Arc

Arc

Arc refers to a curved line or segment of a circle or other curve. In geometry, an arc is a portion of the circumference of a circle or other curved shape. It can also represent a continuous portion of a differentiable curve between two points. In electrical engineering, an arc can refer to an electrical discharge through the air that occurs when a high voltage difference exists between two points, leading to ionization of the air and a visible plasma. The concept of an arc is fundamental in various fields, including mathematics, physics, engineering, and computer graphics.

Definition and Properties

In geometry, an arc is defined as a segment of a curve, particularly a circle, enclosed by two distinct points on the curve. The length of an arc is known as its arc length, which can be calculated using different formulas depending on the type of curve the arc belongs to. For a circular arc, the arc length L is given by L = rθ, where r is the radius of the circle and θ is the central angle in radians.

Electrical Arcs

In electrical engineering, an arc, or electric arc, is a visible plasma discharge between two electrodes that is caused by electrical current flowing through a normally nonconductive medium, such as air. This phenomenon occurs when the voltage difference between the electrodes exceeds a certain threshold, causing the medium to become ionized and electrically conductive. Electrical arcs are used in various applications, including arc welding, lighting (e.g., arc lamps), and electrical discharge machining.

Arc in Mathematics and Physics

In mathematics and physics, the concept of an arc is used to describe the path between two points on a curve. This is particularly important in the study of motion, where the trajectory of a moving object can often be approximated or described as an arc. Additionally, in the field of optics, the arc can describe the path of light rays in media with varying refractive indices, such as in the phenomenon of a rainbow.

Arc in Computer Graphics

In computer graphics, arcs are used to draw curves and circles on digital displays. Algorithms for rendering arcs are fundamental in the development of graphical user interfaces (GUIs), computer-aided design (CAD) systems, and digital art. The efficient rendering of arcs requires the use of mathematical models and algorithms to approximate the appearance of a smooth curve with a finite number of pixels.

See Also

• Circle
• Curve
• Electrical discharge
• Geometry
• Plasma (physics)

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