Text 2.History of Arithmetic

Text 2. History of Arithmetic

The word “arithmetic” comes from the Greek arithmos (“number”). Many thousands of years ago there was a world without numbers. Everyone knew what belonged to him and what not. But when people acquired more and more property they began to count. Counting represents a very important milestone in the progress of civilization. The earliest documents show that the concept of number is equally present in many ancient civilizations: Babylonian, Egyptian, Roman, Greek and Chinese.

Some time before 2000 B.C. the Babylonians developed a base-sixty or sexagesimal system of numeration with the positional principle that still useful in astronomical calculations. The early Egyptian system of numeration used a base of ten with no more than three symbols to express any number less than 100 – one for units, one for tens, and one for hundreds, the zero symbol was unnecessary. The Romans used seven capital letters to represent numbers, they mixed them together to form many different combinations. The ancient Greeks’ nonpositional system of numeration employs twenty-four letters of their alphabet to produce letter-numerals and special symbols for large numbers. The traditional Chinese-Japanese system of numeration is a base-ten system with nine numerals and symbols for the place value. In the Hindu-Arabic decimal-position system of numeration there are ten digits to express any number, so our present-day number symbols are Hindu characters. Binary system is of recent origin and extremely important in cybernetics. It needs only a sequence of two digits, 0 and 1, to represent numbers of any size.

Mathematicians differentiate natural numbers (whole positive integers) from cardinal numbers through the notions of “order”, “sense” and “power”. We may interpret the number 5 in the cardinal or quantitative sense as the number which represents the size of the power of a definite set of objects with 5 members. Thus, the number 5 may be both “natural’ and “cardinal”. The main categories of natural numbers are: one-many, even and odd.

Words:

1. to belong (to) – принадлежать (кому-л., чему-л.)

2. to acquire – приобретать

3. property – собственность

4. to count – считать

5. to represent – представлять

6. milestone – этап, рубеж, веха

7. to show – показывать

8. ancient – древний

9. base – основа

10. sexagesimal system – шестидесятиричная система

11. still – всё ещё

12. to calculate – вычислять

calcula tion – вычисление

13. to express – выражать

14. any – любой

15. unit – единица

16. ten – десяток

17. hundred – сотня

18. capital letter – заглавная буква

19. to mix – смешивать

20. together – вместе

21. to employ = to use – использовать, применять

22. to produce – производить, представлять

23. numeral – цифра

24. place value – вес разряда (в позиционной системе счисления)

25. decimal – десятичный

26. digit – цифра

27. present-day – современный, нынешний

28. character – письменный знак

29. binary system – двоичная система счисления

30. recent – недавний, современный

31. origin – происхождение

32. extremely – очень, чрезвычайно

33. to need – нуждаться, быть необходимым, требоваться

34. sequence – последовательность

35. to differentiate – различать

36. notion – понятие

37. sense – смысл

38. power – множество

39. quantity – количество

quantita tive = cardinal – количественный

40. definite – определённый

41. set – набор

42. thus – так, таким образом

43. both … and … - как … так и …

44. main = principal – главный, основной

45. even – чётный

46. odd – нечётный

Exercises:

I. Прочитайте и переведите интернациональные слова, встречающиеся в тексте:

progress, civilization, document, positional, astronomical, to form, numeration, principle, symbol, alphabet, traditional, cybernetics, natural, positive, to interpret, category

II. Прочитайте и переведите следующие собственные наименования, встречающиеся в тексте:

Greek, Babylonian, Egyptian, Roman, Chinese, Japanese, Hindu, Arabic

III. Назовите форму Past Simple следующих глаголов:

a). to belong, to acquire, to count, to develop, to use, to form, to express, to represent, to mix, to employ, to produce, to need, to differentiate, to interpret

b). to come, to be, to know, to begin, to show

IV. Вставьте подходящие по смыслу слова:

1. People began to ………. when they acquired more property.

2. The concept of ………. is equally present in many ancient civilizations.

3. The Babylonians developed a ………… system of numeration.

4. For their …………… the ancient Egyptians used a base of ten with no more than three symbols to express any number less than 100.

5. The Romans used seven ………….. to represent numbers.

6. The ancient Greeks’ system of numeration employs ………… of their alphabet and special ………..

7. The Chinese-Japanese system of numeration is a ………… system with nine numerals and symbols for the place value.

8. In the Hindu-Arabic system of numeration there are ten ……… to express any number.

9. …………. uses only a sequence of two digits, 0 and 1, to represent numbers of any size.

10. Mathematicians differentiate …………. numbers from ………….. numbers.

V. Переведите предложения, обращая внимание на модальные глаголы:

1. Много тысяч лет назад люди могли обходиться (do without) без чисел.

2. Мы можем назвать использование счёта важным этапом в развитии цивилизации.

3. Студенты должны больше узнать об истории систем счисления.

4. Людям пришлось использовать числа, чтобы подсчитывать свою собственность.

5. Нам следует различать натуральные числа и числа, выражающие количество.

6. Вы можете интерпретировать числа как натуральные и выражающие количество.

7. Натуральные числа могут быть чётными и нечётными.

VI. Ответьте на вопросы:

1. What does the word “arithmetic” mean?

2. Why could people do without counting many thousands of years ago?

3. What made (заставило) people use numbers?

4. What civilizations is the concept of number present?

5. What system of numeration did the Babylonians develop?

6. What can you say about the early Egyptian system of numeration?

7. What did the Romans use for numbers?

8. What do you know about the ancient Greeks’ system of numeration?

9. What is he Chinese-Japanese system of numeration like?

10. What is the base for our present-day system of numeration?

11. What is binary system?

12. What are the main categories of numbers?

VII. Прочитайте текст и ответьте на вопросы:

1. How many stages of the number systems are there at present?

2. What does each stage include?

Nowadays mathematicians separate the number systems into five principal stages. Each stage has got a long history of its development. The first stage is the system of natural numbers or positive integers only. The next stage comprises positive as well as negative integers and zero. The third stage includes the rational numbers which combine integers and fractions. The forth stage comprises the real numbers that include irrational numbers such as. The last stage contains the complex numbers that include the so-called “imaginary” number as. In modern maths there are several new number systems. Of these modern systems three occupy an exceptionally significant place in maths, namely, quaternions (triplets), matrices and transfinite numbers.

Words:

1. to separate – разделять

2. stage – этап, фаза

3. to comprise = to contain – содержать

4. as well as – а также

5. complex – сложный

6. imaginary number – мнимое число

7. to occupy – занимать

8. significant – важный, значительный

9. namely – а именно

10. matrix – матрица

Дата добавления: 2015-11-04