# Math Myth: What is 360°?

• I
• Greg Bernhardt
In summary, there are different ways to measure angles, including degrees, radians, and grads. However, degrees can be confusing and should be treated as a historical sidenote. In Software Engineering, the most efficient method is used, which is often using modulo arithmetic with integer values. The gradian, or grad, is also a unit of measurement for angles, but is not commonly used.

#### Greg Bernhardt

From @fresh_42's Insight
https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/

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.