I. Найдите в тексте интернациональные слова, переведите их.
II. Выберите в колонке В эквиваленты к словам колонки А.
| A
1. application
2. equation
3. curved lines
4. surface
5. polyhedron
6. icosahedron
7. linear
8. differential
9. cube
10. circle
11. integral
| B
a) окружность
b) цельный
c) возводить в куб
d) линейный
f) многогранник
e) дифференциал
g) двадцатигранник
h) поверхность
i) кривая линия
j) уравнение
k) применение
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III. Заполните пропуски подходящими по смыслу словами.
1. The same special problem finds… in the most diverse and unrelated branches of mathematics.
a) duplication b) calculation
c) equations d) application
2. The students know the theory of … and the theory of equation.
a) curved lines surfaces b) polyhedra, curved lines
c) icosahedron, surfaces d) linear differential equations
3. The rules of … with natural numbers were discovered in this fashion.
a) cube b) squaring of the circle
c) calculation d) duplication
4. The oldest problems in the theory of curves and the differential and... calculus belong to mechanics astronomy and physics.
a) integral b) linear
c) squaring d) cube
Text III
But it often happens also that the same special problem finds application in the most diverse and unrelated branches of mathematics. So for example, the problem of the shortest line plays a chief and historically important part in the foundations of Geometry, in the theory of curved lines and surfaces, in mechanics and in the calculus of variations. And F. Klein convincingly pictured, in his work on the icosahedron, the significance which is attached to the problem of the regular polyhedra in elementary Geometry, in group theory, in the theory of equations and in the theory of linear differential equations.
After referring to the general importance of problems in mathematics, let us return to the question from what sources this science derives its problems. Surely, the first and oldest problems in every field of mathematics spring from experience and are suggested by the world of external phenomena. Even the rules of calculation with natural numbers were discovered in this fashion in a lower stage of human civilization, just as the child of today learns the application of these laws by empirical methods. The same is true of the first unsolved problems of antiquity, such as the duplication of the cube, the squaring of the circle. Also the oldest problems in the theory of the solution of numerical equations, in the theory of curves and the differential and integral calculus, in the calculus of variations, the theory of Fourier series and the theory of potential to say nothing of the abundance of problems properly belonging to mechanics, astronomy and physics.
But, in the further development of the special domain of mathematics, the human mind, encouraged by the success of its solutions become convinced of: its independence. It evolves from itself alone, often without appreciable influence from outside by means of logical combination, generalization, specialization, by separating and collecting ideas in elegant ways, by new and fruitful problems and the mind appears then as the real questioner and the source of the new problems. Thus arose the problem of prime numbers and the other unsolved problems of number theory, Galois' theory of equations, the theory of algebraic invariants, the theory of abelian and automorphic functions; indeed, almost all the nicer problems of modern arithmetic and function theory arose in this way.
IV. Выберите правильный ответ на вопрос в соответствии с содержанием текста.
1. In what branches of mathematics can the same special problem find application?
a) in the related branches.
b) in the most diverse and unrelated branches of mathematics.
c) in the connected branches of mathematics.
d) in the different branches of mathematics.
2. What problem plays a chief and historically important part in the foundations of Geometry?
a) the problem of the shortest line.
b) the problem of the longest line.
c) the problem of Three Bodies.
d) “the problem of quickest descent”.
3. Where do the first and oldest problems in every field of mathematics spring from?
a) the nature b) experience
c) the human mind d) the external phenomena
4. What happens with the human mind, encouraged by the success of its solution?
a) it becomes unconvinced of its independence.
b) It becomes convinced of its independence.
c) It becomes sure in itself.
d) It becomes clear.
V. Выберите заголовок для данного текста, в соответствии с его содержанием.
a. The sources of mathematical problems
d. The rules of calculation
c. The application of mathematical problems
d. Galois’ theory of equations
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