Angle

Key facts and history

Eudemus of Rhodes regarded an angle as a deviation from a straight line, while Carpus of Antioch regarded it as the interval between intersecting lines.^[3] Euclid adopted the third concept: angle as a relationship.^[3] The use of degrees to measure angles harks back to the Babylonians, whose sexagesimal number system was based on the number 60.^[4] For millennia, philosophers have debated whether an angle is a measure (a quantity), a shape defined by its bounding lines (a qualitative relation), or both, as noted in a commentary on Euclid's Elements.^[5]

Thales of Miletus is credited by Eudemus of Rhodes with proving the vertical angle theorem.^[6] The degree, radian, and turn are the most frequently used units for measuring angles.^[7]

What the research sources say

The same source notes that half a full rotation is called a straight angle, and a quarter of a full rotation is called a right angle.^[4] Weisstein also states that an angle less than a right angle is called acute, an angle greater than a right angle but less than a straight angle is called obtuse, and an angle greater than a straight angle but less than a full angle is called reflex.^[4] The radian is described by Weisstein as the most useful angle measure in calculus because the derivative of trigonometric functions does not require insertion of multiplicative constants.^[4] Weisstein adds that a ruled semicircle used for measuring and drawing angles is called a protractor.^[4]