Pronunciation: [ˈɑːk lˈɛŋθ] (IPA) 
The spelling of the word "arc length" is quite straightforward. The first syllable is pronounced as "ark" /ɑrk/, like the animal. The second syllable is pronounced as "length" /lɛŋθ/, with a long "e" sound and a hard "th" at the end. The word refers to the distance along an arc of a circle. It is often used in geometry or trigonometry to calculate various measurements, such as the area or circumference of a circle.
Arc length is a term used in geometry and trigonometry to describe the distance along the circumference of a curve or circle. It refers to the length of a specific segment of the curve measured between two endpoints. In simple terms, it is the distance covered by moving from one point on the boundary of the curve to another point on the boundary.
To calculate the arc length, one must consider the radius of the circle or curve and the angle made by the two endpoints. The formula to find the arc length is θ/360° × 2πr, where θ is the central angle formed by the endpoints, and r is the radius of the circle or curve. This formula relies on the fact that a complete circle encompasses an angle of 360°, corresponding to the circumference of 2πr.
Arc length is crucial in various fields of mathematics and physics, as it allows for the measurement and calculation of curved segments, such as circular paths, arcs, or circular sectors. It is widely used in trigonometry to understand the relationship between angles and distances along curves, enabling the calculation of various quantities, such as angular velocity or the length of a circular movement. Additionally, arc length plays a fundamental role in calculus, specifically in the study of integration and the measurement of continuous quantities along curved paths.
The word "arc" originated from the Latin word "arcus", which means "bow" or "arch". It was first used in English in the 14th century to refer to the curved path or line formed by a bow or arch.
The word "length" comes from the Old English word "lengþu", which means the state, quality, or fact of being long.
The combination of these two words, "arc length", refers to the measure of the distance along the curved line or path formed by an arc. The term is commonly used in geometry to quantify the distance between two points along a curve or arc.
