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Curved Line

A “Curved line” or simply a ” Curve” is a line that is not straight. We see curves everywhere around us. Be it art or decoration or a general thing, and curves can be seen around us. In this article, we are going to learn the definition of a curved line, different types of curved lines with many examples.

What is a Curved Line?

A curved line is one that is not straight and is bent. Ideally, it is smooth and continuous. In other words, a curve is defined as a group of points that resemble a straight line that falls between two neighbouring points. We know that the curvature of the straight line is zero. Hence, if the curvature of a line is not zero, then we can call it a curved line. The following figure shows the different types of curved lines.

curved lines

Difference Between Straight and Curved Line

Straight Line Curved Line
A straight line is the shortest line that joins any two points.

It always moves in one direction.

A bent line that is not straight is called a Curved Line.

It doesn’t move in one direction.

Examples of Curved Lines

There are many examples of curved lines like the alphabets – C and S. Whereas the letters A, M, N, L, etc are not examples of curves since they can be formed by joining the line segments (or straight lines).

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Different Types of Curved Lines

The curved lines can be classified into different types. They are:

  • Simple Curve
  • Non-simple Curve
  • Algebraic Curve
  • Transcendental Curve

Simple Curve

A simple curve is defined as a curve that doesn’t cross itself.  We know that the open curve has two endpoints whereas a closed curve has no endpoints. A closed curve creates a path that may begin from any point and terminate at the same point. Thus, the simple curve may be open or closed.

Example of Curved Line

 

Non-simple Curve

The non-simple curve is a type of curve that intersects with itself while changing its direction. Like simple curves, the non-simple curves can also be open or closed.

Algebraic Curve

A plane curve where a set of points are located on the Euclidean plane and are represented in terms of polynomials is called Algebraic Curve. The polynomial’s degree denotes the degree of the curve.

C = {(a, b) ∈ R2: P(a, b) = 0}

Transcendental Curve

This curve is different from the algebraic curve. The curve that does not represent the algebraic form, then it is called a transcendental curve. This curve might have many intersecting points together with the straight line. Hence, a transcendental curve is not a polynomial based on a and b.

Practice Question

Question: Identify the open and closed curves from the below figure.

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Frequently Asked Questions on Curved Line

What is a curved line?

A curved line is a type of straight line with bent. In other words, it is a geometrical object similar to the line having curvature.

What are the examples of curved lines?

There are many examples of curved lines in the English alphabet such as C, S and O.

Why we use curved lines?

Curved lines are used mainly in the graphical representation of different types of functions.

What are the types of curves?

There are two types of curves namely simple open curves and simple closed curves. For example, “C” is the simple open curve and “O” is the simple closed curve that we can see in alphabets.

What is a simple curve?

A curve that doesn’t cross itself is called a simple curve, otherwise, it is a complex (or non-simple) curve. For example, “U” is the simple curve and “8” is the non-simple curve.

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