I will write a lot about Euclidean Geometry the next time. This means I need to denote angles.
The symbol we use in class looks like \sphericalangle
, but I've just seen that there is an \angle
symbol / command:
Now I have three questions:
 What is the semantic difference of those three symbols? (And maybe other symbols you know for angles)

\measuredangle
is quite long and I don't think that I will need more than one symbol for angles (it depends on your answer to question 1). So I would like to redefine\angle
so that I get the symbol of\measuredangle
. I think the way to do this would be\renewcommand{\angle}{\measuredangle}
is that correct? When I do this, is there any way to get the original symbol of \angle
?
(Not part of my main question, but I hope to get some comments about this:
Is it a bad idea to use another symbol than \angle
? How wellknown is the difference of those symbols? (I know this is open, I just want to read what you think about it. I think semantics are important).)
Best Answer
[Answer for 1] I have a guess for your first question, but I think it is a reasonable guess.
\sphericalangle AOB
= angle between two intersecting arcs on a sphere, specifically the angle between the two planes containing the arcs [There seems to be a distinction in notation where the center letter is O, not B]\measuredangle ABC
= the actual measured angle between points A and C at point B\angle ABC
= angle between points A and C at point B (the middle letter is the vertex) [I have also seen this used to define angles in Euclidean triangles].[Answer for 2] You could use
\newcommand
instead of\renewcommand
and define your own new command that is shorter but distinct (e.g.,\mangle
).