ChatGPT is right, although I'm not sure how historical the notation is.
∠ is traditionally a function from points to axiomatic geometric objects. ∠ABC is the angle at B oriented so that we start at A, go to B, then to C.
Your text seems to be using ∠ either as a kind of type annotation (indicating by ∠B that B is an angle) or (perhaps more likely) is just suppressing the other letters in the triangle and is short for something like ∠ABC.
Since ∠B is an axiomatic Euclidean object, it has no particular relation to the real numbers. m is an operator or function that maps axiomatic angles to real numbers in such a way that the calculations with real numbers provide a model for the Euclidean geometry. Why call it m? I'm not aware of it being historical, but almost certainly it comes from measure, like the μ in measure theory.
Obviously ∠ is a graphical depiction of an angle, and my guess is it probably evolved as a shorthand from the more explicit diagrams in Euclid.
Traditionally angles are named with variables from the beginning of the Greek alphabet: α, β, γ. Then we skip to θ presumably to avoid the Greek letters that look nearly identical to Roman letters.
I conflated this with another ChatGPT conversation where it gave 3 possible historical sources for another symbol that I fell over and then had trouble proceeding.
∠ is traditionally a function from points to axiomatic geometric objects. ∠ABC is the angle at B oriented so that we start at A, go to B, then to C.
Your text seems to be using ∠ either as a kind of type annotation (indicating by ∠B that B is an angle) or (perhaps more likely) is just suppressing the other letters in the triangle and is short for something like ∠ABC.
Since ∠B is an axiomatic Euclidean object, it has no particular relation to the real numbers. m is an operator or function that maps axiomatic angles to real numbers in such a way that the calculations with real numbers provide a model for the Euclidean geometry. Why call it m? I'm not aware of it being historical, but almost certainly it comes from measure, like the μ in measure theory.
Obviously ∠ is a graphical depiction of an angle, and my guess is it probably evolved as a shorthand from the more explicit diagrams in Euclid.
Traditionally angles are named with variables from the beginning of the Greek alphabet: α, β, γ. Then we skip to θ presumably to avoid the Greek letters that look nearly identical to Roman letters.