Analytic Geometry (coordinate geometry, or Cartesian geometry) – is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry, which treats certain geometric notions as primitive, and uses deductive reasoning based on axioms and theorems to derive truth. Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete, and computational geometry.
Differential Geometry - a geometry that applies differential and integral calculus to curves, surfaces and other geometric entities.
Comprehension
I. Translate the following phrases into English:
Форма, размер; свойства пространства; длина, площадь, объем; задать стандарт; вычислять площадь и объем; источник геометрических задач; кривая в плоскости; проективная геометрия; обогатить предмет геометрии; испытать радикальные преобразования; планиметрия; многоугольник; определить величину угла и длину стороны треугольника; подход; дедуктивное рассуждение; геометрические понятия; получать (выводить) истину; применить дифференциальное и интегральное исчисление к геометрическим объектам.
II. Complete the sentences:
1) The word “geometry” came from the ancient Greek phrase meaning “m___________ of the earth”.
2) Geometry arose as a body of practical knowledge concerning l_______, a_______, and v_______.
3) The introduction of c________ by René Descartes in the 17th century and the concurrent developments of algebra marked a new stage for geometry.
4) P______ geometry studies the properties of plane figures or geometrical shapes of two dimensions, such as t______, a______, s______, polygons, conic sections.
5) The examples of geometrical shapes of three dimensions include p______, s________, c________, p______.
6) Synthetic a_________ of Euclidean geometry treats certain geometric notions as primitive, and uses deductive r_______ based on axioms and theorems to d__________ truth.
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