Slicing the Circle
Angles measure rotation and geometry. There are primarily two ways humans have decided to slice a circle: based on arbitrary Babylonian math (360) or based on the mathematical constant $\pi$.
Babylonian Base 60
- Degree (°): 1/360th of a full circle.
- Arcminute ('): 1/60th of a degree. Crucial for astronomy and longitude/latitude.
- Arcsecond (''): 1/60th of an arcminute.
Trigonometric Radians
- Radian (rad): The angle made by taking the radius and wrapping it along the edge of the circle. Equivalent to $180/\pi$ degrees (approx 57.3°). It is the standard unit of angular measure in all higher mathematics and calculus.
Surveying and Military
- Gradian / Gon: A metric attempt to decimalize angles, where a right angle is 100 grads (400 per circle). Used heavily in surveying.
- NATO Mil: Used in artillery and sniper scopes. A circle is divided into 6400 equal mils.