Reply To: Chidushim on Daf Yomi – Eruvin

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.