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I've just seen that LaTeX offers at least three symbols for denoting angles:

$\text{\sphericalangle}:\sphericalangle ABC \\\text{\measuredangle}:\measuredangle ABC\\\text{\angle}: \angle ABC$

I think I've understood that a spherical angle is something different than an angle in euclidean geometry.

So I have some questions to the notation of angles:

  • What is the semantic difference of $\angle ABC$ and $\measuredangle ABC$?
  • Which symbol is commonly used in literature? Please note:
    • The symbol might be not in the list from above
    • I know this is a loose quesiton. Please give at least one book that makes use of the notation you think is most common. (e.g. these German lecture notes make use of $\angle$ and $\sphericalangle$. The difference seems to be that $\measuredangle$ is the size of the angle whereas $\angle$ denotes the angle itself. So when I understand it correctly, in a rectangle ABCD you could say: $\sphericalangle ABC = \sphericalangle BCD$ and $\angle ABC \neq \angle BCD$)
    • If there is a "mathematical style guide" that makes notes which notation to use for angles it would be an answer I'd appreciate very much!
  • Are there differences in German mathematics / English mathematics? E.g. just like I think Americans write $1/4$ rather than $\frac{1}{4}$ in contrast to Germans.

(I would also like to know what you think which symbol I should use for angles in euclidean geometry. How well known is the difference of these notations? So, do you think the choice of symbol matters?)

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I think there is no definite standard: every author uses the symbol he/she prefers and this varies with time and with place.

In Italy, for instance, the widespread notation for angle $ABC$ is $A\hat{B}C$.

Marvin Jay Greenberg in his "Euclidean and non-Euclidean geometries" (1974) uses instead $\sphericalangle ABC$.

And I could go on with a lengthy list of different examples.

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