## 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.

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## 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.
- Roads: Roads on hills and mountains are curvy.

## Facts About Curves

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

## What is Curve? - Definition Facts & Example

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

A cuboid does not have any curved sides.

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

It is a simple curve because it does not cross itself.

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

It is a simple closed curve because it does not cross itself and its ends meet to enclose space.

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

An ellipse is a closed curve because its ends join to enclose space.

### 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?

An ellipse is a closed curve, and you are standing inside its enclosed space.

## Frequently Asked Questions

**Is a polygon a curve?**

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.

**What are the types of curves you see in graphs?**

Graph curve types include the following:

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

**What is the highest or lowest part of a curve called?**

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

**What is the main difference between a curve and a straight line?**

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

**What is the difference between a simple and a non-simple curve?**

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.