I Is 360° Really the Correct Measurement for a Full Angle?

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The discussion highlights the confusion surrounding angle measurements, particularly the use of degrees, radians, and grads. It points out that while 360° is commonly accepted for a full angle, alternatives like 400° and 2π are also valid, though 400° is rarely used. The conversation emphasizes that radians, represented as multiples of π, are more mathematically relevant. Additionally, the use of hexadecimal notation in software engineering illustrates how angles can be expressed in various formats, further complicating the understanding of degrees. Overall, the thread suggests that degrees may be viewed as an outdated system in mathematical contexts.
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From @fresh_42's Insight
https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/

Please discuss!

The measuring of angles in degrees is at best confusing. Even the calculator on the computer allows three versions of a full angle: ##360°, 400°, 2\pi##. And whoever used the ##400°##? Anyway, ##2\pi## is what it should be: the ratio of the circumference of a circle of radius ##1## to its radius##1##. It is how angles are used in mathematics: multiples of ##\pi##. Degrees should be treated like Roman numbers: a historical sidenote.

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Interesting opinion.
In Software Engineering, you use what best works.
A common way of expressing angles into take advantage of the inherent modulo arithmetic commonly used to denote integers.

To show this, I will use hexadecimal notation with 16-bit 2's complement arithmetic:
0000: zero degrees.
4000: 90 degrees.
8000: 180 degrees
C000: 270 degrees

Note that 8000 can denote either 16,384. or -16,384. - reflecting the equivalency of 180 and -180 degrees.
When overflow is ignored (as it commonly is with integer values), then 6000+6000+6000 = 2000;
corresponding to 135 degrees + 135 degrees + 135 degrees = 45 degrees.
 
Greg Bernhardt said:
The measuring of angles in degrees is at best confusing. Even the calculator on the computer allows three versions of a full angle: 360°,400°,2π. And whoever used the 400°?
No one uses 400°. The actual unit is a gradian, or grad in abbreviated form, and is defined as 1/100th of a right angle. A full turn is 400g (400 grads). The unit originated in the French Revolution. For more info, see https://en.wikipedia.org/wiki/Gradian.
 
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