'LoveMaths Stories' book is on Amazon

 My new book 'LoveMaths Stories'  is already on Amazon. 

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Новата ми книга 'LoveMaths Stories' може вече да се намери в Амазон.

  Here is the link:

 https://www.amazon.co.uk/LoveMaths-Stories-Dr-Elena-Lyubenova-ebook/dp/B08LZL1BGQ/ref=tmm_kin_swatch_0?_encoding=UTF8&qid=1603817621&sr=8-1

PATTERNS

The idea of patterns accompanies human life since the early years of human civilisation. It is an abstract and very powerful idea which holds human life in order and good structure. Everything we do in life is subject to rules, models and repetitions. Since we were born this is the only way how to discover the world around us, by following certain patterns. In every area in our work or personal life,  we obey some models, examples and rules. This is the only way to learn new things by investigating and identifying the force that caused the patterns. We learn by repeating some knowledge in a certain way, following certain patterns. A pattern is a way in which something is done or organised, or in which something happens. We can talk about weather patterns, behaviour patterns, shape patterns, colour patterns and many other types of patterns depending on the nature of activities we are involved. The idea of patterns is an abstract philosophical one with great applications in every aspect of human life. Whatever we do we instinctively organise ourselves in a way that repeats itself again and again, throughout space in an identical but not random way; especially if the patterns are a good model and show progress and development, we tend to keep this pattern for next time as well.  Lack of everyday patterns that we could follow is a signal for our brain for chaos and can cause mental health problems, we will feel lost and frustrated like something is not right. We naturally like patterns and we recognise them, it is part of our human intelligence. We can not imagine our lives separated from the patterns because the ability to organise ourselves in a specific way and to maintain this way it is what makes us humans as well. Pattern recognition is what allows us to do everything from recognising individuals, people’s emotional states to solving jigsaw puzzles and sensing when a storm is to come.
In our greatest teacher nature, patterns are visible regularities of form found everywhere. They create the structure of the plants for example. Tree branches grow in a certain pattern. When we make patterns, it happens as a result of our plan to put the elements into a certain place. In nature, somehow natural forces agree to create patterns that look beautiful.

'LoveMaths Stories' book

My new book is on its way! Keep an eye out for any announcements during the next few months!

THE DIMENSIONS WE LIVE IN

The concept of ‘dimension’ is something that is interesting to all of us. Thanks to many science fiction texts the first association that comes to our minds is with something that refers to parallel or alternate universes. It is something profound that communicates to us about our deep levels of existence.

The shortest definition of ‘dimension’ according to the dictionary is ‘Dimension is a measurement of something in a particular direction, especially its height, length, or width; part or feature or way of considering 'something'.

As main synonyms of ‘dimension’ often are used ‘direction’ and ‘size’. In Physics it can also mean any physical measurement such as length, time or mass. The concept of ‘dimension’ is so important that famous mathematicians, scientists, philosophers, artists and literary people have shown interest in it. They have been trying to study and to find the properties of three-dimensional shapes by taking into account one or two aspects of theirs. The interest of the scientists is more about the dimensions we experience in our life on the planet Earth than comparing it with what we know of the dimensions of other objects in wider space. There are many questions that stay without answers because the way we can explore the universe is so limited by our experiences here on Earth. With the development of technology, it is interesting to see what answers the scientists will get about it - How many dimensions do we live in? Do we live only in three dimensions, or are there others which we are not capable of seeing? Is the situation in the universe the same or are there many more dimensions? What about time? Is time a different dimension or do we consider only the physical ones that refer to the concept of ‘space’? If we consider time as a dimension, that changes our image of the world, the scientific and the linguistic one. There are many three dimensional objects in nature.

CIRCLES

Vassily Kandinsky 'Squares with Concentric Rings'

For centuries people have been fascinated about circles. Many scientists, philosophers, mathematicians, artists, and religious people have been working with the symbol of the circle and giving it different meaning according to the applications of the circle in real life. And there is one great reason for that interest. Above us in the sky every day we can see the big and magical solar ring. People depend on the sun in so many ways. It gives us warm, light, it is always up there as a loyal friend. People from the whole human world have the solar ring as a very important symbol in their cultures. In mythology the sun is usually a symbol of the divine and superior God. It is full of mysterious power. The shape of the sun is a circular one. There has been a great respect and fear about the sun for centuries. Even people from ancient cultures were realising that the sun is something that they cannot control and has a behaviour they cannot predict, so they cannot ignore the giant circle. It is like a big ball that could bring either life or destruction. All the changes happening with that giant circle were affecting human lives in so many ways. The solar eclipses for examples were seen as a very bad sign which was a warning before God's punishment. So the sun represented the God Himself in many cultures.

The circle is a universal symbol with extensive meaning. It represents the totality, the wholeness, the original perfection, the Self, the infinite, the eternity, the timelessness, all cyclic movement. Being a symbol of God, the circle doesn’t have a circumference. Or it is not in the human power to find and to calculate the circumference of the circle as a symbol of God. Its circumference is everywhere, there are no limits. From a spiritual point of view God is the centre as well. The symbol of the circle also implies in the idea of movement, and symbolizes the cycle of time, the motion of everything that moves, the planets' journey around the sun (the circle of the zodiac), the great rhythm of the universe. The circle is also zero in our system of numbering, and symbolizes potential, or the embryo. It has a magical value.

TIME

Time and space are the two main features to describe our existence. Every second of our lives we are located somewhere. We can’t describe our activities separately from time and space. After the question ‘When’ comes straight away the question ‘Where’. Time remains one of the most mysterious aspects of the world in which we live. Time connects our existence in a process with the past, present and the future. Many philosophers and scientists are still trying to define the concept of time. It is so characteristic for our lives that we cannot imagine our everyday existence without it being measured with time, like just one continuous process. The human brain is designed in a way that it feels more comfortable and secure if everything is structured and in order. Without time there would be a great chaos. We need time to plan our lives and to make them more organised. Time management is important for our daily lives. We tend to think that we can manage time. Time goes only forwards, not backwards. In many fictional stories the plot includes the invention of a time machine. The time machine enables people to relive past periods of time and change the events of the future ones, eventually. The time machine gives people the illusion that we can control time. This is quite a great illusion because the time we measure and the way we control it is not the same time that is in the vast space. Any definition of ours will not be able to describe in depth what the nature of time is. But scientists believe memory formation is the basis for human perception of time.

MONEY

Money has a long journey in human societies. It has gone through barter deals and exchange of goods, metal coins, copper coins, golden and silver coins, paper notes, debit and credit cards to transform themselves to something we call ‘electronic money’. Today we live in societies in which money is almost invisible. They have a discrete but powerful electronic presence. But what is money? I am sure we all know the answer to this question and even more that we all have some kind of connection with money itself or with the idea of money. And writing about money could take different directions. In this text we will try to look at the historical development of money, about how money is used in mathematics and about the money’s influence in our lives.

Money is best described as a medium of exchange. The concept of money has been around since the dawn of human civilization. Money allows an individual to trade what they have for what they need or want. What is considered to be money has varied over the ages and has included diverse items. Currently, there are over 150 currencies used worldwide. 70% of the monetary value in the world is denoted in the U.S. dollar, Euro, U.K. pound, Japanese Yen, and Chinese Yuan.

Resources for GCSE Maths Foundation

Lessons presentations for non-profit educational purposes only!! The content of the presentations is from various sources.

1. PLACE VALUE
2. ROUNDING
3. ADDING AND SUBTRACTING
4. MULTIPLYING and DIVIDING
5. TERMS AND EXPRESSIONS
6. SIMPLIFYING EXPRESSIONS
7. INDICES
8. EXPANDING AND FACTORISING
9. ANGLES AND LINES
10.  TRIANGLES AND QUADRILATERALS
    

PROBABILITY

People are always interested in their future, and what will happen tomorrow is sometimes more important to us than what is happening now. Tomorrow is like compensation and a nice revenge for us. Most people are fascinated by tomorrow - What would our life look like? Am I going to be richer and prettier? It is like an escape from today. Because today is always guilty for something. That’s why we often try to predict the future. Sometimes our predictions are based on what we know and we have some choices to choose between. In this case we just use some techniques and methods to give more chances to some possible events to others. This kind of predictability is an object of Mathematics. When our predictions are not based on real fact it is hard to decide which event has more chances to occur in the future. In this case it is like playing blind game with no certain rules.

In this short text it won’t be possible to describe everything that relates somehow to probability. We will try to open the door so as to allow the curiosity to come in.

There are many situations in real life where we have to take a chance or risk. Based on certain situations, the chance of occurrence of a certain event can be easily predicted. In simple words, the chance of occurrence of a particular event is what we study in probability. 

ROMAN NUMERALS

My short LoveMaths text this time is about Roman numerals. Roman numerals are very interesting for many historical and cultural reasons and it is not fair that they have a limited use and are almost forgotten. Roman Numerals are the numbers that ancient Romans used. This is just a short reminder about these beautiful numerals, which are still very much alive in some occasions although with some limited and more specific uses. One of the greatest disadvantages is that they form a very big chain of letters.

Rome was the capital of the expansive Roman empire which encompassed almost the entire continent of Europe, along with Mediterranean territories in Asia and Africa. The Roman empire was one of the most powerful empires of the ancient world. Historians believe that the earliest Roman settlements began in 753 BC. The Roman Empire was divided into the Western Empire and the Eastern Empire. Its glory was at its peak in 200 AD, and the entire empire spanned over an area of 2.5 million square miles. Romans will forever be remembered as inventors and establishers: inventors of a modern form of administration and establishers of a number of science and engineering practices which had been around, but were ushered in for daily use by them. The Romans were extremely innovative builders and engineers (they invented the aqueducts, the paved roads, and the construction of the drains). Architecture, Science, Popular culture, Law and Governance, Arts and Literature - all this was highly developed in ancient Rome. Did you know that the Romans founded even London? They had named it ‘Londinium’.

 Romans even invented their own numeral system based on the symbols of Latin letters. We call these numerals Roman numerals. It was the main way of writing numbers in the whole European continent until the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. There are main seven symbols, each with a fixed integer value:

Symbol: I, V, X, L, C, D, M,

Value: 1, 5, 10, 50, 100, 500, 1000

That means: I=1, V=5, X=10, L=50, D=500, M=1000.

MATHS IN DAILY LIFE

Mathematics is the universal language of our environment, helping people to explain and create. When am I ever going to use maths? Students often wonder if, when, and how they will ever use maths in "real life" situations. The truth is that we use maths all the time!

But how well do we know and how well do we remember the mathematical language? Let us try to answer this question. If we know the mathematical language relatively well do we use it in our everyday real life? Everybody in their daily life uses mathematical languages to some extent. Often we are so used to this language that we don’t even think that we should be grateful to mathematics for developing its symbolic language which serves us in so many ways. Let us try to remember and summarise some of the applications of Maths which we all use without being mathematicians. The mathematical language is part of human civilization, in fact, it helped a lot to shape human civilisation and culture.

Maths isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is mirrored through with it. Maths allows us to see the hidden structures underneath the chaotic surface of our world. With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way.

Let us mention some of the mathematical applications which for sure everybody uses in his daily life.

Managing Money and family budgets, Shopping for the best price:

We live in a consumer society and everyday in shops we have to solve the dilemma - which product gives us the best money for value? That means which product is the cheapest. Unfortunately, maybe not everybody in the shop would be able to decide which product is best to buy. In shops there are very often discounts. It is a useful skill to be able to calculate how much money you need to pay.

Yes, money is the thing that causes so many problems in the world, or it will be precise to say, not money itself, but the human desire to possess more and more money. But with money we can do so many good things, which could be for everybody to use. We count money, we add, subtract, multiply and divide money. We dream about money. We try to detach ourselves from the power of the metal so we can concentrate more on the spiritual part of life. Sometimes it is easier to achieve this but sometimes it is so hard. It is an internal battle.

INFINITY

The purpose of my texts  is not to try to say everything about the topic, not at all, mainly because this is not possible. Even a book, for example, about Infinity will not be able to say everything, in a book you always choose what to present and what to leave for the next book. My main purpose is to make you think not only about the specific topic but to try to find the connection between everything in real life, where there are no limitations and borders of our imagination and knowledge. So let’s challenge ourselves, this is the only way to develop ourselves more and more. There is no limit of development. Remember what I said: Thinking (together with Love) is one of the best joys we can experience. This is actually a good example of Infinity - human curiosity. 

The topic of Infinity is so interesting and bigger that I will need a lot of paper and time to say what  I would like to say about it. Don’t worry, I will try to keep it short. 

Infinity is not really a strictly a Maths topic, although in Maths there are examples of the idea of infinity. Remember, we said that mathematical language reflects real life and the life of nature and tries to find an abstract way with symbols to express it so later we can use its tools to carry on exploring life. It is like a circle. There is no beginning and end, everything is one. The idea of infinity is applied in nature, in human life, in  religion, in human languages (there is vocabulary about infinity), in art, in philosophy, in science and in Maths language as well.

SYMMETRY

Writing about symmetry is a great challenge and a joy at the same time. It is a challenge because it is like the topic of infinity - it is all around us, but it is so profound and deep that there is a great risk that by trying to say something we will not manage to say even a little. I will take this risk mainly because I am not aiming to achieve the impossible thing - to say everything. No, I will need to do a lot of research for that and I will need more knowledge that I don’t have for the moment. I will try to lift the cover of the topic and to make connections, on one hand, with its Mathematical language and how it reflects real-life in order to develop tools for describing and working with symmetry in a more practical way. On the other hand, the mathematical language that we mentioned many times, developed from the people’s practical needs to deal with practical issues so we need to make a connection with other areas.

Symmetry is one of the most fundamental and important ways that nature structures itself. It is one of the laws of nature which we, humans, just copy in our everyday activities. We are naturally attracted to symmetry. When we say the word ‘symmetry’ and ‘symmetrical’ what is the first association that comes to your mind? Is it about something beautiful? What about ‘asymmetrical’? Are your associations rather not very positive? It is not only you, don’t worry. The idea and the principles of symmetry lies in the fundamentals of how we see, perceive and understand the world. Symmetry is what holds different parts of the world together and makes it more pleasing for the eyes. Everything is in a harmonious proportion when it is symmetrical. Nature itself is governed by the idea of symmetry that creates balance not chaos. In many ways symmetry represents order, a beautiful peaceful ordered world. It helps us to make sense of the world around us.

THE MAGIC OF FIBONACCI NUMBERS

Let us ask ourselves - why do we learn mathematics? For calculations and  applications. And because of inspiration. The connection of Maths and nature is inspiring and makes us think. Maths teaches us to think. Mathematics  is not just solving for X. It is also finding out how and why. 

 The Fibonacci sequence is one of the most famous formulas in mathematics. It has been part of people's lives for centuries. It proves one more time that we cannot draw a line to separate one knowledge from another and if we do this this is just for some practical reasons like educational subjects and exams. More often we borrow knowledge and theories from different disciplines in order to find better understanding and explanation in our own discipline. 

The Fibonacci numbers are proving that the whole universe is one whole - the space itself, the galaxies, nature and the human knowledge which is trying to understand the bigger picture.  The Fibonacci sequences came to Maths from real life observations and provoked ancient mathematicians to find reasonable and practical explanations to some natural facts which everybody observes. From the Fibonacci sequence we can calculate the Golden Ration and after that the spiral. The spiral design could be seen in the natural world and in the universe. We can see the pattern of the spiral everywhere. The spiral is like a mathematical and spiritual symbol of life energy and of rebirth. It is like the connection that holds everything together. It is like God’s brand that is saying to us that everything - from the huge objects like galaxies to the smallest ones - like fingerprints - have been made following the same design of the spiral. The spiral that keeps everything in the universe connected and in order.  Galaxies have the same spiral shape as so many things in nature. Nature’s design copies the space one. The spiral is a symbol of growth and evolution.

If space-time is shaped as a spiral that explains why the Creator used this great design to form the galaxies and nature in that way. It looks like we do live in a golden ratio divine universe. The galaxies have the same shape as  snail shells, sea shells, sunflowers, fossils, the structure of human lungs, spirals in plants, cabbages, pineapples, strawberry seeds, animal horns, flower petals, pine cones, snakes, embryo, ears, storms, DNA, curly hair, hurricanes, turnados,  tree branches, roots, and even galaxies are spirals. 

MATHEMATICAL LANGUAGE AND NATURAL HUMAN LANGUAGES

       

 I will try to compare natural human languages and mathematical language in order to try to answer the question '''Is Maths really a language?' This is a very big question which will require a lot of writing and my purpose is not to make you feel bored but to fire your curiosity about the topic, and after that you will carry on exploring by yourself. That's why I will do this comparison briefly. 

Maths is really very often called a language and it is true that Maths is used in many other areas of human knowledge as a tool. Remember engineering, science, geography and almost every other area, they use something from Maths. It looks like the Maths language exists to serve  others by offering them a lot – arithmetic, statistical graphical ways to represent certain knowledge, probability, which is part of a risk assessment, geometry is everywhere in building business and algebra is just sometimes so annoying with her constant effort to find ‘X’ in our lives. But this is what we are doing very often in our lives – we are detectives who are trying to solve our own little mysteries. So, we agree, Maths is present in every aspect in our personal and professional lives.

What is a natural human language then? By 'natural' I mean languages which are spoken by people and which develop through the centuries.  They could be official state languages or a dialect, which is a language which is spoken locally and it doesn't have official state status. There are more than 6000 languages in the world and most of them are disappearing, mainly due to migration. Some of the languages are big – many people use them, such English, Arabic, Russian, Spanish and some others. Some are little and some of them are micro-languages. I spent some time of my university career doing research about one very little Slavic micro-language – the Upper Sorbian language and I even wrote two books about this language. It is spoken in Eastern Germany and it is a disappearing language (only around 50 000 people are speaking it), people are bilingual – they know German as well. Their  main cultural place is called Bautzen. It is 60 km from Dresden. They have a Sorbian institute there in Bautzen and I have been there many times to do research about my books.

What is the definition of a natural human language? We want to compare Maths language with human languages so we need to have a starting point and we need to know that the things we are comparing are comparable.

HAPPY 'PI' DAY

МАТЕМАТИЧЕСКА ВЕРОЯТНОСТ

Математическата вероятност се занимава с това какъв е шансът нещо да се случи. Шансът, вероятността нещо да се случи или да не се случи, може да се изрази както с думи, така и с дроби и с проценти. Всички ние в ежедневието си постоянно се изправяме пред някаква дилема, когато трябва да преценим каква е вероятноста нещо да се случи. В повечето случаи нещата са в областта на предсказанията, които ние не можем да направим, но има и такива случаи, в които при наличието на достатъчно налични условия и обстоятелства, ние можем чисто математически, с цифри или думи, да отговорим на въпроса каква е вероятността нещо да стане. Ние не предсказваме какво точно ще се случи, а даваме само най-общи указания.

Например, когато хвърляме монета, за да направим случаен избор за нещо, имаме два варианта – монетата да се падне на „ези“ или „тура“. И двата избора имат равна вероятност и шанс и тя е 50%, защото изборът е между две неща. 

Много събития от реалния живот не могат, разбира се, да се предскажат с абсолютна точност. Ние можем само да кажем колко вероятно е нещо да се случи на фона на нещо друго, и то при наличието на достатъчно информация.

Скала на вероятността.

 

Съществува т. нар. „скала на вероятността“, която показва как дадено събитие може да се изрази с думи, с дроби и с проценти. Ето няколко случая на вероятност:

·    „Сигурно“. Пълната вероятност нещо да се случи винаги е равна на 100%, което е 1 или, изразено с думи е „сигурно“.

·    „Невъзможно“. Когато вероятността нещо да се случи е много ниска, то се изразява като невъзможно да се случи. Тогава шансът да се случи е равен на 0%.

·   „Равен шанс“. Когато вероятността нещо да се случи и в същото време да не се случи е равна по сила, тогава то се измерва с 50% или като ½, или като 0.5.

·    „Много вероятно“. Когато нещо е много вероятно да се случи, но не е сигурно и няма равен шанс, то стои на скалата на вероятността между 50% и 100% и се изразява с цифри като 75%, ¾ или 0.75.

·  „Малко вероятно“. На скалата на вероятността стои между невъзможно и равен шанс и се изразява с 25%, ¼ или като 0.25.

·     „Взаимноизключващи се събития“. Когато две събития взаимно се изключват, т.е. те се отнасят до две напълно противоположни действия и състояния. Тогава вероятността и двете да се случат по едно и също време е равна на 0%.

 

СРЕДНИ СТОЙНОСТИ НА ДАННИТЕ И ДИАПАЗОН

Разглеждахме вече как се събират данни, как се организира анкета, как се съставя въпросник за анкетата. Представихме също така и няколко основни и най-често използвани вида графики, таблици и диаграми, в които графично и визуално може да се организират събраните данни. Графичните средства на представяне на данните улесняват следващия етап, този на интерпретиране и анализ на събраните данни и информация. Предполагам, че когато стане въпрос за статистика и нейните анализи, изводи и заключения, мнозина са скептични точно в този последен етап на проучването. Скептицизмът идва най-вече от това доколко можем да се доверим на крайните анализи и изводи на статистическото проучване, доколко то е достоверно. Защото, съгласете се, че ако в анкетата са събрани данни от 2000 души например, то не е реалистично в крайните изводи и анализи да бъде споменат всеки един от тези 2000 души, заедно с предоставената от него информация. Вместо това, се работи с така наречените „средни“ данни, които са няколко вида. Тези средни данни се възприемат като  представителни, типични  за голяма група от данни при проучването.   Защото едно от най-важните неща при всяко статистическо проучване са тенденциите, които се наблюдават и които могат да бъдат уловени чрез събраните данни. За тази цел средните стойности на данните, представителните,  наистина помагат анализът да е максимално достоверен. 

Като цяло се работи с четири вида средни стойности на данните: 1. Средноаритметична стойност (на англ.: Mean); 2. Медиан (на англ.: Median); 3. Мод (на англ.: Mode) и 4. Диапазон   (на англ.: Range):

Дефиниция на средните стойности и на диапазона:

   1.     Средноаритметична стойност (на англ.: Mean).  Намира се чрез събирането на всички числа в множеството и след това разделянето на броя на стойностите в множеството.

   2.       Медиан (на англ.: Median). Това е стойността в средата, когато множество от данни е подредено по големина.

  3.     Мод (на англ.: Mode). Това е числото, което се среща най-често в множеството от данни.

  4.        Диапазон (на англ.: Range). Диапазонът не представлява средните данни, но той може да покаже в какъв обхват се разпростират данните. Обикновено това е разликата между най-голямата стойност и най-малката.

ПРЕДСТАВЯНЕ НА ДАННИ В СКАТЪР ГРАФИКА //„SCATTER GRAPH“

Скатър графиката е интересен начин да се представи взаимоотношението между две категории данни, които се разглеждат като двойка и се предполага, че са взаимозависими. Събраните данни трябва да са количествено изразени.  Чрез този вид диаграма се показва дали има връзка, или не между две категории. Например, ако искаме да  разгледаме и паралелно да намерим връзката между данни, събрани от измерените килограми на група хора и техния ръст. Интересуваме се например дали ръстът, височината влияе на по-голямото количество килограми. С две думи, по-тежък ли е човек, ако е по-висок. Но може да се интересуваме да проследим графично и дали има пряка връзка между две категории, които извън математиката съществуват относително самостоятелно, каквито са например цветът на косата и тежестта на тялото. Интуитивно ние усещаме, че връзката между тях ще е отрицателна корелация.

Какво е нужно, за да построим една семпла скатър графика:

1.     Таблица със събрани данни по двата показателя. Определена група от деца например, на които сме измерили ръста и които сме измерили колко тежат като килограми.

2.     На хоризонталната координата (х) поместваме независимата  категория, например тази за височината, а на вертикалната категория (у) нанасяме данните на зависимата категория, в случая тази за тежестта. Двете координати се разделят през равен интервал, който отговаря на събраните данни.

3.     Нанасяме данните, които вървят по двойка, като ги засичаме по двете координати. Там, където се срещнат, отбелязваме точка. Там, където се наслагват точка върху точка, ги поставяме една до друга.

4.     Ако точките естествено се оформят в линия, се опитваме да начертаем тази линия, като обхващаме възможно най-много точки.

5.     Ако линията върви отляво надясно и нагоре, то е налице положителна взаимовръзка. Ако линията върви отдясно наляво и нагоре, то е налице отрицателна взаимовръзка.  Ако точките не могат да оформят линия, то между двете сравнявани категории, няма никаква връзка, което означава, че промяната в едната не води до промяна в другата.

6.     В графиката за ръстта и килограмите на децата, се оказва, че взаимовръзката е положителна.  Това означава, че промяната в ръста, може да води допромяна в килограмите. 

 

ПРЕДСТАВЯНЕ НА ДАННИ В ЛИНЕЙНА ГРАФИКА //„LINE GRAPH“

Линейната  графика е още един вид графично средство да се визуализира серия от данни. Името и идва от крайния вид на графиката, която представлява линия. Линейната графика представя квантитативни данни през определен период от време. Тя се използва най-вече, когато трябва да се покажат тенденции и да се анализира как данните се променят с времето. Линията се получава от съединяването на точките, които се отбелязват при срещата на двете координати (x)  и  (y). Посоката на линията е като показател за това каква е тенденцията на данните. Ако линията върви нагоре, то стойностите се повишават, ако линията отива надолу, то тенденцията е стойностите да се понижават. Една графика може да се състои от няколко линии, които отразяват промените при няколко вида данни. 

Графики с една линия.

Например графиката по-долу представя промяната на температурата в течението на един ден – от сутринта до вечерта. 

Какво ни е нужно, за да начертаем линейна графика като тази:

  1.     Задаваме заглавие на графиката. Заглавието зависи от вида на данните. Например заглавиета на линейната графика по-горе може да е: „Промяна на температурата за един ден“.

  2.     Наличие на предварително събрани данни, чиято промяна за определен период от време искаме да отбележим визуално чрез графика, за да анализираме тенденциите. В този случай е нужно да измерим температурата през деня, като избираме пет времеви опорни точки.

  3.     Построяваме хоризонталната координата (х), на която поместваме времевите опорни точки. Построяваме вертикалната координата   (у), на която отбелязваме градусите, които са част от събраните данни, те трябва да включват най-високата температура и най-ниската. Ако температурните данни включват и отрицателни температури, трябва да удължим вертикалната координата надолу, за да можем да отбележим отрицателните числа.

  4.     Нанасяме събраните данни, например температурата в 9 ч. сутринта е 9 градуса, отбелязваме го с точка или с кръстче. По същия начин нанасяме и останалите данни.

  5.     С линия съединяваме нанесените точки или кръстчета.