# What is Curve? – Definition Facts & Example

## What Is a Curve?

A curve is a continuous and smooth flowing line without any sharp turns. One way to recognize it is that it bends and changes its direction at least once.

## What Are Curved Shapes?

A shape made of curves is called a curved shape. A curved shape can be two-dimensional, like circles, ellipses, parabolas, and arcs. Curved shapes can also be three-dimensional figures like spheres, cones, and cylinders.

## What Are Some Types of Curves?

Here are the different types of mathematical curves:

1. Upward Curve: A curve that turns in the upward direction is called an upward curve. It is also known as a concave upward or convex downward curve.

2. Downward Curve: A curve that turns in the downward direction is called a downward curve since it is curved downward. It is also known as a concave downward or convex upward curve.

3. Open Curve: An open curve does not enclose any area within itself and has two endpoints. Some of the open curves are given in the figure below:

4. Closed Curve: A closed curve has no endpoints and encloses an area (or a region). It is formed by joining the end points of an open curve together. Circles and ellipses are formed using closed curves.

5. Simple Curve: A simple curve changes direction but does not cross itself while changing direction. It can be open and closed.

6. Non-Simple Curves: A curve that crosses its own path is called a non-simple curve.

## Curves Around Us!

• Race track: The track from the figure looks like a closed curve.

Here are some interesting facts about curves:

•  A curve is made up of many small line segments joined from end to end. If you look at it very closely, you will be able to see the lines!
• The inside of a closed curve is called its interior.
• The outside of a closed curve is called its exterior.
• Open curves like parabolas and spirals are of infinite length.

## Solved Examples

1. What is a curve?

Solution: A curve is a continuous, smooth flowing line that bends or changes direction at least once.

2. Is the letter U an upward curve?

Solution: Yes, the letter U is an upward curve because it bends upwards.

3. Is an ellipse a closed or open curve?

Solution: An ellipse is a closed curve because its ends meet, and it encloses space within it.

4. Is the shape of the number 8 a simple or non-simple curve?

Solution: It is a non-simple curve because it crosses its own path.

5. Your friends are playing inside a closed, circular field, and you are standing outside the field’s boundary. Who is in the interior of the curved playground boundary? Solution: The friends are in the interior because they are inside the closed curve that is the playground boundary.

## Practice Problems

1

### Which of the following is not a curved shape?

Cone
Cylinder
Cuboid
Sphere
CorrectIncorrect
A cuboid does not have any curved sides.
2

### Which of the following types of curves is the letter C?

Closed
Simple
Upward
Non-simple
CorrectIncorrect
It is a simple curve because it does not cross itself.
3

### Which of the following types of curves is the shape of figure zero?

Non-simple
Open upward
Simple open
Simple closed
CorrectIncorrect
It is a simple closed curve because it does not cross itself and its ends meet to enclose space.
4

### Which of the following is a closed curve?

Parabola
Hyperbola
Ellipse
Arc
CorrectIncorrect
An ellipse is a closed curve because its ends join to enclose space.
5

### You are standing in a sports field that has a boundary shape of an ellipse. Your friend is standing beyond the boundary of the field. Which of the following is correct?

You are on the exterior of the curved boundary
You and your friend are both on the exterior of the curved boundary
You are on the interior of the curved boundary
There is no interior and exterior since the shape is an ellipse
CorrectIncorrect
Correct answer is: You are on the interior of the curved boundary
An ellipse is a closed curve, and you are standing inside its enclosed space.

No. A curve is made up of curved lines and may or may not be closed whereas a polygon is a closed figure made up of straight lines.

Graph curve types include the following:

• Parabola graph
• Hyperbola graph
• Downward curve graph
• Upward curve graph
• Circle graph
• Ellipse graph

The point where a curve is the highest or lowest is called a vertex.

While a regular straight line runs continuously in a linear direction, a curve can turn upwards, downwards, inwards, or outwards.

Both simple and non-simple curves can be open or closed but a simple curve does not cross itself whereas a non-simple curve crosses its own path at least once.

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## Conclusion

A curve is not just a line but can also make up a shape or a three-dimensional figure. It’s helpful to know the different types of curves.

Apart from the geometry of curves, the curve shape is also used in graphs.