[Maths Class Notes] on Curved Lines Pdf for Exam

A curved line is defined as a line that is not straight but is bent. Ideally, a straight line holds a zero curvature, whereas a curved line has a non-zero curvature and is continuous and smooth. Curves are prominent figures found everywhere around us. You can spot curves in an art or a decoration or a general thing, and curves are figures that can be seen everywhere around you. Initially, lines could be curved or straight. In today’s mathematical usage, for a precise distinction, a curve is something that is bent, whereas a line is something that is straight.

 

Curved Lines are frequently used in the graphical representation of functions as it is one of the vital topics in the field of Mathematics.

 

Differentiate Between Curved Lines And Straight Lines

 

Examples of Curved Lines

There are numerous curved line examples. The most common and prominent example of curved lines is the Alphabets- C and S. These letters of the alphabet are bent. In contrast, other letters like L, N, A, Z, and others are suitable examples of straight lines since they are neither curves but are joined segments of two or more consecutive lines.

 

Types of Curved Lines

There are numerous and different types of curved lines. However, a few prominent types of curved line are-

1. Open Curve

A curved line or a curve is said to be open if the endpoints do not meet. In an open, curved line, the endpoints never meet.

 

A Parabola is a perfect example of an open curve line.

 

2. Closed Curve

A curve is stated to be closed if its starting point is the same as its ending point.

 

A circle or an eclipse is a perfect example of a closed curve line.

 

3. Simple Curve

A simple curve does not intersect itself. Some curves are self-intersecting; however, a simple curve line does not self-intersect.

 

4. Algebraic Curve

An algebraic curve is a plane curve where a set of points are placed on the Euclidean plane and are represented in terms of polynomials. The degree of a curve is denoted by the polynomial’s degree.

 

For example- C = {(a, b) ∈ R2: P(a, b) = 0}

 

5. Transcendental Curve

A Transcendental Curve is different in its features from that of an Algebraic curve. A transcendental curve comprises an infinite number of inflexion points and multiple intersecting points which will be straight. It is not a polynomial in a and b points.

 

6. Isoquant Curve

The term Isoquant is an amalgamation of two terms- ‘Iso’ implies equal, and the word ‘quant’ refers to the quantity. Thus, the term isoquant is defined as a convex-shaped curve formed by the joining of the points. The isoquant curve helps organisations and businesses in adjusting inputs in order to maximise production and profits.

Curved Line

A “Curved line,” or simply a “Curve,” is a non-straight line. Curves can be found everywhere around us. Curves can be found all around us, whether in art, décor, or everyday life. In this post, we will study the concept of a curved line, as well as the various types of curved lines and several instances.

What is the Definition of a Curved Line?

A curved line is one that is bent rather than straight. It should be smooth and continuous in the ideal situation. To put it another way, a curve is a collection of points that resemble a straight line and fall between two points. The curvature of a straight line is zero, as we know. As a result, we can label a line curved if its curvature is greater than zero. The various sorts of curved lines are depicted in the diagram below.

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What Makes a Straight Line Different from a Curved Line?

A Straight Line 

Curved Line 

Curved Lines of Various Types

Curved lines can be divided into several categories. They are as follows:

A simple curve is one that does not cross over itself. We know that an open curve has two endpoints and that a closed curve does not. A closed curve is a path that can start at any point and end at the same place. As a result, the basic curve can be either open or closed.

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A non-simple curve is one that intersects with itself while changing direction. Non-simple curves can be open or closed, much like simple curves.

Algebraic Curve is a plane curve with a set of points on the Euclidean plane that are expressed in terms of polynomials. The degree of the polynomial denotes the curve’s degree.

C = {(a, b) ∈ R2: P(a, b) = 0}

This curve isn’t the same as the algebraic curve. A transcendental curve is defined as a curve that does not represent the algebraic form. Along with the straight line, this curve could have a lot of intersecting points. As a result, a polynomial based on a and b is not a transcendental curve.