МЕТ_1к_1ч

5.Work in small groups. In three minutes, write down a list of things which are usually

round (Earth, marbles, tires, ...., ...., ....,);

square (table, ...., ...., ....,).

6.Look at the two paintings. What do they have in common? Do you like them?

READING

7.Underline the stressed syllable in each word as in the example. Choose any 4 words and use them in your own sentences.

millennium, spiritual, universe, array, integer, infinite, horizontal, diagonal, vertical, innovative, combinatorial, subsquare, likewise

8.What does the word "quadramagicology" mean? What information do you expect to read?

9.Look at the picture of a turtle and tell what is special about it. How might it be connected with the text? Share your ideas with your groupmates. Read the text to find out if your guesses were right.

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10.Some sentences have been removed from the text by mistake. Put each sentence into appropriate place in the text (1−5).

A.The corners of any 4-by-4 subsquare also sum to 34, as do the four corners of any 3-by-3 subsquare, and likewise those of any 2-by-2 subsquare.

B.The magic constant is the sum of each row's values.

C.In one evening in his 40s he composed a 16x16 square which, abandoning modesty, he called "the most magically magical of any magic square ever made by any magician".

D.It was also recorded in Book of Changes that the 3,000-year-old Chinese literature of philosophy was inspired by the magic square.

E.It is the only magic square that uses each number from 1 to 9 exactly once.

11.What do you remember after reading the text? Mark the following statements as true (T) or false (F). Then check your answers in the text.

1.A 3-by-3 magic square is order-5.

2.Loh Shu was interpreted by the Chinese as a supernatural sign of order in the universe.

3.An order-4 magic square has 25 cells.

4.Benjamin Franklin delighted in creating magic squares as a kind of mental exercises.

5.Some cultures believed that magic squares possess mystical powers and wore them as talismans.

6.In a conventional magic square, the sum of the entries of any row, any column, or any broken diagonal is the same.

7.An antimagic square is a square in which all the rows, columns and diagonals equal

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QUADRAMAGICOLOGY

Perhaps no other area of non-practical mathematics has been so popular for so long as magic squares. Mathematicians, artists and mystics have long been fascinated by the mesmerizing patterns that they produce.

A traditional magic square is a square grid of numbers in which the values of each row, column, and diagonal add up to the same sum. A magic square's order is the number of cells in each row. 1) …… . For a magic square of consecutive natural numbers starting with 1, let n equal the magic square's order and C equal the magic constant. Then, for an order-3 magic square starting with 1, C = 15.

Mathematicians trace an order-3 magic square back to ancient China, Babylonia, and Mayan culture. In India amulets with magic squares were worn as protective charms, while in western Europe Renaissance astrologers equated them with planets.

According to the legend the Loh Shu was the first magic square, turning up in the dots on the shell of a tortoise that crept out of the Yellow

River in China about four millennia ago. 2) …… . The Chinese gave it spiritual importance, believing that it encapsulated the harmonies of the universe. Feng Shui, the Chinese system of arranging objects, is in part based on the Lo Shu. 3) …… .

The first documented magic square in the West was a 4x4 array of integers one through to 16 which appeared in an engraving Melancholia created by

Albrecht Dürer in 1514.

A magic square from the 12th-century temple at Khajuraho in India gives an idea of the extra possibilities offered by a 4-by-4 square. Its magic constant is 34, but there's a new twist. Place the table next to copies of itself, and it creates an infinite "magic carpet": any four adjacent entries along a straight line − horizontal, vertical or diagonal − sum to 34. 4) …… .

Squares with the magic-carpet property were called panmagic. Soon they were joined by antimagic squares − in which all the row, column and diagonal

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sums were different − and by nested and knight's-tour magic squares, in which each number from 1 to 64 is a chess knight's move apart from the next one.

Some great mathematicians studied magic squares – such as Leonhard Euler in the 18th century, and Édouard Lucas and Arthur Cayley in the 19th. The

American statesman and scientist Benjamin Franklin liked to spend his spare time constructing innovative variations of magic squares. 5) ……. .

Today, magic squares are studied in relation to factor analysis, combinatorial mathematics, matrices, modular arithmetic, and geometry.

12.Look through the list of words and phrases and check if you know their Ukrainian equivalents. Take turns to ask each other. Use the MINIDICTIONARY section to Unit 8 if necessary.

13.Explain the meaning of words and phrases below. Choose 3 words / phrases you like and write sentences with the words / phrases chosen. protective charms, mystics, a grid, a tortoise, Feng Shui, adjacent entries, to give a new twist, magic-carpet properties, row’s values, statesman

14.Find words or phrases in the text that match the meanings (a−e).

a)technique of making prints from metal plates;

b)ancient Chinese book of prophecy and wisdom;

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c)the period in European civilization that marked the transition from medieval to modern times;

d)object or formula that credulity and superstition have endowed with the power of warding off harmful influences;

e)edifice or sometimes merely an enclosed area dedicated to religious worship.

15.Match the words and collocations (1−8) with their definitions (a−h).

16.Arrange the following words in pairs of synonyms.

equate, fascinate, date back, infinite, condense, spellbind, appear, encapsulate, trace back, turn up, charm, mesmerize, endless, relate

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17. Fill in the blanks with the appropriate words from the list below.

reconstruct, shapes, participates, arcs, determine, reinvented, sequence, forms, represents, described, space

In Cubism, the subject of the artwork is transformed into a

1) ….. of planes, lines, and 2) …. . Cubism has been 3) ….. as

an intellectual style because the artists analysed the 4) ….. of their subjects and

5) .…. them on the canvas. The viewer must 6) ….. the subject and 7) ….. of the work by comparing the different shapes and 8) ..… to 9) ..… what each one 10)

….. . Through this process, the viewer 11) ..… with the artist in making the artwork make sense.

18. Fill in the chart below with the missing words.

Now see how quickly you can find the answer to this rather long sum.

Four add two, divide by three, subtract one, multiply by eight, take away four,

times three, plus two, minus four, halved, equals what?

19.Put the appropriate verb of measurement into the sentences, changing its form if necessary. Pay attention to the tenses.

A drop; gain; last; lose; measure; take; weigh

1.It was a long lecture: it … three and a half hours.

2.It was a big project: it … three weeks to finish.

3.That box looks heavy. How much does it…?

4.The time is 8:00. My watch says 7:55. It has … five minutes.

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5.The time is 8:00. My watch says 8:05. It has … five minutes.

6.It was a cold evening, and temperature … 10 degrees in an hour.

7.The field mouse is quite a small animal: it … about 4 cms from nose to tail.

B contain; cover; hold; register; seat; spend; total

1.The petrol tank is small: it only … 25 litres.

2.The bill for maintenance alone … $750,000 a year.

3.It is a big farm: it … more than 25,000 acres.

4.This equipment measures sound: it can … up to 100,000 decibels.

5.I … several hours every day just adding up figures.

6.This encyclopedia … over 25,000 references.

7.It is a huge hall: it can … 2,500 people.

20.Match the parts of the sentences from three columns to make complete sentences that have sense. Translate them into Ukrainian.

21. A. Fill in the chart with the appropriate forms of the words.

B. Match the pictures with the words that describe shape.

spherical with an uneven surface; crescent shaped; pear-shaped; cylindrical with a convex top; round with a concave top; triangular, three-sided (acute triangle); prismatic; round with a serrated edge; spiral; pentagonal, regular hexagonal; semi-circular

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22.Match the adjectives on the left with a suitable noun on the right. Use each word only once. Translate the collocations into Ukrainian.

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23.A drawing game. Try to draw each of the items below spending just a few seconds on each.

a dotted line; a crooked line; an octagon; a jagged edge; a rough sea; a steep heel; a sharp bend; a gentle curve; a smooth surface; rolling hills; wavy hair

24.Label the shapes with the suitable words. Then check your answers in the text below.

Two-dimensional, or 2D shapes have sides. Where two sides meet they make an angle. A circle only has one side and the distance all the way round this is called the circumference. When we measure a circle, the distance from one side to the other through the centre is the diameter and the distance from the side to the centre is called the radius. Three-dimensional, or 3D shapes are more complex because you can measure the height, width and depth. The surfaces on a 3D shape are called faces. Where two faces meet are the edges. Where two edges meet there is a corner. For example, a cube has twelve edges and eight corners.

25.A. What do you think life will be like in 100 years?

Useful words and phrases:

perhaps, probably (not), certainly, I (don’t) think, I’m sure, I hope, I’d like to imagine

Example: I think the world will still be powered mainly by fossil fuels.

B. Write 3 sentences to say what you are doing this evening / tomorrow /

next week.

Example: I’m doing my exams next week.

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