Заполните пропуски подходящими по смыслу словами из задания 5. Не забывайте при необходимости менять форму слова и ставить глаголы в нужном времени

1) The historical record shows quite a different path towards the ………..

2) The ………. were pressed into soft clay tablets with the slanted edge of a stylus and so had a wedge-shaped appearance.

3) Although we have evidence of zero from tablets in the Selucid era, it is possible that zero ………. before that time.

4) The scene now ………. to India where the numerals and number system was born.

5) The classical Greeks had a different system, with different letters for each ………. from one to nine, and yet more ………. for ten, twenty and so on.

6) The use of positional system ………. fractions was introduced around 1579 AD by Francois Viete.

Найдите в тексте предложения, в которых говорится, что

1) zero has the fundamental significance for different fields of mathematics.

2) zero was independently invented by different civilizations.

3) zero has two meanings.

4) there were only two signs to represent numbers.

5) there were symbols to indicate zero.

6) the Mayans used a placeholder for their everyday needs.

7) the Indian mathematicians made an error in using zero in some arithmetic operations.

8) the Arabian mathematician was the first to operate on equations that equaled zero.

Ответьте на вопросы по содержанию текста.

1) Why is invention of zero so important?

2) What problem did the development of zero solve?

3) When does the history of zero go back to?

4) How can you explain the fact that zero was independently invented several times? Did the ancients use zero first as an idea or as a symbol?

5) Who began to understand zero both as an idea and as a symbol?

6) In what way did they indicate a placeholder (zero)?

7) Who wrote zero in the way it is known to us now?

8) What is Mohammed ibn-Musa al-Khwarizmi famous for?

9) What civilizations had taken part in the development of zero before it reached Europe?

Переведите текст на английский язык.

Первое, что нужно сказать о нуле, это то, что имеется два варианта его использования, оба очень важные, но немного различные. Первый – это указатель пустого разряда в нашей позиционной системе счисления. Так, в числе 2106 нуль служит для того, чтобы позиции 2 и 1 были верными. Очевидно, что 216 значит совершенно иное. Второй вариант использования нуля – это число, которое мы обозначаем «0».

Имеются также разные аспекты применения нуля, внутри каждого из которых понятие, обозначение и название.

TEXT 4

A BRIEF HISTORY OF ALGEBRA