## Thursday 21 September 2023

Degree is the union of the Latin roots de, down, and gradus, step.  Gradus is actually derived from the Greek word for "to walk" or "go".  Related words with the same root are congress (come together), regress (go back), and of course grade (the step you are on in school, or earned on an evaluation).  Degree as the measure (or step) of an angle dates back at least to the writings of Chaucer who used the word both in his Canterbury Tails (Squires Tale)  in 1386, and his more famous (then) book on the Astrolabe in 1400.

Degrees, why 360 in a circle I have seen many responses to why we use 360<sup>o</sup> in a circle, but the one that most impressed me was by the one below by the late Alexander Bogomolny.  I have copied the entire thing from his response to a question on  geometry discussion site, so here's why there are 360<sup>o</sup> in a circle,
"Babylonians used base 60 notation, which is convenient to divide a whole into 2, 3, 4, ... 30 parts.  Early Greeks then probably divided the radius of a circle into 60 parts. Hence, the diameter must have 120 parts. As Pi was known to be close to 3, the circumference would have 360 parts.
This argument may be used to exonerate the Bible (I Kings. 7:23 and II Chronicles, 4:2) which is said to quote 3 as the value of Pi. Not being a geometry manual, the Bible just picked out a simple approximation to Pi to convey the order of magnitude of the measured quantity. ...
Some history of the sexagesimal (base 60) notaions appear in D. E. Smith, History of Mathematics, v2, Dover"
DEGREE for angle measure is found in English in about 1386 in Chaucer's Canterbury Tales: "The yonge sonne That in the Ram is foure degrees vp ronne" [OED]. He again used the word in about 1391 in A Treatise on the Astrolabe: "9. Next this fole with the cercle of the daies, that ben figured in manere of degres, that contenen in nombre 365, dividid also with longe strikes fro 5 to 5, and the nombre in augrym writen under that cercle."
Gradian/Grade/Grad/Gon  In trigonometry, the gradian, also known as the gon (from the same Greek root for angle that gave us the gon in polygon) is a unit of measurement of an angle, defined as one hundredth of the right angle; in other words, there are 100 gradians in 90 degrees.
Grad or grade originally meant one ninetieth of a right angle, but the term is now used primarily to refer to one hundredth of a right angle.  Some eary scientific calculators had a key labled DRG for selecting between degrees, radians, and grads.  The Sharp EL501X2BWH Engineering/Scientific Calculator shown has the key in the top row 2nd from left next to 2nd Function key.

The OED2 shows a use of grade in English in about 1511, referring to one-ninetieth of a right angle.

The OED2 shows a use of grade, meaning one-hundredth of a right angle, in 1801 in Dupré Neolog. Fr. Dict. 127: "Grade .. the grade, or decimal degree of the meridian."

The OED2 shows a use of grade in English in about 1511, referring to one-ninetieth of a right angle.

The OED2 shows a use of grade, meaning one-hundredth of a right angle, in 1801 in Dupré Neolog. Fr. Dict. 127: "Grade .. the grade, or decimal degree of the meridian." (being French and at this period when France had tried to decimalize clocks, calendars, and pretty much everything, it may be where the first use of grad as 1/100 of a degree began.
One major problem to Grads in Trig is that 30 and 60 degrees become fractions

 400 degree compass