What is a tangent? (multiple meanings)

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Discussion Overview

The discussion revolves around the various meanings of the term "tangent" in scientific contexts, particularly in mathematics and geometry. Participants explore how these meanings might lead to misunderstandings in academic articles.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant identifies two meanings of "tangent": as a trigonometric function (tan) and as a geometric concept where two objects touch at a point.
  • Another participant elaborates on the geometric meaning by describing a tangential line on a unit circle and its relationship to the angle θ and the tangent function.
  • A participant shares a visual representation to aid understanding of the tangent function and its geometric implications.
  • One participant argues that the two meanings are significantly different and emphasizes the connection between the tangent function and the tangential line.
  • Another participant notes that the terms tangent, tangential line, and tan may share etymological roots but serve different purposes in usage.
  • A participant reflects on the importance of context in language, stating that they have not experienced confusion between the tangent line and the tangent function in their STEM experience.

Areas of Agreement / Disagreement

Participants express differing views on whether the meanings of "tangent" are likely to cause misunderstandings, with some asserting that context mitigates potential confusion while others highlight the differences in usage.

Contextual Notes

Participants do not resolve the potential for misunderstanding stemming from the different meanings of "tangent," and the discussion remains open regarding the implications of these meanings in academic contexts.

graphking
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how many different meanings do you guys know, towards the word "tangent"?
in science, I already know 2 meanings: the functions similar to sin, cos, cot, and it is tan;
it means two geometry objects are intersected, and they touch each other closely.
so I wonder if the different meanings would cause misunderstanding of the academic article.
P.S. I haven't met misunderstandings like this in academics for years.
 
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Two meanings you show have common sense, say unit circle centered at the Origin has tangential line at (1,0), the part of tangential line between intersection with line of counter clockwise angle ##\theta## measured from x-axis through the Origin and (1,0), has length ##\tan \theta##.
 
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Thanks! But I still think the two meanings are really of great difference, though:
anuttarasammyak said:
Two meanings you show have common sense, say unit circle centered at the Origin has tangential line at (1,0), the part of tangential line between intersection with line of counter clockwise angle ##\theta## measured from x-axis through the Origin and (1,0), has length ##\tan \theta##.

have figured that tan is equal to some part of a tangential line.
 
They have different usage. That is why we coin the words tangent, tangential line, and tan. I just mention they may have a same roots in coining.
 
Like most language, it's all about context. In many decades in STEM, I don't recall confusing a tangent line with the tangent function. I think you'll find lots of homonyms in STEM, which is why we like mathematical descriptions so much.
 
Yes, thank you for your reply!
 
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