I. Read and decide which of the statements are true and which are false. Change the sentences so they are true.

1. A curve can be considered as the path of a moving point.

2. There're two types of curves: algebraic curves and transcendental curves.

3. Open curves have no end points and closed curves have a lot of end points.

4. A curve that does not lie in a plane is a skew or twisted curve.

5. A curvature is the rate of change of direction of a curve at a particular point on that curve.

6. The angle δψ through which the tangent to a curve moves as the point of contact moves along an arc PQ is the total curvature of this arc.

7. We define the mean curvature of any arc taking into account both the total curvature and the arc length.

8. At any point on a surface the curvature doesn't vary with direction.

II. Match the terms from the left column and definitions

from the right column:

curvature	a) any straight line extending from the center to the periphery of a circle or sphere, b) the length of such a line
graph	the rate of deviation of a curve or curved surface from a straight line or plane surface tangent to it
arc	a curve or surface showing the values of a function
radius	any part of a curve, esp. of a circle

III. Read the sentences and think of a word which best fits each space.

a)1. The Egyptians were mostly concerned with applying … to their everyday problems.

2. In 300 B.C. all the known facts about Greek geometry were put into a logical sequence by … .

3. Today geometry includes not only the study of the … and … of the earth and all things on it, but also the study of relations between geometric … .

4. The most fundamental idea in the study of geometry is the idea of a … .

5. You cannot see a … , feel a … , or move a … , because it has no dimensions.

For ideas: shape, point (4), size, geometry, Euclid, object.

b)1. ... are generally studied as graphs of equations using a coordinate systems.

2. Only ... curves (or arcs) have end points.

3. A curve that does entirely in a plane is a ... curve.

4. A curve that does not lie in ... is a skew or twisted curve.

5. The rate of change of direction of a curve at a particular point on that curve is called a ...

6. The angle δψ through which the tangent to a curve moves as the point of contact moves along any arc is the ... of this arc.

7. The ... of any arc is defined as the total curvature divided by the arc length.

8. The circle of curvature at any point on a curve is the circle that is ... to the curve at that point.

9. There are two ... in which the radius of curvature has an absolute maximum and absolute minimum.

10. The principal curvatures at the point are the curvatures in two ... di­rections.

TEXT II.

ANGLES

An angle is a configurationof two lines (the sides or arms) meeting at a point (the vertex).Often an angle is regarded as the measure of rotationin­volved in moving from one initial axisto coincide with another final axis (termed a directions angle). If the amount and sense of the rotation are speci­fied the angle is a rotation angle, and is positive if measured in an anticlock­wisesense and negative if in a clockwisesense.

Angles are classified according to their measure:

- Null(or zero) angle- zero rotation (0°).

- Right angle- a quarter of a complete turn (90°)

- Flat (or straight) angle- half a complete turn (180°).

- Round angle(or perigon) - one complete turn (360°),

- Acute angle- between 0° and 90°.

- Obtuse angle- between 90° and 180°.

- Reflex angle-between 180°and 360°.

- The angle of elevationof a point A from another point В is the angle between the line AB and the horizontal plane through B, with A lying above the plane. The angle of depressionis similarly defined with A lying below the plane. The angle at point В made by lines AB and CB is denoted by ÐABC.

I. Read and decide which of the statements are true and which are false.

Change the sentences so they are true.

1. An angle is often regarded as the measure of rotation involved in moving from one initial axis to coincide with another final axis.

2. There’re eleven types of angles in their classification according to their measure.

3. 90° - it is the measure of an acute angle.

4. An angle is positive if it is measured in a clockwise sense.

5. The measure of a reflex angle is between 180°and360°.

6. The main difference of an angle of elevation of a points and its angle of depression is the following one: in the case of the angle of elevation the point A lies above the plane and in the case of the angle of depression - below the plane.