Arc vs. Curve — What's the Difference?
By Maham Liaqat & Fiza Rafique — Updated on March 12, 2024
An arc is a segment of a circle's circumference, defined by a central angle, whereas a curve is any smoothly flowing, continuous line or shape without sharp angles.
Difference Between Arc and Curve
Table of Contents
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Key Differences
An arc is specifically a portion of the circumference of a circle, characterized by its subtended angle and the length of the circular path between two points. Whereas, a curve represents a broader category of lines that bend or change direction without forming any angles, and can include shapes like ellipses, spirals, and parabolas.
Arcs are defined within the context of circular geometry, making them a subset of curves that have specific geometric properties, such as being the path traced by a point moving at a constant distance from a fixed point. On the other hand, curves can be described by various mathematical equations and are not restricted to the geometry of circles, allowing for greater flexibility in form and function.
The measurement of an arc is typically done in terms of its length or its subtended angle, which requires understanding of the circle's radius and the central angle. Curves, however, are often analyzed based on their curvature, tangent lines, and the rate at which they change direction, which can be determined through calculus.
Arcs play a significant role in the study of circles and circular motion, with applications in fields like engineering and astronomy where circular paths are common. Curves, due to their broader definition, find applications in numerous areas, including design, physics, and even economics, wherever smooth, continuous lines are needed.
In terms of representation, arcs are usually denoted by their endpoints and sometimes the center of the circle they belong to. Curves can be represented in various ways, including parametric equations, function graphs, or geometric shapes, providing a wide array of descriptive methods.
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Comparison Chart
Definition
A segment of a circle's circumference
Any smooth, continuous line or shape
Geometric Context
Always part of a circle
Can be part of any shape
Representation
Defined by endpoints and central angle
Defined by an equation or graphical shape
Measurement
Length or subtended angle
Curvature, tangent lines, rate of change
Applications
Circular motion, engineering, astronomy
Design, physics, economics, broader fields
Compare with Definitions
Arc
Measured by its central angle.
The pizza slice's tip creates a 45-degree arc on the pizza's edge.
Curve
Can be represented by equations.
The curve of the graph represented the data's trend.
Arc
Defined by two points on a circle and its center.
The architect used the arc between points A and B for the bridge's design.
Curve
Found in various applications.
The curve of the road was designed for safety at high speeds.
Arc
A component of circular shapes.
Each arc of the wheel contributed to its perfect roundness.
Curve
Not restricted to circular shapes.
The artist drew an intricate curve that twisted and turned.
Arc
Used in geometric calculations.
Calculating the arc's length helped in designing the round window.
Curve
Any line that smoothly bends.
The curve of the river followed the landscape's contours.
Arc
A section of a circle's edge.
The arc of the moon visible tonight forms a perfect semicircle.
Curve
Analyzed using calculus.
Understanding the curve's slope at different points required differential calculus.
Arc
Something shaped like a curve or arch
The vivid arc of a rainbow.
Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point.
Arc
(Mathematics) A segment of a circle.
Curve
A line that deviates from straightness in a smooth, continuous fashion.
Arc
An electric arc.
Curve
A surface that deviates from planarity in a smooth, continuous fashion.
Arc
(Astronomy) The apparent path of a celestial body as it rises above and falls below the horizon.
Curve
Something characterized by such a line or surface, especially a rounded line or contour of the human body.
Arc
A progression of events suggesting narrative cohesion, especially one that rises to a climax and settles to a final conclusion.
Curve
A relatively smooth bend in a road or other course.
Arc
To form an arc.
Curve
A line representing data on a graph.
Arc
To move or seem to move in a curved path
The stars that arc across the sky.
Curve
A trend derived from or as if from such a graph
"Once again, the politicians are behind the curve" (Ted Kennedy).
Arc
(astronomy) That part of a circle which a heavenly body appears to pass through as it moves above and below the horizon.
Curve
A graphic representation showing the relative performance of individuals as measured against each other, used especially as a method of grading students in which the assignment of grades is based on predetermined proportions of students.
Arc
(geometry) A continuous part of the circumference of a circle (circular arc) or of another curve.
Curve
The graph of a function on a coordinate plane.
Arc
A curve, in general. Category:en:Curves
Curve
The intersection of two surfaces in three dimensions.
Arc
A band contained within parallel curves, or something of that shape.
Curve
The graph of the solutions to any equation of two variables.
Arc
(electrics) A flow of current across an insulating medium; especially a hot, luminous discharge between either two electrodes or as lightning.
Curve
(Baseball) A curve ball.
Arc
A story arc.
Curve
(Slang) Something that is unexpected or designed to trick or deceive.
Arc
(mathematics) A continuous mapping from a real interval (typically [0, 1] ) into a space.
Curve
To move in or take the shape of a curve
The path curves around the lake.
Arc
(graph theory) A directed edge.
Curve
To cause to curve.
Arc
The three-point line.
Curve
(Baseball) To pitch (a ball) with a curve.
Arc
(film) An arclight.
Curve
To grade (students, for example) on a curve.
Arc
(ambitransitive) To move following a curved path.
Curve
(obsolete) Bent without angles; crooked; curved. Category:en:Curves
A curve line
A curve surface
Arc
(transitive) To shape into an arc; to hold in the form of an arc.
Curve
A gentle bend, such as in a road.
You should slow down when approaching a curve.
Arc
(intransitive) To form an electrical arc.
Curve
A simple figure containing no straight portions and no angles; a curved line.
She scribbled a curve on the paper.
Arc
A portion of a curved line; as, the arc of a circle or of an ellipse.
Curve
A grading system based on the scale of performance of a group used to normalize a right-skewed grade distribution (with more lower scores) into a bell curve, so that more can receive higher grades, regardless of their actual knowledge of the subject.
The teacher was nice and graded the test on a curve.
Arc
A curvature in the shape of a circular arc or an arch; as, the colored arc (the rainbow); the arc of Hadley's quadrant.
Curve
(analytic geometry) A continuous map from a one-dimensional space to a multidimensional space.
Arc
An arch.
Statues and trophies, and triumphal arcs.
Curve
(geometry) A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.
Arc
The apparent arc described, above or below the horizon, by the sun or other celestial body. The diurnal arc is described during the daytime, the nocturnal arc during the night.
Curve
(algebraic geometry) An algebraic curve; a polynomial relation of the planar coordinates.
Arc
To form a voltaic arc, as an electrical current in a broken or disconnected circuit.
Curve
(topology) A one-dimensional continuum.
Arc
Electrical conduction through a gas in an applied electric field
Curve
The attractive shape of a woman's body.
Arc
A continuous portion of a circle
Curve
(transitive) To bend; to crook.
To curve a line
To curve a pipe
Arc
Something curved in shape
Curve
(transitive) To cause to swerve from a straight course.
To curve a ball in pitching it
Arc
Form an arch or curve;
Her back arches
Her hips curve nicely
Curve
(intransitive) To bend or turn gradually from a given direction.
The road curves to the right
Curve
(transitive) To grade on a curve (bell curve of a normal distribution).
The teacher will curve the test.
Curve
(transitive) (slang) To reject, to turn down romantic advances.
I was once curved three times by the same woman.
Curve
Bent without angles; crooked; curved; as, a curve line; a curve surface.
Curve
A bending without angles; that which is bent; a flexure; as, a curve in a railway or canal.
Curve
A line described according to some low, and having no finite portion of it a straight line.
Curve
To bend; to crook; as, to curve a line; to curve a pipe; to cause to swerve from a straight course; as, to curve a ball in pitching it.
Curve
To bend or turn gradually from a given direction; as, the road curves to the right.
Curve
The trace of a point whose direction of motion changes
Curve
A line on a graph representing data
Curve
A baseball thrown with spin so that its path curves as it approach the batter
Curve
The property possessed by the curving of a line or surface
Curve
Curved segment (of a road or river or railroad track etc.)
Curve
Turn sharply; change direction abruptly;
The car cut to the left at the intersection
The motorbike veered to the right
Curve
Extend in curves and turns;
The road winds around the lake
Curve
Form an arch or curve;
Her back arches
Her hips curve nicely
Curve
Bend or cause to bend;
He crooked his index finger
The road curved sharply
Curve
Form a curl, curve, or kink;
The cigar smoke curled up at the ceiling
Common Curiosities
What defines a curve?
A curve is any line or shape that smoothly bends without sharp angles, defined by mathematical equations or graphical representation.
Are all arcs curves?
Yes, all arcs are curves, but not all curves are arcs, as curves can belong to various shapes and forms.
What is an arc?
An arc is a segment of a circle's edge, defined by two points and the center of the circle.
How is an arc measured?
An arc is measured either by its length or by the central angle it subtends in a circle.
How are curves represented?
Curves can be represented by mathematical equations, parametric forms, or graphical shapes.
How do arcs and curves differ in geometry?
Arcs are specific to circular geometry, defined by a circle's parameters, whereas curves can describe any smooth, continuous line or shape in geometry.
What applications do curves have in design?
In design, curves are used to create aesthetically pleasing and functional shapes, from product design to architecture.
What is the importance of curves in mathematics?
Curves are important in mathematics for studying the properties of smooth, continuous lines and shapes and their applications across various fields.
Can a curve be part of a circle?
Yes, a curve can be part of a circle, in which case it's specifically referred to as an arc.
What is the role of an arc in circular motion?
In circular motion, an arc represents the path or portion of the path that an object or point moves along the circumference of a circle.
Can arcs be found in non-circular shapes?
No, arcs are specifically segments of a circle's circumference and cannot be part of non-circular shapes.
How do arcs and curves differ in their applications?
Arcs are often used in contexts requiring precise circular geometry, like engineering and astronomy, while curves have broader applications across various fields, including design, physics, and economics.
How are arcs used in astronomy?
Arcs are used in astronomy to measure angles and distances between celestial bodies, as they often move or appear to move along circular paths.
Are there specific types of curves?
Yes, there are many types of curves, including parabolas, hyperbolas, ellipses, and spirals, each defined by unique mathematical properties.
How does calculus relate to curves?
Calculus is used to analyze curves, particularly to study their curvature, rate of change, and tangent lines at various points.
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Written by
Maham Liaqat
Co-written by
Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.
