Curved Line

A curved line is one that bends instead of straightening. It should be smooth and continuous in the ideal situation. A curve is a group of points that resemble a straight line and fall between two points, to put it another way. As we all know, the curvature of a straight line is zero. 

Curves piqued people’s interest long before they were studied mathematically. This may be observed in a variety of prehistoric examples of their decorative application in art and on everyday goods. Curves, or at least their graphical representations, are easy to make with a stick in the sand on a beach, for example.

The term line was once used instead of the more contemporary term curve. To distinguish what is now known as lines from curved lines, the phrases straight line and right line were coined. A line, for example, is described as a “breadthless length” in Book I of Euclid’s Elements, whereas a straight line is defined as “a line that lies evenly with the points on itself”. Later commentators categorized lines using a variety of techniques. As an example:

• Lines that are composite (lines forming an angle)
• Lines that are incompatible
• Decisiveness (lines that do not extend indefinitely, such as the circle)
• Indefinitely (lines that extend indefinitely, such as the straight line and the parabola)

Other types of curves had been investigated by the Greek geometers. One motive was their desire to solve geometrical difficulties that could not be handled using a traditional compass and straightedge. Some times of curves are as follows:

• Apollonius of Perga investigated the conic sections in depth
• Diocles’ cissoid, which he investigated and employed as a means to double the cube.
• Nicomedes’ conchoid, which he investigated as a way for doubling the cube and trisecting an angle.
• Archimedes researched the Archimedean spiral as a way to trisect an angle and square a circle.
• Apollonius had researched the specific sections, which were portions of tori studied by Perseus as sections of cones.

Examples of Curved Lines

Curved lines can be found in various places, such as the letters C and S in the alphabet. The letters A, M, N, L, and so on, on the other hand, are not examples of curves because they can be constructed by combining line segments (or straight lines).

Point

In geometry, a point is the most basic figure. It is a point in space that has no dimensions. It has no length, width, thickness, or depth. However, if you have two points and link every point between them, you’ll get a straight line.

Let us understand the Difference Between a Straight and a Curved Line,

A Straight Line 

The shortest path between any two points is a straight line, which always proceeds in the same direction. A straight line is defined as the set of all points connecting and extending beyond two points. A line is a primitive object in most geometries that has no formal qualities other than its single dimension, length.

Curved Line

A curved line is a bent, non-straight line that does not follow a straight path. Various Types of Curved Lines:

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

1. Simple Curve
2. Non-simple Curve
3. Algebraic Curve
4. Transcendental Curve

Let us discuss about each category in detail:

1. Simple Curve

A simple curve is a straight line that does not cut itself.  A closed curve does not have two endpoints, but an open curve does. A closed curve is a path that can start at any point and end at the same place. 

1. Non-simple Curve

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

1. Algebraic Curve

Algebraic Curve is a plane curve with a set of points on the Euclidean plane that are represented in terms of polynomials. 

C = {(a, b) ∈ R2: P(a, b) = 0}

1. Transcendental Curve

A curve that does not represent the algebraic form is called a transcendental curve. This curve could include a lot of intersecting points in addition to the straight line. Thus , a polynomial based on a and b is not a transcendental curve.