25. . Put the verbs in brackets into the correct passive form.

1. Nowadays all bags ______________ at airports. (check)

2. A man ______________ by a shark yesterday. (bite)

3. The connection between fractals and leaves _____________ to determine how much carbon is contained in trees. (currently / use)

4. When they got home, the fence between the two houses ___________ but no one knew who was responsible. (remove)

5. An election ________________ next autumn. (hold)

6. Fractal signals can ____________ to model natural objects, allowing us to define mathematically our environment with a higher accuracy than ever before. (also / use)

7. Hotel rooms must _________ by 12 noon. (vacate)

8. A lecture _________ in the main hall at the moment. (give)

9. Hopefully, all forms of discrimination ____________ by the end of this century.(wipe out)

10. Benoit ____________ the alphabet and never learned multiplication tables past fives. (never / teach)

26. Fill in ‘by’ or ‘with’.

1. Who was Australia discovered ……?

2. Before Mandelbrot, the academic math world was dominated …… arithmetics, geometry was relegated to a secondary inferior position.

3. The food will be provided …… caterers.

4. All through January, the fields were covered …… snow.

5. Two of the climbers were injured …… falling rocks.

6. No.5 sold for $140M was painted …… Jackson Pollock.

7. The window had been smashed …… a hammer taken from the tool-shed.

8. The turkey was stuffed …… chestnuts, and was very tasty.

9. The order behind the chaotic production of numbers created by the formula z -> z^2 + c can only be seen …… the computer calculation and graphic portrayal of these numbers.

27. Help your friend to translate the following sentences into English.

1. Дерева, блискавка, бронхи і кровоносна система людини мають фрактальну форму, ідеальними природними ілюстраціями фракталів називають також папороті та капусту брокколі.

2. Фрактал - це нескінченно самоподобна геометрична фігура, кожен фрагмент якої повторюється при зменшенні масштабу.

3. У фізиці фрактали природним чином виникають при моделюванні нелінійних процесів, таких, як турбулентний плин рідини, складні процеси дифузії – адсорбції.

4. Фрактали використовуються при аналізі та класифікації сигналів складної форми, наприклад, у фізиці твердого тіла, для стиснення зображень.

5. Структури, схожі на фрактали, можна виявити в оточуючій нас природі: хмари, межі морських узбереж, зимові візерунки на склі.

6. Методи фрактального аналізу і фрактальної геометрій сьогодні широко використовуються в різних галузях науки.

SPEAKING

28. Discuss the following questions in small groups or pairs.

1. Do you like the fractals in Gothic and Hindu architecture?

2. Do you see fractal architecture as calming and harmonious, or do you have more of an Euclidean frame of mind?

3. Why is Euclidean geometry often described as ‘cold’ and ‘dry’?

4. Have you ever listened to fractal music?

5. What do you think about computer-generated fractal art?