and vegetable cell?
  2. What is the difference between the animal cell from plant?
  3. What is the similarity in the structure of cells of various organisms?
  4. Write on the board, from what basic, the main parts consists of a cell (pay attention to the literacy of writing words).
  5. Function, value, role: cell membrane, cytoplasm, kernel.
  6. Why is the cytoplasm call the internal medium of the cell?
  7. List the cellides of the cell (they are also called by special cellular organs).
  8. What cells do not have the kernel? How else are they called?
  9. What are the organisms call, in the cells of which the core?
  10. What studies cytology?
  11. The history of the occurrence of cytology.
  12. What is called cloth?
  13. how many chemical elements In the periodic system of Mendeleev?
  14. How many chemical elements are contained in an animal cell?
  15. Macroelements are ...
  16. What is the value of carbon?
  17. Write chemical signs of macroelements.
  18. What is the value of macroelements?
  19. Microelements are ...
  20. Write chemical signs of trace elements.
  21. What is the importance of trace elements?
  22. What diseases arise with the lack of trace elements?
  23. What chemical compounds are in a cage?

IX. Check jobs at the board

COMPUTER SCIENCE

X. Computer modeling (computer science teacher)

A visual way of representing information models is graphic images: maps, drawings, schemes, graphics.

The spreadsheets (as well as databases) can be viewed as information models of real objects or processes.

The method of visual representation of numeric data is a diagram.

The type of diagram is established depending on the data presented in the data diagram and the need to obtain the resulting descriptions of numerical dependencies.

The diagram consists of several elements that can be sequentially and independently edit from each other, highlighting the desired object with a double mouse.

On the material of biology on the topic "Cell" we build a graphical information model

Students work in pairs (one fulfills the role of a consultant and answers questions on "spreadsheets", the other - performs the task on the computer on the construction of the model)

Task #1.

Build an information graphic model (a column chart), reflecting the content of cell chemical elements, Microsoft Excel spreadsheets.

Elements Number (in%)
Oxygen 70
Carbon 15
Hydrogen 9
Nitrogen 2,2
Calcium 2
Phosphorus 1
Potassium 0,4
Sulfur 0,2
Chlorine 0,1
Magnesium 0,03
Sodium 0,03
Microelements 0,025
Iron 0,015

Questions on the topic "Electronic Tables":

  1. What tabular processor?
  2. What functionality Does spreadsheet?
  3. What is called a cell in the spreadsheet?
  4. How are the cells are called?
  5. What information can be stored in cells?
  6. How to introduce a formula into a cell?
  7. What is the difference between the formula display mode and the display mode of the values?
  8. What happens in the spreadsheet as a result of the replacement of the number in the cell to a new value?
  9. What needs to be done to highlight the entire line?
  10. What needs to be done to highlight the entire column?
  11. In which formats, electronic tables can represent numeric data?
  12. What are diagrams used for?
  13. What types of diagrams are familiar to you?
  14. What shows the legend?
  15. When is the scientific or exponential format of numbers apply?
  16. What built-in functions are in spreadsheets?

Xi. Regional component

XII. Fizminutka

BIOLOGY

XIII. System analysis

  1. What is the meaning of water?
  2. What is the significance of minerals?
  3. What is the meaning of organic substances: proteins, carbohydrates, fats (lipids), nucleic acids?
  4. Why is the cell is considered the most complex chemical laboratory?
  5. What vital processes occur in cells?

COMPUTER SCIENCE

XIV. Computer modelling

Task№2.

Build an information graphic model (circular diagram), reflecting the content in the cell of chemical connections, Microsoft Excel spreadsheets.

XV The influence of external environmental factors on the body's life activity

(Alcohol, Nikitin, Drugs, Environmental Pollution)

Conversation with students.

XVI. Summarizing:

IT-teacher:

Biology teacher:

Homework:

COMPUTER SCIENCE

Disposable to the notebook words studied theme, difficult to memorize (exponential, model, spreadsheet, computer experiment).

Advanced task:

  • "Spreadsheets and mathematical modeling"
  • Using spreadsheets for scientific purposes (for forecasting)
  • Communication messages on this topic from other sources.

BIOLOGY

Relying on the paragraph from the textbook "Cell Building", to prove that the cell-biosystem.

4.8 Graphic information models.

The graphic information model is a good way to represent objects and processes in the form of graphic images. These include: drawings, graphs, charts, shaped models, diagrams (cards, graphs, block diagrams).

Graphic (geometric) information models transmit external signs of the object - dimensions, shape, color, location. Graphic information models for visual display of objects use conditional graphic images (shaped elements). Often graphic models are complemented by numbers, symbols and texts (iconic elements). In this case, they are called mixed models.

The figurative models are visual images of objects recorded on any carrier of information (paper, photo and film and dr.). These include drawings, photos.

Scheme- This is the presentation of some object in the general, main features with conventions. Scheme - This is a graphical display of the composition and structure of a complex system. With the help of circuits can be presented and appearance object, and its structure. The scheme as the information model does not pretend to complete the provision of information about the object. With the help of special techniques and graphic designations, one or more features of the object under consideration are more relocated.



In the computer science, the construction of flowcharts occupies a special place. Flowchart Vividly reflect the algorithm, i.e. Sequence of actions when solving the problem. They are built under programming - the creation of new programs.

Map Describes a specific locality that is an object of modeling for it. This is a reduced generalized image of the earth's surface on a plane in a particular symbol system. .

The card is created with certain goals for determining:


  • locations of settlements;

  • terrain relief;

  • the location of motorways;

  • measurements of distances between real objects on the ground

  • etc.
Now they got a big distribution of geo-information models (for example, http://maps.google.ru/ - satellite shooting of the map of the area).

Drawing - accurate geometric copy of the real object. Drawing- Conditional graphic image subject with an accurate ratio of its size obtained by projection. The drawing contains images, dimensional numbers, text. Images give views of the geometric form of the object, the number is the magnitude of the object and its parts, the inscriptions - about the title, scale in which images are made. The drawings are created by designers, designers, they must be very accurate, because They include all the necessary dimensions of the real object. There are a lot of different computer media for creating design drawings: autocadus, adem, compass, 3D MAs - for three-dimensional modeling, etc.


Graphs and charts are information models that are visual form represent numerical and statistical data.

Schedule- A line that gives a visual idea of \u200b\u200bthe character of the dependence of one value (for example, paths) from another (for example, time). Schedule - mapping and visualization of various processes (natural, economic, public and technical). The schedule allows you to track the dynamics of data change.

Diagram- a graphic image that gives a visual idea of \u200b\u200bthe ratio of any values \u200b\u200bor several values \u200b\u200bof one value, about changing their values. More details are the types of diagrams and methods for their construction will be considered when studying spreadsheets.


Graphs occupy a separate place among graphic models.


4.9 graphs
Graphs are wonderful mathematical objects, with their help you can solve a lot of different, externally similar to each other tasks. In mathematics there is a whole section - theory of graphswhich studies graphs, their properties and application. Programs are built in computer science. In this paragraph, only the most basic concepts, graph properties and some ways to solve problems are considered.

If the objects of some system are depicted by points (circles, ovals, rectangles ...), and the relationship between them - lines (arcs, arrows ...), then we will obtain the information model of the system in question in the form of a graph. Graphit is a set of vertices and connecting their ribs. The vertices of the graph can be indicated by letters, numbers, words ...

If the edge of the graph is characterized by some for more information (pronounced numbers), called it weighted, and numbers - weighsröber. The weight of the Ryber can match, for example, the distance between the objects (cities).

If the edges of the graph indicate the direction (represented by arrows), then the graph is called oriented (Orgraf). Movement in an oriented graph is possible only in one direction (by arrows). Communication between objects - vertices in this case is considered asymmetric. A non-oriented graph of communication between objects - vertices is symmetrical.



The same, but differently drawn graphs, called isomorphic. The same vertices are connected in isomorphic graphs.

Degreethe vertices of the graph are called the number of edges coming from it. A vertex having an even degree called even vertex, A vertex having an odd degree is called an odd vertex.In the drawing of the vertex A, B, D - even. Their degree is 2. The vertices with, e - odd. Their degree is 3.

One of the main theorems of the theory of graphs is associated with the concept of the top of the vertex - the number of odd vertices theorem.

Theorem : Any graph contains an even number of odd vertices.

To illustrate, consider the task.

In the city of small 5 phones. Is it possible to connect them with wires so that each phone is connected exactly with 3 others?

Decision: Suppose it is possible to connect phones. Then imagine the graph in which the peaks indicate the phones, and the ribs are wires, connecting them. We calculate how much the wires will turn out. Exactly 3 wires are connected to each telephone, i.e. The degree of each vertex of our graph - 3. To find the number of wires, it is necessary to sum up the degrees of all vertices of the graph and the resulting result is divided by 2 (because each wire has two ends and when the degrees are summarized, each wire is taken 2 times). (3 * 5) / 2 \u003d 15/2 \u003d 7.5

But this number is not a whole, that is, the number of wires will be different. It means our assumption that you can connect every phone exactly with five others, turned out to be incorrect.

Answer. Connect phones is thus impossible.
There is another important concept relating to the graphs - the concept of connected. Count is called svyaznoye, if any two tops can be connected way, those. Continuous sequence of ribs. There are a number of tasks whose solution is based on the concept of connectivity of the graph. The graph appears below has three components of the connectivity (consists of three separate parts).

A vertex that does not have a Röbebe called isolated The vertex is a separate component of connectivity. The vertex having only one edge is called terminal or hanging.

The path to the vertices and the edges of the graph, in which any edge of the graph enters no more than once, called chain (1) . Chain, initial and final vertices of which coincide, called cycle (2). Wood (hierarchy) - This is a graph in which there are no cycles (3), i.e. in it, it is impossible to go from some vertices to several different edges and return to the same vertex. A distinctive feature of the tree is that there is a single way between any two peaks.

(1)
(2)
(3)

Any hierarchical system can be represented by wood. The tree highlights one main vertex called its root. Each vertex of the tree (except the root) has only one ancestor, designated by it the object is in one class1 of the highest level. Any vertex of the tree can generate several descendants - vertices corresponding to the lower level classes. This principle of communication is called "one-to-many". The vertices that do not have generated vertices are called leaves.

For example, related links between family members are conveniently represented using a graph called a genealogical or pedigree tree.

Count with a cycle called network.If the heroes of some literary work are presenting the vertices of the graph, and the existing communication between them is a picture with Rybrachi, then we will get a graph called semantic network.

4.10 Using graphs when solving tasks
Example 1. In order to write down all three-digit numbers consisting of numbers 1 and 2, you can use the graph (wood)

The tree can not be built if you do not need to write all possible options, and you just need to specify their number. In this case, it is necessary to argue like this: in the discharge of hundreds can be any of the numbers 1 and 2, in the discharge of dozens - the same two options, in the discharge of units - the same two options. Consequently, the number of different options: 2 2 2 \u003d 8.

In general, if you know the number of possible options for choosing at each step of constructing a graph, then all these numbers need to calculate the total number of options multiply.

Example 2. Consider a somewhat modified classical task of crossing.

On the banks of the river there is a peasant (k) with a boat, and next to him - a dog (c), fox (l) and goose (D). The peasant should cross himself and transport the dog, foxes and goose to the other side. However, the boat except the peasant is placed either only a dog or only fox, or only goose. Leave the dog with a fox or fox with Guses without supervision. - The dog is dangerous for fox, and Fox is for a goose. How should the peasant organize the crossing?

D. to make this task to make a graph, whose vertices will be the initial placement of characters on the river bank, as well as all sorts of intermediate states achieved from the previous ones per step of crossing. Each vertex-state of the crossing is denoted by oval and connect Ribs with states formed from her. Invalid under the condition of the state problem are highlighted by a dotted line; They are excluded from further consideration. The initial and final state of the crossing is highlighted by a bold line.

The graph shows that there are two solutions to this task. We give a corresponding transfer plan to one of them:


  1. the peasant transports the fox;

  2. the peasant returns;

  3. the peasant transports the dog;

  4. the peasant returns with the fox;

  5. the peasant is transporting a goose;

  6. the peasant returns;

  7. the peasant transports the fox.
Example 3. Consider the following game: First, 5 matches lie in the pile; Two players remove matches in turn, and for 1st course you can remove 1 or 2 matches; Wins the one who leaves a match in a bunch. Find out who wins with the right game - the first (I)or the second (Ii)player.

Player I can remove one match (in this case they will remain 4) or 2 (in this case, there will remain 3).

If player I.left 4 matches, player II.can leave 3 or 2 matches as its move. If after the course of the first player there are 3 matches, the second player can win, taking two matches and leaving one.

If after the player II.3 or 2 matches left, then player I.each of these situations has a chance to win.

Thus, with the correct strategy of the game, the first player will always win. To do this, he must take one match.

In fig. 2.8 shows the graph called tree game;it reflects all possible options, including erroneous (losing) strokes of players.

Control questions.


  1. What information models refer to graphic?

  2. Give examples of graphic information models with whom you have:
a) when studying other items; b) in everyday life.

  1. What is a graph? What is the peaks and edges of the graph? Specify on your own graph-example.

  2. Which graph is called oriented?Weighted?

  3. What graphs are called isomorphic?

  4. What is the degree of vertices? Specify the degrees of the vertices in your graph.

  5. Formulatetheorem about the readiness of the number of odd vertices.

  6. What graph call connected? Picture graph with two connected components.

  7. What vertex is called isolated? Hanging? Specify on your own example - a column.

  8. What is the path? Chain? Cycle?Give examples of chains and cycles available in your graph.

  9. What is a tree? What systems can trees serve as models? Give an example of such a system.

  10. Make a semantic network in the Russian folk fairy tale "Kolobok".

Checking homework Give various examples of graphic information models. Give various examples of graphic information models. Graphic model of your apartment. What is this: card, scheme, drawing? Graphic model of your apartment. What is this: card, scheme, drawing? What is the form of a graphic model (map, scheme, drawing, graph) Applicable to display processes? Give examples. What is the form of a graphic model (map, scheme, drawing, graph) Applicable to display processes? Give examples.


Dynamic modeling






The meaningful setting of the problem in the process of tennis players' training machines are used to throw the ball into a certain place of the site. It is necessary to set the required speed and the angle of throwing the ball to enter the site of a certain size at a certain distance.




High-quality 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 ground, so it can be considered a material point; The change in the height of the ball is not enough, so the acceleration of the free fall can be considered a permanent value G \u003d 9.8 m / s 2 and the movement along the Y axis can be considered equivalent; The change in the height of the ball is not enough, so the acceleration of the free fall can be considered a permanent value G \u003d 9.8 m / s 2 and the movement along the Y axis can be considered equivalent; The thrust rate of the body is small, so the air resistance can be neglected and the movement along the x axis can be considered uniform. The thrust rate of the body is small, so the air resistance can be neglected and the movement along the x axis can be considered uniform.


The mathematical model x \u003d v0 · cosα · ty \u003d v0 · sinα · t - g · t 2/2 v0 · sinα · t - g · t 2/2 \u003d 0 t · (v0 · sinα - g · t / 2) \u003d 0 v0 · sinα - g · t / 2 \u003d 0 t \u003d (2 · v0 · sinα) / gx \u003d (v0 · cosα · 2 · v0 · sinα) / g \u003d (v0 2 · sin2α) / g s x s + L - "hit" if X S + L, then this means "Flight".


Computer model In the language of Pascal, the computer model in Pascal Program S1; Uses Graph; (Connecting a graphic module) Uses Graph; (Connecting a graphic module) 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 Computer model in Turbo Pascal Begin G: \u003d 9.8; G: \u003d 9.8; READLN (V0, A, S, L); gr: \u003d detect; initgraph (GR, GM, ""); (Challenge GRAPH) LINE (0,200,600,200); (Shames OH) Line (0,0,600); (blacksy axis OU) SetColor (3); (set blue color) Line (S * 10,200, (S + L) * 10,200); (diameters pad)
Computer model in Turbo Pascal language Computer model in Turbo Pascal X: \u003d 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 result of the flight) readln; Closegraph; END.



What examples of information models can be brought to educational institutions? How can teachers use them in their work? Let's try to find answers together to questions.

What is a model

What are iconic information models? Examples of them are used in their work all teachers who own modern information technology. IN general The model is different methods Representations of the analyzed reality.

Varieties

You can give examples of information models of the material and ideal species.

Washing options are based on an objective example, they exist independently of man, his consciousness. Currently, they are divided into physical and analog options, which are based on the phenomena associated with the subject being studied.

The ideal models are associated with human thinking, his perception, imagination. Among them can be noted intuitive, which are not suitable for any variant classification.

When applying examples of a figurative information model, you can mention one of these models. Consider more of their classification.

Text ideal models

Verbal models apply teachers of the humanitarian cycle. They help to describe with successive proposals a specific area, phenomenon, object, event. What will the lesson information model look like? Example Take from the course of literature. When studying the novel L. N. Tolstoy "War and Peace", the teacher describes the image of Natasha Rostova. For this, he uses the text model. Guys, listening to the teacher, create on the basis of his perception of the image of this heroine, their image of the heroine of Tolstoy.

If the history teacher asks for his pupils: "Give examples of the shared information model of events that occurred during the Kulikov battle, based on viewed fragments," the guys create their own image of that battle. They transmit it in the form of suggestions related to the story.

You can cite examples of information models of verbal species and from the course of physics. When studying the topic "Pressure of solid bodies" in the seventh grade, the teacher tells children how difficult it is to move around the loose snow without skis. Then, schoolchildren are invited to explain the cause of this phenomenon, to identify the parameters on which the studied physical value depends. The image that arises into the consciousness of the guys after the story of the teacher, helps them to answer the question.

As examples of such a model, a textbook, road rules can be noted.

Mathematical models

They are considered a wide class of iconic models. Mathematical models are based on the use of relations, comparisons, other methods used in this science. The resulting examples of information models based on mathematical methods can be mentioned by the solution of square equations, the preparation of proportions. All sections of geometry involving the conclusion and proof of the theorems are also associated with the construction of a mathematical model. Does not do without them and such a school subject as an economy.

Information models

They are considered a class of iconic models that describe any information processes: appearance, transmission, change, application of information in different systems. Examples of tabular information models at school can be founded in the course of grade 10. When studying economic geography, a tabular model helps to visually see the main characteristics of the country, use the material to compile a full story.

In addition, examples of tabular information models can be found in any school course. In chemistry, this is the solubility table of the compounds, as well as the periodic system of Mendeleev. In physics, without tables, the teacher is difficult to explain the main terms studied in the topic "Electricity". In history with their help, knowledge systematization is carried out, the guys enter in one column important historical dates, and in the other - describe the events that corresponded to them.

Interconnection of models

There is a conditional face between informational, mathematical, verbal models. All 3 examples of information models are found in school disciplines. So, for mathematics, physics, computer science, mathematical and informational options are considered the most sought-after. But without a verbal model, the guys will not be able to explain the phenomena, algorithms, equations and inequalities.

Simulation features

Before considering examples of graphic information models, find out the features of modeling. The model is an object created artificially. This is necessary to simplify the presentation of this object or phenomenon. The model fully reflects all the features of the most source process. If task is given: "Give an example of an information model", it is necessary to understand the essence of the process.

We are talking about building a model that is intended to study information phenomena, processes. In computer science, as such an item, you can consider programming. Using a specific mathematical programming language, you can submit text material in graphical form.

Modeling involves the construction of the model that is designed to study and study the source object, phenomena, process. The created copy is only endowed with the qualities and properties that are characteristic of the original item, but allows some deviations from the ideal.

Activity approach

Full models can be obtained by using a system approach. This is especially true in educational institutions. The transformations that touched the schools in recent years have made it possible to establish a logical connection between individual disciplines.

Such an activity option contributes to the formation of a harmoniously developed personality that understands the unity of the living world, the relationship of individual processes and phenomena.

If teachers ask: "Give an example of an information model", it can safely choose any academic subject. There is no such discipline in which tables, graphs, diagrams, presentations would not be used.

Features of modern school

New standards that were introduced into Russian schools suggest a consideration of one phenomenon from different points of view. For example, from the course of physics, the guys learn that the electrons are necessary for the flow in metals. electric current. They receive information about the charge of this negative particle, determining their number of different metals. At the lessons of chemistry, schoolchildren talk about the probability of electron location in the energy levels.

When studying the topic "Redox reactions", schoolchildren appear information about what is happening with these negative particles during chemical interaction. Despite the fact that information is provided from different positions, we are talking about one object - electrons. A similar systematic approach allows the formation of a complete picture of the structure of the substance, its transformations in the consciousness of schoolchildren.

In the example above, the studied object is considered as a complete system, component Single whole (substance). Depending on the educational discipline Use certain characteristics, additions. In the case of a systematic approach, the first place is not causal explanations of the existence of an object, but the need to include other component parts from it.

Of particular importance is the formation of universal models acquires with experimental activities. Using a personal computer, you can calculate the parameters that will be associated with the analyzed object.

Such modeling is important for scientific knowledge of natural phenomena. In the school course of informatics, such actions are called the computing experiment, which is based on three important concepts: models, algorithm, program.

School use personal computer Perhaps in three main options:

  • conducting direct calculations using PC;
  • creating a database, transformation into a program or a specific algorithm;
  • maintaining between computer and schoolboy interface.

Signs of models

Among the most common signs that can be classified by all models, we will highlight: the purpose of application, the scope of knowledge, a temporary factor, a representation option.

Depending on which purpose is set in front of the model, you allocate experienced, educational, game, imitation, scientific and technical options for models. For example, at the initial stage of school education, the most applicable and significant game technologies that allow the guys to feel themselves as a teacher, a doctor, a policeman. Game models in children seven-eight years are well formed, because in pre-school educational institutions, they are used as a mandatory element in the formation of the personal qualities of the child.

Varieties of models

Depending on the field of knowledge for which the model is drawn up, currently allocate economic, biological, sociological, chemical species. For example, it is important for the natural science cycle to form a model that would allow to explain the phenomena that occur in a living and inanimate nature. In sociology, the emphasis on the processes occurring in society.

According to the temporary factor, static and dynamic variants of models are distinguished. The static variant characterizes the parameters and structure of the object, allows you to describe the selected phenomenon (object) at a particular period of time, helps to receive reliable and timely information about it.

Any model has a specific form, view, version option, description. The school suggests a consideration of more material and intangible models, depending on the specifics of the academic discipline.

Material models involve a real embodiment, they fully repeat the inner or external structure of the object itself. For example, in geography as such a reduced model, the globe layout (globe) stands on which all seas and oceans, continents and islands are applied. These models are directly related to the research approach to learning modern schoolchildren. They are needed in teaching chemistry, physics, biology, astronomy, geography.

Intangible modeling involves the use of theoretical method of knowledge.

Conclusion

Any information model is a set of information about the phenomenon, object, process. With it, it is possible to characterize any process that occurs in a living and inanimate nature. A variety of graphs, cards, tables, charts that are actively used by teachers on all levels of learning, give their positive result.

Intuitive (mental) modeling contributes to the creation of the first impression on the process occurring in chemistry or biology. Due to the combination of all options for information models, the younger generation of our country has an adequate assessment of the unity of the living and non-living world. School graduates can independently build any models, use them to explore, analyze, evaluate events and phenomena.