A question about the Frénet–Serret Apparatus

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SUMMARY

The discussion centers on the Frénet–Serret formulas, specifically addressing the expression for the unit tangent vector T = (dr/ds) / |dr/ds|. Participants noted that since |dr/ds| equals 1 in this context, including the norm is unnecessary. The Wikipedia article correctly omits this term in subsequent sections, indicating a lack of clarity in the initial presentation. This highlights the importance of precision in mathematical definitions and the potential for confusion in educational resources.

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swampwiz
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I was reading the Wikipedia article about this, and I've noticed something that doesn't seem to make sense:

https://en.wikipedia.org/wiki/Frenet–Serret_formulas

The article says that the unit vector for the tangent direction is:

T = ( dr / ds ) / | dr / ds |

OK, that's the standard way to express a unit vector, but it seems that in this case, | dr / ds | is 1, so what is the point of including this term?
 
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You're correct, there is no point. Wiki has it without the norm in the very next section and gets it correct in other places.
 

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