Measuring angles: What is (historically) deg rad and grad?

Answer

Dear Jos,

Geometry was mainly practiced in the study of the stars. Because the year has 365 days, the circle was divided into a comparable number of degrees. For example, the binoculars had to be turned about 1 degree every night. Radians were probably introduced because the sine function then got some nice properties: the derivative of the sine is then -cosine and the derivative of the cosine is the sine. This is only possible if you express the sine in radians. Moreover, there is a nice interpretation for the trigonometric circle: if your alpha centimeter runs along the circle, the cosine is the distance to the y-axis and the sine is the distance to the x-axis. GRAD was used to have more logic in our unit system. A right angle is 100 degrees and that fits our decimal preference, but this system didn’t make it.