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There room a variety of meanings for words "arc" in mathematics. In general, an arc is any kind of smooth curve joining 2 points. The size of one arc is well-known as that is arc length.

You are watching: The distance along a circle between two points on the circle

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

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

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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) yet not constantly (e.g., Jurgensen 1963) denoted
*
.

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

An arc who endpoints lie on a diameter of a circleis called a semicircle.

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For a circle of radius

*
, the arc length
*
subtended through a main angle
*
is proportional come
*
, and if
*
is measure up in radians, climate the consistent 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 space perpendicular to each other,


*

(3)

(Wells 1991).

An arc that a topological room

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is a homeomorphism
*
->S" />, where
*
is a subspace the
*
. Every arc is a path, however not conversely. An extremely often, the surname arc is offered to the photo
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of
*
.

The prefix "arc" is additionally used to denote the inverse features of trigonometric functions and also hyperbolic functions. Finally, any path v a graph which passes through no vertex double is called an arc (Gardner 1984, p.96).


SEE ALSO: apologize Surface, Arc Length, Arcwise-Connected, main Angle, Chord, Circle-Circle Intersection, one 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, particle of Life, Semicircle, Three-Arc Illusion, Triangle Arcs, Venn Diagram, Yin-Yang

Portions that this entry contributed by MargheritaBarile


REFERENCES:

Gardner, M. The Sixth publication of Mathematical games from clinical American. Chicago, IL: university of Chicago Press, 1984.

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

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

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


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