Class 6 Maths Basic Geometrical Ideas Curves

Curves

Curve can be defined as the continuous movement of points in any and every direction. It means that all possible shapes can be classified as curves because all the shapes are formed by the movement of the points in single or multi dimension.

Regarding the above definition, is straight line a curve?

In general life, no straight line is not a curve. We define curve as an entity that is not straight.

In mathematics, even a straight line is a curve. We define curve as the movement of points.

Example of curves:

Types of Curve:

  • Simple Curve: The curve which does not cross itself. From the above, image (ii), (iii), (vi) and (vii) are simple curves as they do not cross themselves.
  • Not Simple Curve: The curve which does not cross itself. From the above, image (i), (iv) and (v) are not simple curves as they cross themselves.
  • Open Curve: The curve which does not form a closed path. From the above, image (iii), (vi) and (vii) are the open curves.
  • Closed Curve: The curve which form a closed path. From the above, image (i), (ii), (iv) and (v) are the closed curve.

Position in a closed curve:

Referring to the above image, it represents a circular cricket ground (i.e. a closed curve). In a closed curve, there are three position.

  • Interior or inside of the curve.
  • Boundary or on the curve.
  • Exterior or outside the curve.

A batsman playing shots while a cricket match, he can hit three types of lofted shots in that ground, six outside the field (i.e. exterior of the curve – shown by a white line), lofted shot inside the field (i.e. interior of the curve – shown by red line) or six on the boundary ropes (i.e. on the curve – shown by green line).

Question: Draw a diagram to illustrate the following: Open Curve, Closed Curve

Solution:

Open Curve:

Closed Curve:

 

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