AI - Arc Length (Lesson)
Arc Length
In geometry, an arc refers to a section of the circumference of a circle lying between two points on the circle. Since the length of an arc of a circle is a portion of the circle's circumference, a formula is easily found to measure the arc's length, ?scale=1 "2\pi r\left(\frac{D}{360}\right)")
2πr(D360), where D is the degree measure of an arc. In calculus arc length refers to the length of a curve that is not necessarily a circle. Finding the arc length of a curve is a bit more difficult since the types of curves can range from a polygon to those defined by y = f(x) where f is a continuous function and a < x < b. More formally, arc length is the length of a curve found by taking the limit of the sum of infinitely many lengths of polygonal paths along a closed interval (definite integral).
View the presentation on the development of a formula for arc length of a curve and how it is applied to solving problems.
The two-part presentation below illustrates how arc length is determined for various situations.
The manufacture of corrugated materials such as iron roofing, building materials, and cardboard for packing and shipping are examples of how arc length is applied in real-world contexts. Bending materials into a regular wave pattern (sine curve) produces a much stronger product than if a flat sheet were used. Determining the length of the original flat sheet of material needed to produce a corrugated sheet of given length requires knowledge of how to determine arc length analytically using calculus.
Arc Length Practice
Arc Length: Even More Problems!
Complete problems from your textbook and/or online resources as needed to ensure your complete understanding of arc length.
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