Final answer:
A radial fitting describes a fraction of a circle and can be represented in radians rather than degrees. This concept is utilized in scenarios where arc lengths are considered, and radians are dimensionless, making them a natural choice for mathematics and engineering.
Step-by-step explanation:
The type of fitting that is described as a fraction of a circle and not in degrees is known as a radial fitting. This terminology aligns with the concept of radians in mathematics, where a radian measures the angle created by taking the radius of a circle and stretching it along the circle's edge; the angle subtended by that arc is one radian. Since there are 2π radians in a full circle, any fraction of a circle can be described using radians rather than degrees, which is why we can discuss arc lengths without specifying angles in degrees.
In the context provided, a radial fitting, such as the circular fitting on a child's toy where a round peg fits through a round hole, is an example of this type of measurement. A degree is a unit of angular measure and corresponds with the fraction of a full turn, and radians provide a more natural approach for a range of mathematical and engineering calculations. This is because radians are dimensionless, being the ratio of two distances: the radius and the arc length corresponding to the angle.
From the discussion, we see that when we consider a small segment of a larger circle (like a pie fitting), we can approximate the length of the baseline to be equal to the arc length (α≈ α'), effectively using the concept of radians. Here, the length of the arc corresponding to a degrees can be directly calculated from the proportionality with the total circumference of the circle (2π radius).