Understanding Arcs in Mathematics | Types, Definitions, and Applications

Arc

In mathematics, an arc is a portion of a curve

In mathematics, an arc is a portion of a curve. It is defined as a continuous section of a curve between two points, known as the endpoints of the arc. The shape of the arc is determined by the shape of the curve it is part of.

Arcs can be classified into different types based on their size or position relative to the whole curve. Here are some common classifications:

1. Minor Arc: This refers to an arc that measures less than or equal to 180 degrees (a semicircle is a special case of a minor arc).

2. Major Arc: This refers to an arc that measures more than 180 degrees (complement to a minor arc).

3. Semicircle: This is a special case of an arc that measures exactly 180 degrees, forming half of a complete circle. It can be considered as the largest possible minor arc of a circle.

4. Central Angle: An angle with its vertex at the center of the circle, formed by the two radii that define the endpoints of an arc.

5. Sector: A sector is a region enclosed by two radii of a circle and an arc connecting their endpoints. It is essentially a pie-shaped portion of a circle.

Arcs are used in many areas of mathematics, including geometry, trigonometry, and calculus. They have applications in various fields such as engineering, physics, and computer graphics. Understanding arcs and their properties is essential for working with circles and curves effectively.

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