Chidushim on Daf Yomi – Eruvin

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    Reb Eliezer

    Repeating what is applicable from Maseches Shabbos.

    Tosfas Shabbos (96,2) ד’ה הוצאה indicates it for carying out and there ד’ה הכנסה indicates it for carying in. Both cases is considered a מלאכה גרועה a weak melacha, as Tosfas 2,1 asks what is the differents carying from a private area to another private area where it is allowed to carry bibliically with karmeles (4 amos wide and less than 10 tefochim high) in between. See SA O’CH 345 There is an argument a public domain 16 wide 600,000 people walking through does that include cars? Reb Moshe holds they walk with their cars but others hold that a car is a a private domain for itself. See in great detail Yabia Omer O’CH (9,33) about making a airuv of tzuras hapesach. A public domain where houses are on each side might limt the movement Traffic lights also limit movement. Intersecting roads also are questionable.

    The Aruch Hashulchan in O’CH 345 explains that in the olden time there was a main road where all other roads would meet. The houses were in an alley closed on one side and meeting this main road on the other side (movo). The main road had doors on each side but open at nigh 16 amos wide. This is derived from the mishkan were all the tents would converge to the Moshe Rabbenu’s tent where all 600,000 people gather and the wagons to the mishkan took up 16 amos.
    Most agree that 600,000 is required. Rav Moshe in Igros Moshe O’CH (4,87) says that a city having 12 mil by 12 mil where this amount of people gather makes it a public domain considering it a platyeh godaloh. The Aruch Hashulchan says that each street is judged for itself.

    The RMA O’CH 346,3 says that currently all of our streets are considered karmelis, only rabbinical. This is the the view of most poskim and therefore we can make an airuv with a tzuras hapesach without actual doors. Most poskim’s view is that cars don’t can included in the count. We have houses on each side of the road with street lights which limit the public movement. There are other roads circumventing the main road, so the main road is not as important as it used to be.

    Reb Eliezer

    Tosfas on 13,1 questions the accuracy of PI the ratiio between the circumderence and the diameter of a circle.
    The Rambam on the mishnah 13,2 which uses the integral value of 3 based on the yam shel shlomo whose diameter was ten amos and ciircumference 30 says that since the value is not known exactly, so any value would not be correct, therefore 3 is taken as a rounded integral value. We use 22/7 or 3 1/7 to approximate it as the Ralbag there in Melachim 7,23. The GRA uses the pasuk to approximate its value by using the written וקוה and the read וקו taking the value of the written excluding the connective vov which is 111 and multuplying by the integral value of 3 for an adjustment which is 333 and dividing by the read value 106, 333/106 = 3.141509 which is correct to 3 decimal places as the value is 3.1415926. Maybe, we can improve on this value by using the conective vov and adjusting the value a little. 117 x 3 = 351 add to tbis the number of letters in the word 4 making it 355 and add a kolel of 1 to the denominator of 112 so we get 355/113 which is 3.1415929 known by the chinese a long time ago as a good approximation correct to 4 decimal places of 3.1416. The denominator has no letters added as they are not all the letters written and numerator has no kolel as it is not read.


    I have looked up the traffic counts. The busiest highway in the US is the George Washington Bridge, with approximately 300,000 vehicles traveling its 14 lanes each day pre-pandemic. (The absolute maximum capacity is roughly 42,000 per traffic lane assuming no backups, no toll booths, and no stop lights.) The majority of those vehicles are single passenger commuters who get counted twice. Six of those 14 lanes are covered and would be considered indoors.

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