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Here I have two issues related to this post.

  1. How can etymological approach to a language be used to improve creativity skills of mathematics in students;
    I think, knowing the evolution which has taken place by gathering information related to the historical developments of a language can be useful to shift the perspectives when generating new ideas in mathematics because mathematics itself is also a language. In that sense the etymological approach of why the word is spelled that way, is based on its roots rather than leaning how to spell, and encouraging students to find words sharing the same root rather than memorizing the meaning can be much effective differentiation tool.
  2. How can etymological approach to terminology be used to find much appropriate terms;
    As many know the present contemporary English form Sine is originated in ancient India as a Sanskrit word and it was transliterated into Arabic. The transliterated word was translated into Latin in 12 th century and finally it was translated into English. Because of that the present word has no connection with original word which stands for half chord. We all know now it's too late to correct that kind of mistake happened very long ago, but this kind of awareness may be important to avoid such situations in the future and it can be helpful to determine much appropriate term by going into roots .
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    $\begingroup$ I don't understand: "Sine" means "half chord", is that good or bad? $\endgroup$
    – Dominique
    Commented May 2, 2023 at 14:57
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    $\begingroup$ @Dominique I think the OP means that sine comes from Latin, sinus, meaning a bent surface or curve, such as a bay or gulf, the fold in a garment, esp. the top part of the toga around the breast, hence bosom, hence love or protection, etc. It did not have the meaning half chord until mathematicians gave it that meaning (see hsm.stackexchange.com/questions/5258/…). $\endgroup$
    – user1815
    Commented May 3, 2023 at 13:58
  • $\begingroup$ @Raciquel yes, I didn't mentioned the whole scenario and what I wanted to emphasize is the the mistake behind translating a transliterated word. Here you have very important point which can be helpful to improve logical thinking. $\endgroup$ Commented May 3, 2023 at 15:55
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    $\begingroup$ Students should not be involved in inventing new mathematical terminology. The subjects studied in school are classical and old and well established terminology is available and should be used because doing so facilitates communication. The invention of new mathematical terminology should be left to those doing new mathematics that needs new terminology. $\endgroup$
    – Dan Fox
    Commented May 4, 2023 at 9:23
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    $\begingroup$ @JanakaRodrigo: Students should learn standard terminology. It may sometimes be useful to indicate that well chosen terminology helps remember the concept it encodes, but this has limited utility as much terminology is not well chosen or was well chosen according to 19th century usage in French. But my comment was directed at the idea that students should be involved in finding "more appropriate terms". The inexpert should learn standard terminology well before engaging in the usually unproductive labor of trying to change it. $\endgroup$
    – Dan Fox
    Commented May 12, 2023 at 9:45

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I think etymology is not useful in the way proposed by the OP.
But here is a case in mathematics where etymology can help with spelling:
parallelepiped
The etymological analysis is: parallel + epi + ped (meaning "parallel upon the foot"). Remembering this helps me avoid errors like: parallelopiped, parallelipiped and such.

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  • $\begingroup$ Thank you very much for sharing your views, I agree with your suggestion as one way of looking into this issue, but what I'm suggesting in my post is something broader than that and sometimes it may be not the way normally many look into this topic. $\endgroup$ Commented May 2, 2023 at 15:36
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    $\begingroup$ I wouldn’t call this an etymology as it doesn’t attempt to explain the historical origin of the word. The etymology is that it comes from the Ancient Greek “παραλληλεπίπεδον” or “parallelepipedon” meaning “with parallel planes.” It appears in Euclid’s Elements 11.25. The word “epipedon” in Ancient Greek meant “flat” or “planar,” in addition to its literal meaning “on the ground.” @JanakaRodrigo Is this more along the lines of what you are referring to? $\endgroup$ Commented May 2, 2023 at 20:13
  • $\begingroup$ @JustinHancock thanks for sharing your views, I think you may have got the point because my aim is not just checking the spellings of a word after choosing it as the required word. I would like to know how this logical approach behind etymology can be utilized to develop creative skills too. Here you have opportunity of getting help from another subject to improve mathematics skills of students. $\endgroup$ Commented May 2, 2023 at 23:46
  • $\begingroup$ Interesting! I never knew that the "epi" from "epimorphism" was "upon". I often tell students the related "sur" from "surjection" meaning "on" in French. $\endgroup$ Commented May 4, 2023 at 17:49
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    $\begingroup$ @StevenGubkin also epicenter, episcopal, epicycle (!), and epilepsy. $\endgroup$
    – KCd
    Commented May 6, 2023 at 21:50

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