There are a variety of meanings for words "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is well-known as the arc length.

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In a graph, a graph arc i am one ordered pair of surrounding vertices.

In particular, one arc is any part (other than the whole curve) that the one of a circle. An arc corresponding to the main angle

is denoted
. Similarly, the size of the main angle subtended through this arc (i.e., the measure up of the arc) is periodically (e.g., Rhoad et al. 1984, p.421) but not always (e.g., Jurgensen 1963) denoted
.

The facility of one arc is the center of the one of whichthe arc is a part.

An arc who endpoints lie on a diameter the a circleis dubbed a semicircle.

, the arc size
subtended through a central angle
is proportional to
, and also if
is measured in radians, then the constant of proportionality is 1, i.e.,

(1)

The length of the chord connecting the arc"s endpointsis

(2)

As Archimedes proved, for chords

and
which are perpendicular to every other,

(3)

(Wells 1991).

An arc that a topological room

is a homeomorphism
->S" />, wherein
is a subspace the
. Every arc is a path, yet not conversely. Very often, the surname arc is given to the image
of
.

The prefix "arc" is also used to signify the inverse attributes of trigonometric functions and also hyperbolic functions. Finally, any path v a graph i m sorry passes with no vertex twice is called an arc (Gardner 1984, p.96).

SEE ALSO: apple Surface, Arc Length, Arcwise-Connected, main Angle, Chord, Circle-Circle Intersection, circular Triangle, 5 Disks Problem, Flower that Life, Graph Arc, inscriptions Angle, Lemon Surface, Lens, Lune, major Arc, young Arc, Piecewise one Curve, Radian, Reuleaux Polygon, Reuleaux Triangle, Salinon, seed of Life, Semicircle, Three-Arc Illusion, Triangle Arcs, Venn Diagram, Yin-Yang

Portions the this entry added by MargheritaBarile

REFERENCES:

Gardner, M. The Sixth book of Mathematical games from scientific American. Chicago, IL: college of Chicago Press, 1984.

Jurgensen, R.C.; Donnelly, A.J.; and also Dolciani, M.P. Th.42 in modern Geometry: Structure and also Method. Boston, MA: Houghton-Mifflin, 1963.

Rhoad, R.; Milauskas, G.; and also Whipple, R. Geometry because that Enjoyment and also Challenge, rev. Ed. Evanston, IL: McDougal, Littell & Company, 1984.

Wells, D. The Penguin dictionary of Curious and also Interesting Geometry. London: Penguin, p.118, 1991.

Referenced top top cg-tower.com|Alpha: Arc
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Barile, Margherita and also Weisstein, Eric W. "Arc." from cg-tower.com--A cg-tower.com net Resource. Https://cg-tower.com/Arc.html

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