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According to Masechet Menachot daf 37, we're supposed to place the box of the arm on the bicep. Why then do we also have a strap that wraps around the arm and hand (according to earliest sources)?

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once heard it has to reach the realm of action – ray May 11 '15 at 19:35
up vote 2 down vote accepted

Menachos 35b records that the tefillin strap of the shel yad must be long enough to reach the finger. Rambam specifies in a responsum (159) that the mitzvah is affixing it to the bicep, while further wrapping is just to "complete the knot" but doesnt sound mandatory.

קשירת הרצועה על הברכה היא אחרי הברכה ובו תהיה קשירה תמה ואין הקשירה על האצבע מוכרח

The Rosh too writes that wrapping the strap around the finger "is not part of the mitvah of tfillin) (responsa klal 3, ch. 2).

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