[Tex/LaTex] Angle symbols in LaTeX

semanticssymbols

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:

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Now I have three questions:

  1. What is the semantic difference of those three symbols? (And maybe other symbols you know for angles)

  2. \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 re-define \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 well-known 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).

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