Question about terminology: ch = cosh?

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Discussion Overview

The discussion revolves around the interpretation of abbreviations used in a paper related to the Lorentz transformation and hyperbolic functions. Participants are trying to clarify whether the abbreviations "ch," "sh," and "th" refer to "cosh," "sinh," and "tanh," respectively, and whether these abbreviations are standard in English mathematical terminology.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the meaning of "ch," "sh," and "th" in the context of the Lorentz transformation, suggesting they might refer to "cosh," "sinh," and "tanh."
  • Another participant agrees that the abbreviations likely refer to "cosh," "sinh," and "tanh," but notes that they are not standard in English.
  • A third participant confirms that they often use "ch" for "cosh," particularly in specific contexts.
  • A later reply emphasizes that the paper discusses the Lorentz transformation in terms of rapidity rather than velocity, supporting the interpretation of the abbreviations as hyperbolic functions.
  • Links to Wikipedia articles on Lorentz transformation and rapidity are provided to support the claims made.

Areas of Agreement / Disagreement

Participants generally agree that "ch," "sh," and "th" likely refer to "cosh," "sinh," and "tanh," but there is no consensus on whether these abbreviations are standard in English mathematical literature.

Contextual Notes

Some participants express uncertainty about the standardization of these abbreviations in English, indicating a potential limitation in the clarity of terminology across different languages or contexts.

nomadreid
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I am reading the draft of a paper written by someone whose native language was not English and so who might not have been using the same abbreviations that I am familiar with, or maybe he was using standard ones and I am simply not familiar with the abbreviations involved. I can't ask him, as he is deceased. I quote:
"The properties of the event plane are described by the homogeneous two-dimensional Lorentz group L:
x' = xchθ + τshθ
τ' = xshθ + τchθ
where the hyperbolic angle θ is the transformation parameter. The relation of θ to the relativity velocity β is given by β = thθ. The coordinate τ = ct,..."

What are ch, sh, and th? Did he mean cosh, sinh, and tanh? Are his abbreviations standard?
Thanks.
 
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nomadreid said:
What are ch, sh, and th? Did he mean cosh, sinh, and tanh?

I think so.

Are his abbreviations standard?

Not in English at least, as far as I know.
 
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nomadreid said:
What are ch, sh, and th? Did he mean cosh, sinh, and tanh? Are his abbreviations standard?
Yes. I often write ch in place of cosh. Especially when I'm in a rh.
 
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Yeah, it can be uncomfortable writing stuff when you have a rash. :biggrin:

I admit I don't read much stuff that uses hyperbolic functions.
 
nomadreid said:
"The properties of the event plane are described by the homogeneous two-dimensional Lorentz group L:
x' = xchθ + τshθ
τ' = xshθ + τchθ
where the hyperbolic angle θ is the transformation parameter. The relation of θ to the relativity velocity β is given by β = thθ. The coordinate τ = ct,..."

What are ch, sh, and th? Did he mean cosh, sinh, and tanh? Are his abbreviations standard?
He is talking about the Lorentz transformation in terms of rapidity rather velocity.
See http://en.wikipedia.org/wiki/Lorentz_transformation#Rapidity and http://en.wikipedia.org/wiki/Rapidity
It is clear from those links that he does mean cosh, sinh, and tanh.
 
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