What is Curve in Maths?

Geometry is a study of shapes. It is broadly classified into two types: plane geometry and solid geometry. Plane geometry deals with one dimensional and two-dimensional figures like curves, lines, polygons, square, circle, rectangle, triangle and many more. Whereas Solid geometry deals with the study of three- dimensional shapes like cube, cuboid, cylinder, cone, sphere, and many more.

Here in this article we will be studying plain geometry concepts: what is curve in maths, polygonal curve, angles and polygons.

A curve is a line which is not straight; it bends and changes its direction at least once.

A curve is a continuous and smooth flowing line that you can draw on a paper without using a ruler, without any sharp turns. Curves bends and changes their direction at least once.

Examples of Curves Around us

A race track is an example of a curve.

Roads on hills and mountains are curvy.

Different Types of the Curve are as Follows:

1. Upward Curve: A curve that faces in the upward direction is called an upward curve. It is also known as a concave upward. Concave Upward also called or “Convex Downward”

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2. Downward Curve: A curve that faces in the downward direction is called a downward curve. It is also known as a concave downward. Concave Downward also called or “Convex Upward”.

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3. Open Curve Shape: An open curve shape is a curve with two different end points which does not enclose any area within itself. Examples of some of the open curve shape are given in the figure below.

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4. Closed Curve: A closed curve is a curve whose endpoints meet each other i.e. it has no end points and encloses an area (or a region).In other words a closed curve is formed by joining the end points of an open curve together. A closed curve can form a well defined geometric shape. For example circles , ellipses are formed from closed curves. Below figure displays some of the shapes that have curves, closed curves.

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5. Simple Curve: A simple curve is a curve that changes direction but does not intersects itself at any point while changing direction. A simple curve can be an open curve and closed curve.

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6. Non-simple Curves: A curve that crosses its own path while changing the direction is called a non-simple curve.

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Angle

The intersection of two lines having a common vertex form an angle. Parts of an angle are described as vertex, arms, interior, and exterior of angles. When two lines intersect at a point they form four angles at the point of intersection. An angle is denoted by the symbol ∠.

From the figure, ∠ ABC is an angle. B is the point of intersection of the two arms AB and BC called the vertex and AB and BC are the sides of the angle. Angles are commonly measured in terms of degree.

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Angles are Classified According to their Sizes as Follows

Acute Angle

The measure between the two arms is less than 900 then an acute angle is formed.

Obtuse Angle

When the measure between the two arms is above 900 it forms an obtuse angle.

Right Angle

When the two arms make an angle of 900 it forms a right angle.

Reflex Angle

When the two arms of an angle, makes an angle more than 1800 and less than 3600 it is called a reflex angle.

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Polygon

A polygon is a simple closed curve. A polygon is a polygonal curve that is the union of three or more line segments whose endpoints meet. A two-dimensional closed figure bounded with three or more than three straight lines is called a polygon. Triangles, square, rectangle, pentagon, hexagon, are some examples of polygons.

The segments are referred to as the sides of the polygon. The points at which the segments meet are called vertices. Segments that share a vertex are called adjacent sides. A segment whose endpoints are nonadjacent vertices is called a diagonal.See the picture below.

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The below figures show some of the examples of polygons or polygonal curves( a closed curve that is not a polygon).

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In figure 1 you can see that all the shapes are polygons, as all the shapes are drawn joining the straight lines only. There are no curved lines. Even the shape in orange color is a polygon because it is formed by joining straight lines and it is a closed figure.

But in figure 2 the shape is not a polygon because it is not fully connected and also has curved lines and such shapes that have curves are called a closed curve that is not a polygon.Circle is the best example of a closed curve that is not a polygon.

The name of the polygon itself implies the number of segments in it. For instance, the triangle is a polygon having three sides, a quadrilateral is a polygon having four sides, etc.

Based on the polygon sides and angles polygons are classified into different types of polygons.

Types of Polygons

Different types of polygons are

Regular Polygon

Irregular Polygon

Convex Polygon

Concave polygon

Solved Examples

1. Identify the type of curves

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Answer:A closed curve that is not a polygon.

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Answer: A open curve shape

FAQ (Frequently Asked Questions)

1. Is Straight Line a Curve?

Answer: No. A curve is not a straight line, at the same time as a straight line is not a curve. A curved line includes points that are not linear to two given points. Further, the curve moves in other directions from the straight line which forms by joining collinear points.

2. Is Polygon a Curve?

Answer: Yes, a polygon is one type of simple closed curve. A polygon is the union of three or more line segments whose endpoints meet. The segments are referred to as the sides of the polygon.