There are 365 negative commandments which correspond to the days of the (solar) year (see Makos 23b; Tanchuma Ki Seitzeh 2). Apparently the prohibition of Gid HaNasheh (sciatic nerve) corresponds to Tisha bAv (Zohar I:170b). Is there a list of the other 364 commandments and their corresponding days?
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The Maharal in "Tiferes Yisroel" perek 4, explains at length why the amount of negative commandments corresponds to the number of days in the solar year and the positive commandments to the limbs in the human body. Basically he says that the purpose of the negative commandments are to keep the world in order similar to the never changing properties of the sun. "Ein Kol Chadash Tachas Hashamesh"-"There is nothing new under the sun"- Koheles. The positive commandments are to elevate a person's body to be B'Tzelem Elokim. (By the way the gimatria of B'tzelem Elokim equals 248.)
No. The Jewish calender is a lunar calender, which actually has 354 days (unless it's a leap year or has the extra day in Kislev). The entire idea of 365 days is from the Julian calendar a solar calender, which has no Judaic origins. This is completely coincidental.