Understanding Arcs in Mathematics | Definition, Classification, and Applications

Arc

In mathematics, an arc refers to a portion of a curve, typically a section of a circle or an ellipse

In mathematics, an arc refers to a portion of a curve, typically a section of a circle or an ellipse. It is a continuous segment that is defined by two endpoints and the length of the curve between them. Picture a circle, for example, and imagine cutting out a portion of the circumference. The resulting curve between the two endpoints is called an arc.

Arcs are often described using their central angle or the measure of the angle subtended by the arc at the center of the circle. This angle helps determine the size or length of the arc. In a circle, a central angle of 360 degrees corresponds to the entire circumference, while a central angle of 180 degrees represents a semicircle.

Arcs can also be categorized as minor arcs or major arcs. A minor arc is an arc that measures less than 180 degrees, while a major arc measures more than 180 degrees. Additionally, there is a special kind of arc called a semicircle, which is an arc that measures exactly 180 degrees, half the circumference of a circle.

Arcs have various applications in geometry, trigonometry, and physics. They are used to calculate distances along curves, find the length of a circular sector, determine the area of a sector, and solve problems involving circular motion or rotational angles.

To summarize, in mathematics, an arc is a portion of a curve, typically a section of a circle, defined by two endpoints and the length of the curve between them. It is often described by its central angle and can be classified as a minor arc, major arc, or semicircle depending on its measure.

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