THAT THING

 What is that thing that follows you?

From morning to night,

From dusk to light?

That Thing,

Like a foreboding shadow,

A shadow that brings terror and fright,

Threatening to engulf the sunlight,

That Thing,

Like the cloak of darkness,

That comes with the frosty night,

Hiding everything nice from sight.

That Thing,

Like the screen of gold,

That hides the darkness and pity

Of the dying leaves in autumn,

That Thing.

GOLDEN RAIN

 

by Suzanne Zahr

With a rustle,

With a creak,

The wind sweeps through

The shaking shrub.

Swirls playfully,

And worries the tree,

Like a child bouncing on granny’s knee.

A few golden leaves flutter,

And fall to the floor,

Like old grey hairs,

From an old man’s scalp.

The wind tugs off a few more,

And picks them up tenderly,

So that they, the dead,

Can come and dance

Among the folds of Autumn’s lively dresses.

'LoveMaths Stories' book is on Amazon

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

* * *

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

GOOD PEOPLE

 What makes a good person?                                     

Somebody who goes and tells the police?

That tattle-tale who is ‘never involved’?

Someone who takes up the matter themselves?

Dives in, head first, without a proper plan?

Somebody who kills, and destroys,

Just to save the world from all the bad things in sight?

Not including them, of course.

And after all the deaths and mourners,

After cruelty battles cruelty,

After you wade through the field

Of limp, lifeless bodies,

And lost hope?

Is that first, tiny idea, to do something right,

Still there?

Or are you now that monster,

Who you tried so hard to overcome?

Who will come and sort you out?

Another person in two minds,

About what is right and what is wrong?

And so it begins again,

The battle against evil,

To do something good.

Will it ever end?

STARRY BLANKET

When the  orange sun lies low,

When the city sleeps below,

When no twinkling lights are found,

When not one creature makes a sound,

When finally comes the end of the day,

When the evening glides away,

When the sun leaves not a mark,

When the night pulls in the dark,

When from the corner of the sky,

In drifts a pearly eye,

When the silver moon appears,

When over her starry blanket she peers,

When her bright light shines down,

Spreading over every village and town,

TRAPPED

Once there lived four mortals,

Who tried to find a way,

To escape death and seek life eternal,

Past the ending day.

You should get to know them,

They've been here a while,

North, South, East and West,

Were four very normal people.

South and East were fair of face,

With posies of roses,

And dresses of lace.

Handsome West sought to please all,

Spent his money for strangers,

Spent his nights on the dance floor.

North was cruel and cold and mean,

He looked down his nasty nose on all.

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.

THE FUTURE IS NOW

Marc Chagall, The blue bird

What if, the birds in the sky,
The swifts and swallows, that fly so high,
Wondered about when they would die?
What if the tigers in the savanna plains,
Knew when the final day would come?
What if the whole animal kingdom,
Was built on the fear of tomorrow,
The final day?
What if every being in the cosmos,
Trembled in terror about
What will happen in the future?

'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.

THE TASTE OF SUMMER

Summer,

The season that is perfectly balanced,

Between spring and autumn,

A salvation from the cold and misery,

Like spring,

But better, longer, and infinitely more wonderful.

Summer isn't just one feeling,

It's several different sensations,

The bright sun rays that pour from the sun,

Hanging in the magnificent, blue canopy,

That stretches above us for ever,

The warm sunshine that kisses my cheeks,

The long, orange grass and sweet wild flowers,

That brush around my knees,

In the gentle, smooth breeze,

Casting pollen into the air.

BRINGER OF JOY

Lucy Pittaway 'The Joy Of Spring'

This morning,

I stepped out of the house,

And my mind was shrouded

In a cloud of misery.

I was alone.

Stranded,

In a never-ending cycle,

Of gloom and despair.

Nothing mattered.

Nothing could improve.

And then,

Out of the blue,

Through the barrier of woe,

Broke a tiny glimmer of light,

Radiating knowledge,

Truth and joy,

In the form of your smile.

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.

EVERY STUDENT DESERVES A GOOD TEACHER

In this short reflection of ours we are not going to write about the characteristics of the good teacher, we will do this separately. Here will try only to defend the student's right to have a good teacher.

Every student deserves a good teacher who will make him to want to fly.

Education is a two-sided process – teaching and learning. There should be an equal effort and an equal honest attitude to the process in depth to achieve something.

Teachers are the most important people in the schools. Together with the students they create the image of education. But if the students still have a more dependent role, the teachers' role is leading. The quality of teaching and learning depends on the teachers. And although there are plenty of brilliant professionals in schools and they create maybe 90% of the teachers, there is still some percentage of teachers who are just not fit for the role. The role of the teacher is extremely demanding and challenging but on the other hand extremely rewarding. The teacher should not only be a brilliant expert on their subject but also a great communicator and a big fan of the students. To be a teacher means that you have a passion and love in your heart for the students. To be a good teacher means that you will always do what is right for the students, doesn't matter how hard this is for you. It means that you have almost angelic patience. You will need a lot of patience.

The teachers create the students' memories and the care about the students' well being and learning should always come first. All that means that you have to embrace in your heart the philosophy of the Humane pedagogy not the philosophy of the Authoritarian pedagogy. 

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.

WORDS OF ADVICE FOR ADULTS

Don't lie to children so they can learn how to be honest.

Love children so they can learn to love.

Talk to the children so that they can learn to talk.

Listen to the children so that they can learn to listen.

Be patient with the children so that they can learn about patience.

Trust the children so that they can learn to trust each other.

Accept them as equals so that they can learn to be accepted as equals.

Love children unconditionally so that they too can learn about unconditional love.

Accept children as they are so that they can learn to be accepted as they are.

Believe in the boundless potential of children so they can learn to believe in their potential.

MEMORIES

Ramona Matei Art

All that we have ever known,

Every moment of our existence,

All that we have loved,

All that we have hated,

All the tears,

All the despair,

All the laughs,

And all the hope,

Is stacked up in our minds,

Like a giant library of memories,

So we can borrow and read them,

Learn our lessons,

To help us with the present and future.

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. 

Приказка на врабчето Рошко за Средната английска земя

Здравей, мой малки приятелю!

Отново ти пиша аз, врабчето Рошко! Надявам се, че си бил послушно дете, докато очакваше следващото ми писмо! Много е важно да слушаш родителите си, защото те знаят кое е най-добре за теб и много те обичат! Надявам се, че си се настанил удобно вече, защото имам да ти разказвам разни неща за големи приключения.

Пиша ти в момента от Средната английска земя. Правилно си се досетил, че тя се намира по средата на страната Англия. Тук е родното място на един голям английски поет – Уилям Шекспир. Ще научиш повече за него, като станеш голям и тръгнеш на училище.

В градчето Уорик пък се намира един от най-старите средновековни замъци на Англия – той така и се нарича „Замъкът Уорик”. Потрепервам само при споменаването му, защото тук ми се случи нещо, което бих искал по-скоро да забравя. Но ще побързам да ти го разкажа, защото ако първо аз го забравя и не го разкажа на никого, то няма да има и кой да помни доброто, което дойде след ужасното приключение.

И така, ще започна своя разказ за една страховита история, от която обаче аз, малкото врабче Рошко, показах на всички, че когато имаш смело сърце и се бориш за доброто, винаги побеждаваш.

Ти помниш вече, че в предното си писмо ти разказвах за топлото слънце на Аржентина. Хубаво е, когато има слънце, защото то ни кара да се усмихваме по-често и да сме добри. Аз лично не обичам студа, не обичам много и дъжда, защото хората са постоянно затворени в себе си, никой не се усмихва, на всички ужасно много им е студено и малките врабчета не могат да играят навън. А трябва постоянно да мисля да си сложа шала, ръкавиците и шапката, защото без тях ще се разболея и мама ще е тъжна. Аз не обичам да гледам моята мама тъжна и затова винаги я слушам за всичко.

Докато се препичах на топлото аржентийско слънце, получих писмо, че съм поканен на рожден ден в Средната английска земя. Един мой стар приятел, патокът Джак, навършваше цели четири годинки и ме канеше да отида заедно да отпразнуваме това голямо събитие. Ти представяш ли си какво е да си на цели четири години? Велика работа е това! И понеже обичам приятелите си, облякох най-новото си синьо палто, сложих си розово шалче, обух си зелените ботушки, нагласих си човката в жълт цвят, прибрах всичките си останали неща в един шарен куфар и се приготвих да потеглям. Обаче трябваше да се върна, защото забравих най-важното нещо за един рожден ден – подаръка. Всички се радваме, когато получаваме подарък на рождения си ден, нали? Сигурен съм, че и Джак щеше да се зарадва.

И понеже бях сигурен, че изглеждам добре, се огледах в огледалото за последно да си се порадвам просто. В първия момент малко се стъписах от това, че като че ли бях попрекалил с цветовете в облеклото си – от огледалото ме гледаше една усмихната дъга и всичките цветове на дъгата ми махаха отсреща. Може би все пак трябваше да си облека нещо по-скромно и да не прекалявам с цветовете? Вие как мислите?

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.

TREE

(Blenda studio)

(a poem by 11 years old Emma)

Once upon a time,

A little tiny acorn,

Passed on the wind,

And past the mouths of many squirrels.

The adventure of a lifetime,

Until it stops,

And there is only darkness,

Buried under heaps of soil,

And there is nothing left to do,

But sit and wait.

After what seemed like a hundred years,

Something soft and warm picks it up,

Cradles it,

Up, into the sunlight,

A brief moment of freedom.

A moment that doesn't last.

It is hidden away,

Under more moist soil.

The little seedling grows,

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.