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Skip to content Menu Menu * Parents * Educators * Teacher * Administrator * Teacher How To’s * Support * Learning App * How it works * All Games * Math Games * ELA Games * All Worksheets * Math Worksheets * ELA Worksheets * Log in * Sign Up WHAT IS CURVE? – DEFINITION FACTS & EXAMPLE Home » What is Curve? – Definition Facts & Example * What Is a Curve? * What Are Curved Shapes? * Curves Around Us! * Solved Examples * Practice Problems * Frequently Asked Questions 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. RECOMMENDED GAMES: Identify Curved Surface Game Identify Curved Surface Game Play 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 Attend this quiz & Test your knowledge. 1 WHICH OF THE FOLLOWING IS NOT A CURVED SHAPE? Cone Cylinder Cuboid Sphere CorrectIncorrect Correct answer is: Cuboid 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 Correct answer is: Simple 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 Correct answer is: Simple closed 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 Correct answer is: Ellipse 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. 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. Related Articles: * Parallelogram * Geometry 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. 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