3 ms·

Is it? I didn't bother to check as it wasn't too relevant. I wasn't stuck anymore. Worst-case it's a memnonic that is untrue. Best case: it is. For actual deriv

Is it? I didn't bother to check as it wasn't too relevant. I wasn't stuck anymore. Worst-case it's a memnonic that is untrue. Best case: it is. For actual derivations I check the work. This is what it wrote by the way. I posted an image and asked: Why is this m m for angle mangle? ChatGPT: In geometry we often need to distinguish the angle itself (a geometric object) from the numerical size of that angle (a real-number measurement, usually in degrees or radians). To keep the two ideas separate we put a little “m” in front of the angle symbol: m∠B reads as “the measure of angle B.” * ∠B refers to the actual wedge-shaped region determined by the two rays that meet at vertex . * m∠B is the single number—e.g. \90∘—that tells you how “wide” that wedge is. So in the worked example the author writes m∠A + m∠B + m∠C + m∠D = 360∘ because they are adding the sizes of the four interior angles of a quadrilateral, not the angles themselves. If you dropped the m you’d be adding geometric objects, which doesn’t make sense; the m reminds the reader that what’s being added are real-number measures. (Some textbooks use ∣∠B∣ or simply write the letter with a bar over it, but “m∠” is by far the most common in U.S. and many international curricula.) So the mysterious “m” isn’t another variable—just a shorthand for “measure of.” --- Edit: this took quite some work to write well as ChatGPT answers don't copy/paste neatly into HN. So I won't be doing this for the other example.

card_zero 1y ago
See slope: https://en.wikipedia.org/wiki/Slope https://en.wikipedia.org/wiki/Slope It isn't customarily used for angles (those get Greek letters). The m stands for mystery. Edit: ah, but I see that this prefixed m for "measure" is also used sometimes. It appears at https://en.wikipedia.org/wiki/Angle#Combining_angle_pairs https://en.wikipedia.org/wiki/Angle#Combining_angle_pairs though I'm not sure why it's necessary. Maybe because you want to clarify absolute magnitude is meant, to avoid adding negative values.
- evertedsphere 1y ago
  yes, it's the equivalent of |AB| for a line segment and is not uncommon in high school maths texts in some parts of the world
namaria 1y ago
I thought it was a different kind of nonsense, but it still has a subtle error. Goes to show even more how risky it is to repeat LLM answers as factual.
- melvinroest 1y ago
  Could you point out what you mean? It's really hard to follow you. You say it's nonsense but it is not clear why. Then I write down a response that took me quite a while to format correctly (and to look up) and you then say "I thought it was a different kind of nonsense." Then you say it still has a subtle error. It is really hard to follow you if you don't explain yourself. I'm not saying it's factual. The reason I showed that answer was simply to verify to see if it was what you thought it was (hence I asked "is it?"). It turns out that it wasn't fully.
ants_everywhere 1y ago
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.
- melvinroest 1y ago
  "I'm not sure how historical the notation is." 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.
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card_zero 1y ago

See slope: https://en.wikipedia.org/wiki/Slope https://en.wikipedia.org/wiki/Slope It isn't customarily used for angles (those get Greek letters). The m stands for mystery. Edit: ah, but I see that this prefixed m for "measure" is also used sometimes. It appears at https://en.wikipedia.org/wiki/Angle#Combining_angle_pairs https://en.wikipedia.org/wiki/Angle#Combining_angle_pairs though I'm not sure why it's necessary. Maybe because you want to clarify absolute magnitude is meant, to avoid adding negative values.

evertedsphere 1y ago
yes, it's the equivalent of |AB| for a line segment and is not uncommon in high school maths texts in some parts of the world

namaria 1y ago

I thought it was a different kind of nonsense, but it still has a subtle error. Goes to show even more how risky it is to repeat LLM answers as factual.

melvinroest 1y ago
Could you point out what you mean? It's really hard to follow you. You say it's nonsense but it is not clear why. Then I write down a response that took me quite a while to format correctly (and to look up) and you then say "I thought it was a different kind of nonsense." Then you say it still has a subtle error. It is really hard to follow you if you don't explain yourself. I'm not saying it's factual. The reason I showed that answer was simply to verify to see if it was what you thought it was (hence I asked "is it?"). It turns out that it wasn't fully.

ants_everywhere 1y ago

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.

melvinroest 1y ago
"I'm not sure how historical the notation is." 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.

deleted 1y ago

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