английский
.pdf7. trigonometry |
g. a branch of pure mathematics devoted primarily to the |
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8. the present day |
h. the geometry of three-dimensional space, the kind of |
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space we live in . |
TRANSLATE INTO ENGLISH
1.Один из величайших математиков Исаак Ньютон родился в 1643 году и умер
в1727. 2. Главная работа Эвклида «Начала» содержит изложение планиметрии, стереометрии и ряда вопросов теории чисел. 3. Мой дядя был родом из богатой семьи. 4. Начала состоят из тринадцати книг.5. В школьную программу входит алгебра и геометрия, а высшую математику студенты изучают в университете. 6. Работы Эвклида повлияли на развитие науки. 7. Эвклид посещал школу Платона в древней Греции. 8. Между двумя точками можно провести прямую линию. 9. Его книга была опубликована в конце 15 в. и с тех пор было продано миллионы копий.
10.Ученый внес большой вклад в математику.
GIVE A SUMMARY OF THE TEXT state the main ideas of the text;
identify the most important details that support the main ideas; write your summary in your own words, except for quotations; express the meaning of the text, not just its details
2. Archimedes
Archimedes (287-212 B.C.) was one of the greatest mathematicians in antiquity, a physicist, astronomer and engineer. He is famed for his inventions and colorful ways to have made them.
Little is known about Archimedes's life. He was born in Syracuse, the seaport city of the Mediterranean Sea. He was the son of an astronomer (someone who studies outer space, such as the stars) named Phidias. Archimedes studied in Alexandria, Egypt, at the school that had been established by the Greek mathematician Euclid (third century B.C). He later returned to live in his native city of Syracuse.
There are many stories about Archimedes discoveries. A famous one tells how he uncovered an attempt to cheat King Hieron. The king ordered a golden crown and gave the crown's maker the exact amount of gold needed. The maker delivered the crown of the required weight, but Hieron suspected that some silver had been used instead of gold. He asked Archimedes to tackle the problem. One day Archimedes was considering it while he was getting into a bathtub. He noticed that the amount of water overflowing the tub was
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proportional to the amount of his body that was covered by water. This gave him an idea for solving the problem of the crown. He was so thrilled that he ran naked through the streets shouting, 'Eureka!' (Greek for 'I have discovered it!').
According to the Greek biographer Plutarch (46-120 B.C.), Archimedes's military inventions helped defend his home city when it was attacked by Roman forces. Plutarch wrote that after Hieron died, the Roman general Marcus Claudius Marcellus (268-208 B.C.) attacked Syracuse by both land and sea. According to Plutarch Archimedes's catapults (machines that could hurl objects such as heavy stones) forced back the Roman legions on land. Later writers claimed that Archimedes also set the Roman ships on fire by focusing an arrangement of mirrors on them (Heat Ray). But despite Archimedes's efforts, Syracuse surrendered to the Romans and Archimedes was killed during the Second Punic War, after the city was taken (it is not known how this occurred).
While in Egypt, Archimedes invented the water screw, a machine for raising water to bring it to fields. Another invention was a miniature planetarium, a sphere which motion imitated that of the earth, sun, moon, and the five planets that were then known to exist. Archimedes continued Euclid's work and extended what is known as the 'method of exhaustion' to determine the areas and volumes of figures with curved lines and surfaces (circles, spheres, pyramids and cones), to figure out the approximate value of pi. He had managed to prove that the surface and volume of the sphere are two thirds of the cylinder, inclusive with
bases. Archimedes's investigation of the method of exhaustion helped to lead to the current form of mathematics called integral calculus.
His tomb carried a sculpture that represented mathematical proof which encompassed a sphere and cylinder with the same height and diameter. Unfortunately the tomb's location isn't known till this day. Archimedes has provided sufficient knowledge for the mathematical society to ponder upon.
COMPREHENSION
1.Read the text and answer the questions
1.Who established the school where Archimedes studied?
2.What did King Hieron suspect the maker of?
3.How did Archimedes get the idea for solving the problem of the crown?
4.Why was Archimedes running through the street shouting 'Eureka!'?
5.How did Archimedes help to defend his native land?
6.Did the Romans win the war?
7.What is the water screw?
8.How did Archimedes continue Euclid's work?
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9. Who invented |
a miniature planetarium? |
10.Where is the 'method of exhaustion' used?
2.Decide if the statements are true or false
1. |
Archimedes studied in his native city. |
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The King ordered a silver crown. |
T/F |
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Archimedes got the idea how to solve the problem of the crown while |
T/F |
he was walking down the street. |
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The inventions of Archimedes helped to win the war. |
T/F |
5. |
Euclid was the first who invented the water screw. |
T/F |
6. |
Archimedes focused an arrangement of mirrors on the Roman ships |
T/F |
and set them on fire. |
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Archimedes was killed when the war began. |
T/F |
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Euclid's book The Elements influenced the inventions of Archimedes. |
T/F |
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The 'method of exhaustion' is outdated now. |
T/F |
10. Archimedes was the son of the mathematician. |
T/F |
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VOCABULARY STUDY
1. Find English equivalents to the following
открытия, город-порт, поселение, астроном, возвратиться, родной город, делать открытия, попытка, разоблачать, доставить, подозревать, размышлять, принимать ванну, количество, решить проблему, военный, нападать, поджечь, направить на (фокусировать), кривая линия, поверхность, устареть.
2. Find Russian equivalents to the following
to be famed for, to establish, to cheat, to order, outer space, to be related to, to hurl, the required weight, to notice, to immerse, to be thrilled, to defend, forces, to surrender to, to kill, to occur, the water screw, motion, to imitate, circle, sphere, pyramid, cone, the method of exhaustion, integral calculus, to exist.
3. Fill in the gaps and translate the text
granulated solids , leak, commissioned, a cylinder, antiquity, worked (2), the hull, agricultural fields, simple, warship, liquids, Invention, industrialized, to remove
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The Archimedes Screw Pump |
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listed among the great ancient inventions. Best known because we know it 2) |
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well. As the story goes King Hieron II 4) |
Archimedes to design a huge naval 5) |
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a ship of this size would 7) |
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Archimedes' screw pump was 10) |
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as one of the greatest inventions? It is still in use today for pumping |
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such as coal and grain, in both the 14) |
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4. Match the terms with their definition |
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1. cone |
a. to set up |
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TRANSLATE INTO ENGLISH
1. У астронома Фейдия был сын Архимед. 2. Он жил в городе-порту и обучался в Египте. 3. Мой родной город - Рим. 4. Архимед известен своими великими открытиями. 5. Римские войска напали на Сиракузу с суши и моря. 6. Короли приказал Архимеду решить проблему с короной. 7. Он попытался обмануть короля, заменив часть золота серебром. 8. Великий ученый Архимед изобрел миниатюрный планетарий. 9. Некоторые методы Архимеда устарели. 10. Начерти кривую линию на этой плоскости.
GIVE A SUMMARY OF THE TEXT state the main ideas of the text;
identify the most important details that support the main ideas; write your summary in your own words, except for quotations; express the meaning of the text, not just its details
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3. Pythagoras of Samos
Pythagoras was born on the island of Samos in 570 BC. His mother was native of Samos and his father was a merchant from Tyre. He studied with the priest of Memphis in Egypt, who was famous for his wisdom. After Memphis, he studied at the temples of Tyre and Byblos in Phoenicia. It is most likely in Egypt where he came up with his geometric principles that would lead to his famous theorems. The evidence of his Egyptian inspirations is called the Berlin Papyrus. Pythagoras did not only think up mathematical principles during his life. He also founded a religious society. His society had very strict rules of conduct. The inner circle of the society was called Mathmetikoi. As a member of the society, you had to live at the school, have no personal possessions and had to follow a vegetarian diet. They did allow students from other areas to attend the school. These students, called Akousmatics, were
permitted to eat meat and own a few personal things. As a whole, the members of this society were known as Pythagoreans and had a very structured life of religious teaching, common meals, exercise, reading and philosophical study. They had to sing to the Greek god Apollo on a regular basis. They believed that they could use the lyre to cure illnesses of the soul and body. One had to do poetry recitations before and after sleep since they believed this exercise could help improve human memory.
The Pythagorean mathematics was summed up by
Aristotle: - Pythagoras thought that all things consisted of numbers. All physical bodies are numbers. All the elements of numbers are the elements of everything. - All units possess magnitude. - Numbers are an expression of the universe. When you are talking about numbers, you are talking about what makes up the universe. - You should regard unity and infinity as substances that form the basis of the universe. Pythagoras had what was called the Ten Principles or the Table of the Opposites. One principle is limit and the other is unlimited. There is an odd and an even. There is one and plurality. There is right and left. There is male and female. Things are at rest and moving. There is straight and crooked. There is light and darkness. There is good and bad. There is square and oblong. Pythagoras believed that this universe was a universe of opposites. Pythagoras believed that Monad was God and the good. The good is the true nature of the One. The One is the Mind. The bad side is the indefinite Dyad who is evil. Evil has to do with material plurality. Pythagoras possibly believed that the sun was the center of the universe. He always supported that fire was the center of the cosmos. The problem is that it is very difficult to know directly about his teachings. There was a vow of silence required by people who first joined his order.
Most information about Pythagoras comes from secondary sources. His original doctrines are unknown and his order scattered all over the known world after 545 BC. In fact, Hicetas, a Pythagorean, was quoted as saying that the earth moved in a circle. These are some
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of the mathematical principles that Pythagoras is known for. One such principle is that the sum of the angles of a triangle is equal to two right angles. His famous theorem stated that when you have a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides. Pythagoras may have discovered irrational numbers. The problem is that it would go against his philosophy that all things are numbers since he meant that a number is a ratio of two whole numbers.
COMPREHENSION
1.Read the text and answer the questions
1.What is Pythagoras famous for?
2.What were the rules of conduct in his religious society?
3.Who summed up the Pythagorean mathematics?
4.What were the believes of Pythagoras?
5.What are the Ten Principles?
6.What is the famous theorem of Pythagoras?
7.What did Pythagoras discover?
8.What was his father?
9.Where did Pythagoras study?
10.What students were called Akousmatics?
2.Decide if the statements are true or false
1. |
Pythagoras came up with his geometric principles in Samos. |
T/F |
2. |
The inner circle of the religious society was called Akousmatics. |
T/F |
3. |
The members of the society were known ad Pythagoreans. |
T/F |
4. |
They had to sing to the Greek god Apollo once a year. |
T/F |
5. |
To improve human memory one had to do the poetry recitation every |
T/F |
morning. |
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Pythagoras supposed that fire was the centre of the universe. |
T/F |
7. |
Pythagoras believed that the universe was the universe of opposites. |
T/F |
8. |
Pythagoras was the son of a priest. |
T/F |
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All members of the society were allowed to live in their own homes. |
T/F |
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Akousmatics had to follow vegetarian diet. |
T/F |
VOCABULARY STUDY
1. Find English equivalents to the following
уроженец, священник, мудрость, храм, основывать, строгие правила поведения, член общества, соблюдать вегетарианскую диету, излечивать, болезнь, душа, состоять, число, вселенная, зло, угол, треугольник, площадь, гипотенуза, цитировать, источники, множество, регулярно, тьма, целые числа, противоположности, обобщать, позволять, внутренний круг, противоречить.
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2. Find Russian equivalents to the following
merchant, to come up with, religious society, the lyre, to possess, magnitude, unity, infinity, substance, straight, crooked, geometric principles, inspirations, personal possessions, structured life, to do poetry recitations, to improve human memory, odd, male/female, to be at rest, to move, square, oblong, the center of the cosmos, original doctrines, the sum, right angles, a right-angled triangle, irrational numbers, side.
3. Fill in the gaps and translate the text
equal, proportion, mathematical laws, geometrical figures, square numbers, harmony, carried on, numbers, the relations, numbered, hypotenuse theorem, training
Pythagoras and mathematics as a part of philosophy and religion
The study of mathematics was looked on as a valuable 1) ___ for the soul. Since all things in the world can be 2) ___ , and 3) ___between things expressed numerically. Eg: the intervals on the musical scale. They identified science with mathematics, maintaining that all things are made up of numbers and 4) ___The Pythagoreans, having discovered the 5) ___ of musical pitch, inferred that planetary motions produced a 'music of spheres' and developed a 'therapy through music' to bring man in 6) with
the celestial spheres. They made important contributions to mathematics, music theory and astronomy.
Among the extensive mathematical investigations 7) ___by the Pythagoreans were their studies of odd and even 8) ___ , and of prime and 9) ___ . From this arithmetical standpoint they cultivated the concept of number, which became for them the ultimate principle of all 10) ___ , order, and harmony in the universe. Through such studies they established a scientific foundation of mathematics. In geometry the great discovery of the school was the 11)___or Pythagorean theorem, which states that the square on the hypotenuse of a right triangle is 12)___to the sum of the squares on the other two sides; "Pythagorean numbers" are numbers so related, for instance, 5, 4 and 3.
4. Match the terms with their definition
1.merchant
2.the angle
3.triangle
4.square
5.a ratio
6.oblong
7.crooked
a.any real number that cannot be expressed
b.not straight or aligned
c.the relative size of an object
d.an abstract concept describing something without any limit and is relevant in a number of fields
e. one of the basic shapes in geometry: a polygon with three corners or vertices and three sides / edges which are line segments
f. a rectangle with length greater than its width
g. the figure formed by two rays, called the sides of the angle, sharing a common endpoint,
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j. a relationship between two numbers of the same kind |
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TRANSLATE INTO ENGLISH
1. Мой брат - уроженец Белгорода. 2. Священники этих храмов известны своей мудростью. 3. Пифагорейцы были членами религиозного сообщества, которое основал Пифагор. 4. Моя сестра соблюдает диету. 5. Этот священник может исцелять болезни тела и души. 6. Чтобы улучшить память - учите стихотворения. 7. Пифагорейцы вели организованный образ жизни, который включал религиозные учения, чтение, физическую нагрузку, вегетарианское питание. 8. Пифагор верил, что огонь - центр вселенной. 9. Квадрат гипотенузы равен сумме квадратов катетов. 10. Пифагор считал, что вселенная состоит из чисел.
GIVE A SUMMARY OF THE TEXT state the main ideas of the text;
identify the most important details that support the main ideas; write your summary in your own words, except for quotations; express the meaning of the text, not just its details
GRAMMAR 1
Tenses. Active voice
Видо-временные формы английского глагола (активный залог)
Simple |
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Perfect Continuous |
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to be+Ving |
to have + Ved/V3 |
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have /has + Ved./V3 |
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now, at present, still, |
ever, |
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just, |
for, since, all life, all |
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at the moment |
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lately, |
this week (month, |
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recently, so |
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often, as |
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today, since, this |
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do/does |
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Past
V (ed) |
was/, were + Ving |
had + Ved./V3 |
had been + Ving |
yesterday, last |
at 5 o'clock, from 5 |
by 5 o'clock, other |
for, those two years, |
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till 6, at the moment |
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all that month, of late, |
week),5 days |
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Future |
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will+ V |
will + be+ Ving |
will+ have+ Ved./V3 |
will + have been Ving |
tomorrow, |
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by 5 o'clock, by |
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from 5 till 6, the |
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The Present Indefinite Tense
The Present simple tense shows an action that happens regularly or permanently
1. Open the brackets using the verbs in the Present Indefinite
(USUALLY) 1. Andrea Schatzzuann, an exchange student from Switzerland, (to live) with the Connor family in San Francisco. She (to get) up at 7 am and (to take) a shower. She normally (not to have) breakfast. At half past seven she (to catch) the bus. Her first class (to start) at a quarter past eight. She always (to have) lunch at 12 o'clock in the cafeteria. The cafeteria food (to be) OK and it (to be) cheap too. Her afternoon classes (to be) from 1.15 till 3.00 pm, so she (to be) at school all day. She usually (to have) dinzier with the Connors at about 8.00. On Saturdays she (to have) lunch at the restaurant. Once a week, usually on Sunday mornings, she (to go) swimming. A few friends usually (to go) along, too. One of her friends has got a car, so he (to pick) them up and then he (to drive) them home. After swimming they often (to go) out for a pizza. On Saturday evenings she sometimes (to go) out with friends to a party or maybe to a concert. Sometimes she (to invite) friends to her
2. Translate the sentences into English putting the verbs in brackets into the Present Indefinite
(ОБЫЧНО) 1. Я работаю. 2. Мы работаем. 3. Они не работают. 4. Вы работаете? - Да. 5. Он работает? - Нет. Он учится. 6. Мой брат не учится. Он работает. 7. Ты носишь очки? 8. Вы помогаете людям? 9. Он любит читать сказки? 10. Она любит играть на скрипке? 11. Моя сестра не читает книг. 12. Наша бабушка любит спать на диване. 13. Вы любите отдыхать в кресле? 14. Мы едим и пьем в кухне. 15. Мой брат не любит читать газеты. 16. Мы спим в спальне. 17.
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Мой брат спит на диване в жилой комнате. 18. Моя сестра одевается перед зеркалом. 19. Мой дядя пишет книги. 20. Мы пишем упражнения в школе. 21. Я трачу свои карманные деньги на мороженое. 22. Он читает все время и не любит смотреть телевизор.
The Future Indefinite Tense
The Future Simple Tense expresses a decision or an assumption with regard to the future.
1. Choose the right variant |
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1. Who |
the next president? |
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a. will be |
b. will being |
c. be |
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2. I can't stay any longer, my friend |
tomorrow. |
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a. will come |
b. will came |
c. will come |
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3. What |
for dinner? |
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a. will we eat |
b. we will eat |
c. we eat |
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4. I |
the house because we are going to rebuild it. |
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a. will clean |
b. will not clean |
c. will not clean |
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5. Next Monday there |
a new comedy on. |
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a. will be |
b. will not be |
c. will |
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6. If you study harder you |
this |
exam. |
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a. pass |
b. will passing |
c. will pass |
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7. What |
for Christmas? |
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a. will you buy |
b. you will buy |
c. will not you buy |
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8. In future people |
less coffee. |
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a. will drink |
b. will drinking |
c. will drink |
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9. At 9 o'clock Bob |
you with information. |
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a. |
will call |
b. is call |
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c. will calls |
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2. Put the verbs in brackets into the affirmative, interrogative and negative forms of the Future Simple
1. I (to do) morning exercises. 2. He (to work) at a factory. 3. She (to sleep) after dinner. 4. We (to work) part-time. 5. They (to drink) tea every day. 6. Mike (to be) a student. 7. Helen (to have) a car. 8. You (to be) a good friend. 9. You (to be) good friends. 10. It (to be) difficult to remember everything.
The Past Indefinite Tense
The Simple Past expresses an action that started and finished at a specific time in the past.
1.Open the brackets using the verbs in the Past Indefinite
1. What your neighbours (to do) yesterday? 2. Mr. Smith (to fix) his car yesterday morning. 3. His wife (to water) plants in the garden. 4. Their children (to clean) the yard
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