This report aims to research the units for angle measure, including their history, their definitions and the conversion between them.Several common types of units are described in detail, the two most important of which are degree and radian. In addition, how to choose the right unitfor angle measure in a specific situation is also discussed.
Angle measure is one of the most basic concepts in mathematics and has been widely used in many mathematical branches, such as geometry, trigonometry, algebra, etc. It’s also used in other fields, such as geography,astronomy and biology. Before using angle measure, it’s necessary to understand the difference of units that measure the size of an angle and the conversion between different types of units. That’s the main purpose of this report.
In geometry, an angle is the figure formed by two rays in a plane. The two rays, called the sides of the angle, share a common endpoint, which are called the vertex of the angle. One ray can coincide with the other by rotating around the vertex, and the minimal required amount of rotation is defined as the size of an angle.
Figure 1 shows three angles. As rotating and translating the two rays simultaneously keep the amount of rotation unchanged, the two angles in (a) and (b) are congruent angles.In addition, the length of the sides has no effect on the size of the angle. Intuitively, the amount of rotation in (c) is larger than those in (a) and (b). But that’s not enough in mathematics.In order to compare the size of two angles quantitatively, it’s necessary tofirstly determine the unit for angle measure. In other words, two angles must be measured in the same unit before being compared.
There are many types of units of angle measure, such as degree, radians and turn.Behind each unit, thereis a long story. Mastering each unit’s story contributes to a better use of angle measure in practice.
As a basic mathematical concept, angle measure has been widely used in many fields. It’s important to master each unit’s definition and history, and their conversion. In practice, the user should select the most appropriate unit for angle measure for the specific task.