Людям з порушеннями зору
Case-lesson "Love is on 5 Continents"

Section: personal (human) values

Level (grade): 5 - 7

Topic: History of mankind

Objective: consider your own idea about love phenomenon and find your own answer to the question “Is there any geographical feature of love?”

What information is waiting for me here?
  • How many heart shapes are situated on the Earth's surface?
  • What volcanoes do fall in love the most often?
  • What kond of wings do the lovers of South America have?
  • What story of love has become a turning point for the whole continent?
  • Is it possible to write the word "love" in the language of mathematics?
7 scans of the subjects, phenomena and practices:

Do you think that a phenomenon like love has some geographical features? Can love on the African continent be more fierce than love of the Alaska inhabitants? Let's go on such a round-the-world journey and visit all five continents, compare their legends and works of love either historical or contemporary in order to find your own answer to the question.

Geography (Worldwide)

Let's start our journey and carefully observe the map of the world. Could the hearts hide somewhere?

If the ordinary card doesn’t help you to find out, then it makes sense to turn to GIS. What is GIS? This is a geoinformation system, a modern computer technology that allows you to combine the model image of the territory (electronic mapping of maps, schemes, cosmic, aerial images of the earth's surface) with tabular type information (statistical data of various types). Given all the seriousness of the definition most of you met with at least one type of GIS: a google map!

Let's have a look at the hidden hearts again with the help of GIS.


Work in groups or teams. Look at the tips where the hearts are located. Now put them on the map of the world! You can do it like a race working in teams with your own card. It is possible to organize a real battle where a separate participant of the team should mark the heart and the next heart can not be marked on the map until the previous one is still on the screen!!

Heart-shaped pond, Columbia Hills Corners, Ohio.

Tupai atoll, French Polynesia.

Heart-shaped lake, Gaislacher See, Tyrol, Austria.

The heart-shaped lake on the way to the peak of Chambray, Vayanad, Kerala.

The island of Halesniak in Croatia, the most famous heart-shaped island.

Man-made ponds in the shape of hearts near Halmstad City Airport, Sweden.

Heart-shaped lake is in the Austrian Alps.

More than a thousand hawthorn trees were planted by Lady Keswick, an owner of the Oare House, in 1999 in memory of her two brothers, Wiltshire, England.

View from ISS: The heart of the Central Asia.

Heart Lake at the Olympic National Park in Washington, DC.

A heart-shaped forest area near Kansas City, Missouri.

A heart-shaped lake on the island of Hokkaido, Japan.

Not far from Hampi, Karnataka, South India.

Makepiece – is a private island on the Nusa River in Queensland, Australia.

Mulvey is a lake in British Columbia.

Water Gardens of the Guandu Park, Taipei, Taiwan.

A heart-shaped volcanic freshwater lake, Auckland, New Pupuke in Zealand.

Salina do Coração, Brazil.

District of San Bruno, CA.

Island hotel, Tavarua Island Resort, Fiji.

An island on the Gutierrez Lake, Patagonia, Argentina.

A small heart-shaped wooded island on the Orinoco River, Ciudad Bolivar, Venezuela.

The Abel Tasman National Park, New Zealand.

Zhuo Yong Cuo – is a lake in Tibet mountains.


And now, look at your map again: what continent came to be the leader by scored the hearts? What continent of the world is "the most in love"?

Literature (Eurasia)

Now let's have a journey to the continents. We will be the first who visits Eurasia. This is a huge continent that unites two parts of the world: Europe and Asia. The continent's culture is extremely mottled. Each part of the continent has unique legends and literary works devoted to love. Let's get acquainted with two of them. The first is a knighthood novel that was created in Western Europe. Do you know such a literary genre?

Romanz is a narrative genre of European medieval literature. It is a form of medieval epic poetry that developed simultaneously with chivalry in England, Germany and France (written in pairs of rhyming eight-slave and first applied in the Anglo-Norman chronicles).

Tristan and Isolde are legendary characters of the medieval knighthood literature of the 12th century. Parallels to the motives of the novel are in the legends of the ancient eastern, antique, Caucasian and others. Hower, in the poetry of feudal Europe this came to Celtic decoration, with Celtic names and with typical everyday features.

The asteroid (211) Isolda discovered on Dec. 10, 1879 was named in honor of Isolde. In 1982 the International Astronomical Union assigned the names Tristan and Isolde to the craters on the Saturn satellite Mimas.

Also in the Asian culture, particular in China, there are works dedicated to love. For instance, it is the Legend about princess Leccean. This legend is associated with the Feast of Lanterns which is celebrated on the 15th day of the first month of the lunar calendar. One of the main ideas of the holiday is the union of the family.

Princess Leccean was a beautiful and clever woman. She lived in the era of the Southern and Northern dynasties (420-589). Leccean and her husband, the palace secretary Xu Deyang, had been living a happy marital life in the kingdom of Chen. But their happiness was in jeopardy when the Sunni kingdom attacked the kingdom of Chen from the North.

One day Xu Dean told his wife, "With your talent and beauty you can be taken away one day by some influential rich man as a wife of his because in the country lawlessness is reigning. Maybe we’ll be divorced forever. But if fate smiles, and we will meet again we must have some kind of our love symbol"

Ancient Chinese believed that all relations were predetermined. Xu was no exception. He believed that if he and the princess were destined to be a couple for life, they would be able to reunite despite the circumstances.

Xu broke the bronze mirror in half and each of the spouses took one half of it. Thus, he entered into agreement with his wife: "If we are separated in the future, we must go to the bazaar every year to try to sell the mirror, and if I see it, then I'll go and look for you."

So the spouses must have faced the test. They had to use a bronze mirror to reunite the family.

The legend has laid the beginning of the Chinese idiom "the broken mirror has been united". It means the reunion of the spouses after forced parting. It is also used when a couple decides to reconcile after a break in relationship.

The idiom is a stable, indivisible turn of speech, conveys a single concept which content is determined by the content of its constituent elements. Task (project work): The material of this scan can be the basis for design work. Students must work either in teams or individually. Also, the student-dubler tool may be used.

The task is to get acquainted with the texts of the cited works, and to write illustrated essays about them or to create small presentations. When the projects are discussed in the class, it will be necessary to compare both works: what is common, and what's different in them.

Geology (North America)

And now let's move to the North America or rather to Mexico. Do you know the legend about the volcanoes?

The Mexican landscape is owen with myths and legends of Aztecs and Maya. The two main Mexican volcanoes have become the symbol of a beautiful and tragic love story.

Volcanoes played an important role for the Aztecs. The patron saint of the Šiuatekutli volcanoes is the God of the day as well as the heat and the fire. He was the embodiment of life after death symbolizing light in the dark, food during hunger and heat among the cold. The Aztecs believed that this deity lives in a turquoise castle in the center of the Earth. It is at the same time the father and mother of all the Gods.

According to the Aztec mythology two volcanoes next to Mexico City were once human beings - a man and a woman in love.

Volcanoes are located in the states of Puebla and Mexico City. Its height is 5426 m. The height of Istraksiwatl is 5230 m. It is the second and third highest peaks of Mexico (the first place is the volcano Orisba or Sittalpettle - 5636 m). Istaxuatl means "White woman" because he has four snow-white peaks which in appearance reminds a woman.

Popocatepetl means "Shimmering mountain", it is an active volcano. Iztaccíhuatl is an extinct volcano. Geological analysis indicates that it has not erupted for a long time.

Legend about volcanoes:

"Popocatepetl and Iztaccíhuatl are shortened names of Popo and Esta. In most versions of the legend we are talking about the brave warrior Popocatepetl and the beautiful princess Istraksiut. Her father was a powerful leader. He decided that if Popo wants to marry his daughter, he must defeat the strongest enemy on Earth. Potokatpetly strongly loved the girl and accepted the condition.

There are many descriptions of the battle, but most often it is said that he has returned with the enemy's head.

Iztaccíhuatl was waiting for him to return for so long that her heart was full of anxiety. One of the rivals of Popocatepetl who wanted to marry a princess decided to lie. He told her that Potokatepetl died during the battle.

Iztaccíhuatl did not assume that someone was able to slander so cruelly, and did not check the news. Life without a beloved lost the meaning. She despaired and plunged into mourning. The girl died of a heart rupture.

Soon Popokatepetl returned. In terrible news he believed with difficulty. He took the dead beloved to his hands and took her to the top of the mountain.

Time went by, snow covered their bodies. They turned into two majestic volcanoes.

When the great warrior Popocatepetl thinks about his beloved, his heart starts beating faster, and because of the passion the volcano erupts. The second volcano sleeps peacefully, and Popocatepetl continues to smoke. "

What are the volcanoes in terms of science? Why is one of them sleeping and the other is releasing smoke? And is there a chance for the sleeping volcano to "wake up"?

Volcano is a geological formation (a geotectonic phenomenon) that occurs over canals and cracks in the earth's crust, through which lava, ash, hot gases, water vapor and debris of rocks are thrown to the surface.

Lava, Crater, Gas, Ash and Stones, The mouth Lava and ash layers, Side crater,Crater from previous eruption.

Volcanic eruptions occur in stages, they can be distinguished in so-called phases:

• the first phase - the flow of glowing liquid lava and periodic explosions.

• the second (gas) phase - the separation of a powerful column of compressed gases that breaks out for several hours with the removal of relatively small amounts of ash and the formation of gigantic igneous clouds.

• third phase ("dark ash") - detachment of black clouds of gas heavily loaded with volcanic debris.

Popocatepetl or "Smoking Mountain" is 70 kilometers south-east of Mexico City, and it is the most active volcano of the country! The volcano is erupting now, and it does so unceasingly since 2005! On the Potokatepetl the lava dome grows and explosions are heard. Ascension jets rise to a height of several kilometers.

Quiet at first glance the volcano can wake up anytime. In order to avoid the catastrophic consequences of such arousal, scientists use different methods of predicting eruptions. Most of the methods are based on the fixation and analysis of seismic activity in the regions where the volcanoes are located. The bubbles of gas formed on the lava surface in the volcano eruption can also be spoken about the addition of an eruption. For this purpose satellites are transmitting information about the height of the magma post, the crystal structures formed in the volcano are used. Unfortunately, none of these methods gives 100% result. Therefore, it remains to be hoped for the rapid progress of technology and scientific developments in this area.


What other interesting legends associated with volcanoes are you aware of? Share them with your classmates.

Zoology (South America)

If in Mexico there is a legend about volcanoes that the inhabitants of South America who lived in the majestic Andes had a legend about the condor.

The legend tells that the condor created the Gods, and he was their holy messenger. But he was lonely, and then he descended into the Ande Valley where he met a charming girl and fell in love with her.

Their love was mutual and despite obstacles and misunderstandings they still managed to get married and create a family. And the girl herself also subsequently turned into a magnificent bird - a condor.

Who is this bird condor? After all, the residents of South America have a very special and respectful attitude towards it. And with it that many legends and myths are connected.

The Andean Condor is otherwise called a Stamp. He belongs to the family of hawks. It is a bird of high flight in the literal sense because it refers to high-flying birds which is not surprising for a mountain resident. And the wingspan has a recordwidth of 3.5 meters. It is therefore not surprising that local Indians believed that such a big bird could carry a girl on her wings.

Condors live up to 50 years and choose a couple for the rest of their lives.

They have one more feature: they can "snap in" which means that they eat once every few days. Such a fed condor becomes unwieldy, difficult to rise, and sometimes can not take off.

And he is also flying out in very interesting way. He needs to make some strong, vigorous swings with his wings. And then he seems to swim in the sky which is not surprising at such a width of wings!


Look for information on whether these birds are listed in the Red Book. What do you think, why do animals and birds fall into it?

Ecology (Australia)

And now we are moving to Australia, Queensland.

It is on the shores of this state where a heart-shaped reef is located:

Coral reefs can only be formed in very clear water!

Reefs are geological formations formed as a result of the life of coral polyps colony and their accompanying organisms capable of extracting lime from sea water. They are formed in shallow water in tropical seas.

In the early 1980s the total coral reef area was about 600.000 sq.km by the year 2000 it decreased to about 250.000 sq.km.

According to forecast estimates by 2030 reefs may be completely destroyed!

Why is this happening? As already noted, they are sensitive to the transparency of water. And what do you think, which water becomes opaque? Correct dirty! Therefore, it is precisely the pollution of water and the destruction of the delicate ecosystem of coral reefs.

An ecosystem is a collection of all organisms living on a certain territory and all elements of the "inanimate nature" of this territory. If you really simplify the idea of an ecosystem, then your class with all the students, teachers, pillows on the windowsill and even spiders somewhere in the corner is the ecosystem of your class. And now, let's imagine that someone took some of the chairs from the classroom (let it be an analogue of elements of inanimate nature). Is it convenient? By no means. After all, now some of them have to stand. So, removing or changing something in the ecosystem we can harm it.

And the coral reefs appear not obvious at first glance, but a significant problem is discoloration. Nothing terrible, you could think these are pale areas ... In fact, the color is given to the corals by special microscopic algae, and they also give them stability. And the area that becomes pale is already deprived of such protective algae. And this means that in course of time it will be destroyed by the effects of sea waves.

All elements of any ecosystem including coral reef ecosystems are important and significant. And changes in one element necessarily induce changes in the entire ecosystem. These changes are not often better.

That is why all the consequences of human exposure to the environment must be taken into account even if they appear to be "small and insignificant" at first glance.


Do you think there is a chance to rebuild coral reefs? How? Perhaps, your ideas will allow not "to break the coral heart" of Australia!

History (Africa)

If William Shakespeare lived in the twentieth century, he simply could not have ignored such an incredible love story.

The heroes of this story met in England in 1947. He was the 26-year-old future king of one of the countries of South Africa, she was the 23-year-old daughter of a British military officer in retirement. The fate of future lovers, unknown to them, was determined by Muriel Williams-Sanderson, sister of Ruth, with whom they were very friendly. Muriel offered to join her at a dance party organized for the families of the military of the London Missionary Society. In the same place, by coincidence, Seretse also turned out to be - a well-educated students of Oxford, a representative of the ancient African family of Bamangvato and the crown prince of Bechuanaland. In addition to the royal title Seretse Khama had an extraordinary mind and very advanced views on modernity, political structure and, most importantly, his own country. Ceretse dreamed of the independence and freedom of his state which was under the British protectorate and was deprived of the opportunity to develop both economically and politically.>

All decided to dance, where despite the prejudices a black student decided to invite a white lady. Love between Ruth and Seretse arose as spontaneously as a hurricane in the steppe arises without any warning, and became the very “ love at first sight”. A year later, they realized that they should get married.

Just at that time, in the Botswana’s neighboring South African Republic (at that time South Africa), the Afrikaner National Party became increasingly popular preaching the ideas of racial segregation in its most extreme forms.

Everyone tried to dissuade Ruth. But if the father and sister simply did not like the idea of intermarrying with a black guy, the British Minister for Commonwealth Affairs gave the girl other political arguments. In fact, the girl was told that if she did not give up her African, this could be the beginning of the end of the British Empire in Africa.

For Seretse Khama the situation was no better. His uncle, who temporarily served as regent, not only opposed him, but had his own plans for the throne and the development of events.

Ceretse and Ruth still have their wedding day scheduled. However, the wedding did not happen: shortly before the ceremony, someone intimidated the priest who was supposed to marry a black groom and a white bride. Realizing that waiting for blessings and help was a vane cause, lovers secretly married in 1948 with the usual civil ceremony.

South African Prime Minister to the whole world declared this union "nauseous" violating ethical interracial laws. Angry telegrams were sent to the British government from Pretoria which condemned the marriage of an Englishwoman and an African. Is it any wonder that the National Party adopted the law on the prohibition of interracial marriage in South Africa (1949)? Britain's relations with South Africa were cracking at the seams plans for the possible accession of Bechuanaland to its southern neighbor were finally crossed out.

The native tribe of Khama, instigated by an uncle who had his own views of the throne, refused to recognize the white queen of the white English. Seretse was demanded to renounce either his wife whose marriage was not approved by the elders or the throne.

In March 1950 Seretse was summoned to London ostensibly to meet with the Commonwealth Affairs Committee to resolve issues relating to his interracial marriage. It was a trap.

British politicians in collusion with the uncle of the king tried to force Kham to give up the right to govern the country, but they were refused. In punishment for the obstinacy Ceretse became a prisoner of the British government, and together with Ruth, until 1956 they could not leave the limits of Great Britain, let alone return to the homeland of Seretse.

Loyalty to his love was not the only merit of the young king. He possessed charisma, was full of real ideas on how to change life in his country for the better and was not at all about to give up under the onslaught of circumstances. This attracted compatriots to him. If Ceretse could not become the king of Bechuanaland, then he should have become its president!

In 1956, the elders of the Bamangvato tribe sent an official request to Elizabeth II to release their leader. The political situation at that time did not imply a refusal. And so Khama, along with his white wife and two children, returned to their homeland. Further events developed rapidly.

Khama renounced the claims to the throne which led to the abolition of the monarchy in the country. A year later he joined the Bechuanaland administration council created the Democratic Party of Botswana in 1961, which 4 years later won parliamentary elections and in 1966 Seretse Khama was elected president of the land in which he was not allowed to become king. He entered the history of Botswana as a man who managed to transform it from one of the poorest countries in Africa into one of the most promising countries on the continent. All this time Ruth was next to her husband. In trouble and in joy relentlessly and faithfully. White-skinned Ruth Wilson Khama became the most influential First Lady of the Black Continent.

Seretse Khama was re-elected president for 14 years until 1980. In 2008 his youngest son Jan Khama became the 4th president of Botswana continuing the work started by his father.

In the fall of 2016 just in time for the 50th anniversary of the inauguration of the first president of Botswana the movie “United Kingdom” based on this incredible romantic story of Seretse Khama and Ruth Williams was released.

Maths (Universe)

Is there anything else besides love that can be common to all continents? Maths! After all, in Europe, and in Africa, and in America, 2 + 2 = 4. Even for the Universe the speech of mathematical formulas and dependencies can become universal. After all, the radio signals that scientists send to space are an interpretation of mathematical dependencies. It is believed that mathematical representations should be universal for any mind. Even for the extraterrestrial ...

But is it possible to say “I love you” in the language of mathematics? It turns out that math can solve such a problem!

How is this implemented? You can use the graphics functions. A graph is a visual representation of a function, one can say its “portrait”. The graph of the function refers to the entire set of points (x, y) for which the dependence y = f (y) is satisfied z.

So, this is a picture in which you can see how the value of Y changes depending on the value of X. As a rule, the values of X are marked on the horizontal line called the x-axis (x), and the value of Y on the straight line called the ordinate (y). These axes together form a coordinate system. Each axis has a direction in which the value of the corresponding coordinate increases. At the point of greatest value draw an arrow indicating this direction. On each axis mark the individual (key) values and sign them with these values. This allows you to roughly estimate other intermediate values. The point with coordinates x = 0 and y = 0 is called the origin.

For example, the word LOVE in the language of graphs can be represented as:

The first letter was formed due to the graphics, which has its own name - hyperbole.

The second letter can appear if we use a circle:

To write the next letter, we use the linear function module.

A linear function is a function that is given by the formula y = bx + c where x is an argument; c, b - constants. The graph of such a function is direct.

And if we need to make a "reflection" of the graphics as in the picture, then we need to use the concept of a module. Absolute magnitude or modulus — in mathematics, magnitude, value, or number regardless of sign. The absolute value of the number x is written | x |. Own module can have not only number, but also function.

Finally, the letter E is a sine wave, only the X and Y axes are swapped. In addition, the module is also used here:

Interesting, is there a mathematical way to draw a heart? Of course there is, and graphics functions are also capable of helping! Here is a kind of “hit parade” of mathematical hearts!

There are complex functions. They have real and imaginary parts, and they are not studied by ordinary mathematics, but the highest. Those who are from the school mathematics course are familiar with the concept of square root know that it is impossible to extract the square root of -1. But for higher mathematics nothing is impossible! There, such a root calmly exists and even has its own name - imaginary unit:

If we use ordinary ones and imaginary functions for the function, it will also have real and imaginary parts, for which you can draw your own graphs. This will be a complex function. And one of them, or rather its real part, will give an image of the heart:

And if the mathematician wants to give his beloved an unusual bouquet, he can even draw mathematical flowers:

However the formula for their creation will also be unusual:

Even the dissertation research of mathematician Gabriel Tobin is devoted to the image of the heart. The image he created got its own name and became a mathematical classics. This is Tobin's Heart:

To describe such beauty the mathematician used the 6th order equation:

So Mathematics can be extremely romantic, beautiful and "in love"!

Task 1:

Find information about any mathematical "image" of the heart. Make a small presentation about it. Do you know the formulas that describe your “find”?

Task 2:

The teacher prepares two images of the coordinate plane with marked axes of coordinates on the blackboard. He must also prepare two columns with the coordinates of points in the form (x; y). These points plotted on a plane and united by a line should give images (heart, flower, leaf, sun ...).

Students are divided into two teams and in turn plot the points with the coordinates indicated in their column on their own coordinate plane. The last student must connect the dots and guess the image.

The winner will be the team which faster and more accurately copes with their task.

The End