II. Read the article and mark the sentences T (TRUE), F (FALSE) or NG (NOT GIVEN).

1. Elementary mathematics has been studied by young boys and girls since ancient time.

2. Arithmetic and geometry were the part of classical education that was developed in medieval Europe due to the needs of masons, merchants and money-lenders.

3. The first mathematics textbooks in English were printed in the fifteenth century.

4. In the Renaissance mathematics was treated as a subsidiary subject to study Natural, Metaphysical and Moral Philosophy.

5. In the 17th century mathematics was normally taught in universities.

6. Newton was taught formal mathematics at school.

7. In all developing countries regular mathematics teaching was not provided by educational institutions in the twentieth century.

8. The International Congress on Mathematical Education has been held every four years since 1969.

9. Only in the 21st century mathematics was recognized as an independent area of research.

10. In the 20th century small children were able to deal with number theory and set theory.


    The following people all taught mathematics at some stage in their lives, although they are better known for other things:

- Lewis Carroll, pen name of British author Charles Dodgson, lectured on mathematics at Christ Church, Oxford

- John Dalton, British chemist and physicist, taught mathematics at schools and colleges in Manchester, Oxford and York

- Tom Lehrer, American songwriter and satirist, taught mathematics at Harvard, MIT and currently at University of California, Santa Cruz

- Brian May, rock guitarist and composer, worked briefly as a mathematics teacher before joining a famous band ‘Queen‘

- Georg Joachim Rheticus, Austrian cartographer and disciple of Copernicus, taught mathematics at the University of Wittenberg

- Edmund Rich, Archbishop of Canterbury in the 13th century, lectured on mathematics at the universities of Oxford and Paris

- Éamon de Valera, a leader of Ireland’s struggle for independence in the early 20th century and founder of the Fianna Fáil party, taught mathematics at schools and colleges in Dublin

- Archie Williams, American athlete and Olympic gold medalist, taught mathematics at high schools in California


III. Search for some information about one of these mathematics teachers and share it with other students. Make a table of the most important facts of his/her biography.


Date      |    Event




Text 2

Reading and Speaking


    Our chief sources of information concerning ancient Egyptian geometry are the Moscow and Rhindpapyri. A Scottish scholar and antiquary, A. M. Rhind discovered in 1858 in Egypt and bought an ancient Egyptian papyrus found in some ruins in Thebes. 1 __________. The papyrus is a copy of 1650 B.C. of much earlier writings of the latter part of the 1900 B.C. The entire work emphasizes the two concepts that particularly characterize the Maths of the early Egyptians: the consistent use of additive procedures and computations with fractions. Most of problems are of practical nature. 2 __________.

    The Moscow papyrus also referred to as the Golenishchev papyrus for the man who owned it before its acquisition by the Moscow Museum of Fine Arts, was probably written about 1850 B.C. 3 __________. This work shows that the Egyptians were familiar with the formula for the area of a hemisphere and the correct formula for the volume of a truncated square pyramid: . 4 __________.There are various conjectures about how the Egyptians could develop this procedure, but the papyrus offers no help. This formula is often referred to as the Egyptians ‘greatest pyramid’ Of the 110 problems in the papyri 26 concern the computation of land areas and volumes. The ancient Egyptians recorded their work on stone and papyrus resisting the ages because of Egypt’s dry climate. There is no documentary evidence that the ancient Egyptians were aware of the ‘Pythagorean theorem’. 5 __________. Egyptian geometry arose from the necessity. The annual inundation of the Nile Valley forced the Egyptians to develop some systems for re-determining land markings; in fact, the word ‘surveying’ means ‘measurement of the earth’. The Babylonians likewise faced an urgent need for Maths in the construction of the great engineering structures (marsh drainage, irrigation and flood control) for which they were famous. Similar undertakings and geometrical accomplishments occurred in India and China. 6 __________.

    In spite of the empirical nature of ancient oriental geometry, with its complete neglect of proof and the lack of difference between exact and approximate truth, mathematicians are nevertheless struck by the extent and the diversity of the problems so successfully attacked. 7 __________.

I. Match the words (1–7) with their definitions/explanations (a–g):

1 chief a someone who studies, collects or sells old books or other historical objects
2 scholar b smth that you have obtained by buying it or being given it
3 antiquary c most important, main
4 acquisition d an intelligent and well - educated person
5 to be familiar with e to have a good knowledge or understanding of smth
6 evidence f the fact of including many different types of things
7 diversity g facts or signs that show clearly that smth exists or is true

    II. Choose from (A–J) the one which best fits each of (1–7). There are two choices you do not need to use.

    A. Some problems may present a challenge even to modern students; e.g. ‘Find the volume of a cylindrical granary of diameter 9 and height 10 cubits.’

    B. One ought not to underestimate the contributions of these ancient civilizations to the development of geometry.

    C. The ancient Indians and Chinese, however, used very perishable writing materials (bark bast and bamboo) and due to the lack of primary sources we know nothing about Mathematics in ancient India and China.

    D. Babylonian Maths refers to any Maths of the people of Mesopotamia from the days of the early Sumerians until the beginning of the Hellenistic period.

    E. The Rhind papyrus is a collection of arithmetical, geometrical and miscellaneous problems, including some area and volume applications.

    F. Nevertheless, early Egyptians surveyors realized that a triangle with sides of lengths 3, 4 and 5 units is a right triangle.

    G. The solution is expressed only in terms of the necessary computational steps for the given numerical values: height of 6 and the bases of sides 4 and 2.

    I. Babylonian Mathematics merged with Greek and Egyptian Maths to give rise to Hellenistic Mathematics.

    J. Although it contains only 25 problems, it is similar to the Rhind papyrus.


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