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Arc

In Euclidean geometry, an arc is a segment of a curve, most often a circle, in a two-dimensional plane. When it is a circle, the arc is called a circular arc. In the strictest definition, an arc is a segment of a curve in a plane. Examples include segments of geometrical forms such as circles, ellipses, and parabolas, as well as irregular arcs defined by analytical functions.

Arcs of circles can be classified by size. A minor arc is one whose length is shorter than one-half of the circumference of a circle. A major arc is one whose length is longer than one-half of the circumference of a circle. An arc whose length is exactly one-half of the circumference of the circle is simply called a semi-circle. The line connecting the endpoints of a major arc or minor arc is called a chord.

Angles subtended by circles can be classified by the location of the vertex. One important type of angle has the vertex located at the circumference. An angle whose vertex is at the center of the circle is called a central angle. Each specific central angle is subtended by only one arc, but each arc subtends infinitely many angles.

KEY TERMS

Circumference The line defined by the collection of points at a distance r from the center of a circle.

Subtend Intersect.

Vertex The point at which the two sides of an angle meet.

An arc of a circle can be measured by length along the circumference or in terms of the angle subtended by the arc. A theorem of geometry states that the measure of the central angle of the circle is the measure of corresponding arc. If the arc lies on a circle of radius (r ) and subtends a central angle (A) measured in degrees, then the length of the arc is given by b = 2π r (A/360), where π is the mathematical constant 3.14159, defined as the ratio of the circles circumference to its diameter.

In the case of irregular arcs, lengths are more complicated to determine. Historically, only approximations were possible by mathematicians. The rectification of a curve, or calculating the length of an irregular arc, can be performed, as noted during the seventeenth century, with the use of calculus and differential geometry.

Kristin Lewotsky

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arc / ärk/ • n. 1. a part of the circumference of a circle or other curve. ∎  a curved shape, or something shaped like a curve: the arc of the sky. ∎  a curving trajectory: he swung his flashlight in an arc. ∎  [as adj.] Math. indicating the inverse of a trigonometrical function. 2. (also electric arc) a luminous electrical discharge between two electrodes or other points. • v. (arced ; arc·ing ) [intr.] 1. move with a curving trajectory: the ball arced across the room. 2. [usu. as n.] (arcing) form an electric arc: check that switches operate properly with no sign of arcing. PHRASES: minute of arcsee minute1 (sense 2). second of arcsee second2 (sense 2).

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Arc

An arc is a segment of a curve , most often a circle . In the strictest definition, an arc is a segment of a curve in a plane . Examples include segments of geometrical forms such as circles, ellipses, and parabolas, as well as irregular arcs defined by analytical functions.

Arcs of circles can be classified by size. A minor arc is one whose length is shorter than one-half of the circumference of a circle. A major arc is one whose length is longer than one half of the circumference of a circle. An arc whose length is exactly one-half of the circumference of the circle is simply called a semi-circle. The line connecting the endpoints of a major arc or minor arc is called a chord.

Angles subtended by circles can be classified by the location of the vertex. One important type of angle has the vertex located at the circumference. An angle whose vertex is at the center of the circle is called a central angle. Each specific central angle is subtended by only one arc, but each arc subtends infinitely many angles.

An arc of a circle can be measured by length along the circumference, or in terms of the angle subtended by the arc. A theorem of geometry states that the measure of the central angle of the circle is the measure of corresponding arc. If the arc lies on a circle of radius r and subtends a central angle (LA) measured in degrees, then the length of the arc is given by b = 2πr(LA/360).

In the case of irregular arcs, the length can be determined using calculus and differential geometry.

Kristin Lewotsky

KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Circumference

—The line defined by the collection of points at a distance r from the center of a circle.

Subtend

—Intersect.

Vertex

—The point at which the two sides of an angle meet.

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arcarc, ark, Bach, bark, barque, Braque, Clark, clerk, dark, embark, hark, impark, Iraq, Ladakh, Lamarck, lark, macaque, marc, mark, marque, narc, nark, Newark, park, quark, sark, shark, snark, spark, stark, Vlach •matriarch, patriarch •tanbark • ringbark • stringy-bark •Offenbach • ironbark • oligarch •salesclerk • titlark • skylark •meadowlark • woodlark • mudlark •landmark • checkmark • Denmark •benchmark • waymark • trademark •seamark • Bismarck • telemark •tidemark • Kitemark • pockmark •Ostmark • hallmark • Goldmark •Deutschmark • bookmark • footmark •earmark • watermark • birthmark •anarch • car park • skatepark •ballpark •Petrarch, tetrarch •hierarch, squirearch •exarch • Pesach • loan shark •Plutarch • aardvark

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ARC / ärk/ • abbr. ∎  Med. AIDS-related complex. ∎  American Red Cross.

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arc Portion of a curve. For a circle, the length (s) of an arc is found either by 2rπ × θ/360 or the product of the radius (r) and the angle (θ), measured in radians, that it subtends at the centre: that is, s = r θ.

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ARC n. AIDS-related complex: see AIDS.

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arc See ISLAND ARC.

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arc of a graph. See graph.

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arc XIV. — (O)F. :- L. arcus bow, arch.

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