In this post we will understand the fundamental definition of curve and different types of curves possible in the real world. Apart from the theory we will also observe the real life examples of curves found in our surroundings.
What is a curve?
A curve is a continuous and smooth flowing line without any sharp turns.
A line is something which is straight but the curve do not have any fixed shape. Do one thing, take a pencil and draw something freely without any sharp edges, that drawing is one form of curve.
Properties of a curve
a. It does not have sharp edges
The curve do not have any sharp edges, the bends are more like circular in shape
b. The curve is not straight line
It just moves freely without any effort. Imagine the movement of snake, the body of snake do not move in a straight line, it moves in a curvy motion.
c. The curves in its representation bends
The curve have at least one bends in its structure. As the curve is non linear figure, you will find atleast one bend in the curve which is not sharp
From the above illustration you can see that the line which is straight and not bend is not a curve. In the next figure you can see a line changing its direction and in process bent slightly, it is the curve.
Some more examples of curves are
you can see the above examples, all are forms of curve
The first figure A is more like a circular path with no fixed direction
The other two figures B & C are basically number 3 and 8 are also form of the curve since they have no sharp edges
Types of Curves
There are mainly 6 different types of curves
a. Upward Curve
b. Downward curve
c. Open curve
d. Closed Curve
e. Simple curve
f. Non Simple Curve
1. Open Curve
A curve whose beginning and end point is different is open curve.
It means that the curve do not form any closed boundary
You can see the above figures A & B
Both are representation of open curves with different beginning and end point, this means that these curves do not form an enclosed area for themselves.
The curve which have no beginning and end point, or whose beginning and end point is the same is known as closed curves. As the curves are closed, they form an enclosed shape whose area can be calculated
You can see from the above two figures that these curves are closed and have no fixed beginning and end points.
Also, all the open curve can be converted into close curves if we join both beginning and end points
Some of the popular figures like circle, eclipse are also examples of closed curves
you can easily calculate the area of circle and ellipse of the closed curve with the help of predefined formula which ou will study in higher classes.
Note – In a closed curve, there are 3 parts –
- Interior (inside) of the curve
- Exterior (outside) of the curve
- Boundary (on) of the curve
A curve that does not crosses its own path is called simple curve.
A simple curve can be open and closed both.
In the above figure, you can see both open and closed curve.
The above curves are simple because they are not crossing their path twice
A curve that crosses its own path is called non-simple curve
From the above figure you can see that the curve is crossing its own path twice at point A and B, these points are also called point of intersection
Note – Non-simple can also be open or closed
The first figure is open curve because it has different start and end point, and it is non simple because it is crossing is own path. The other figure is simply closed curve as it has no start and end point.
A curve that turns in the upward direction is called an upward curve. It is also known as “Concave upward” or “Convex downward”
A curve that turns in the downward direction is called a downward curve. It is also known as “Concave downward” or “Convex upward
Some Real Life Examples of Curves
the logo of MC Donald is an example of downward open curve.
The curve is open as it have distinct beginning and end point, and the curve is downward because it is moving towards downward direction
Railway track is basically a mixture of line and curve.
Most of the part the railway tracks are straight line but when change in direction is required the tracks get curvy shape.
Shapes which are formed by curves
2-Dimensional shapes – Circles, ellipses, parabola, hyperbola, arcs, sectors and segments are examples of 2-dimesional curve shapes.
3-Dimensional shapes – Spheres, Cylinders and cones are the examples of 3-dimensional curve shapes.
Application of curves – In higher classes, questions will be there like finding the area enclosed by the curve using graphs.