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

  • I
  • Thread starter Thread starter Greg Bernhardt
  • Start date Start date
AI Thread Summary
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 Overall, the thread suggests that degrees may be viewed as an outdated system in mathematical contexts.
Messages
19,793
Reaction score
10,750
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.

Angles.png

 
Last edited:
Mathematics news on Phys.org
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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Back
Top