On the Daf the gemorah says the ratio of circomference to diagnal is 3:1 when even the Greeks new it was 3.14:1. That means that the sefer torah which was 6 tefachim long would be only about 1.9 tefachim wide - enough to fit nicely inside the 2 tefachim space. Our chachomim should have know this by then, why is that not spoken about.

Shai Mandel, Yerushalaim

Here is something the Kollel wrote on the subject in Eruvin 14. You can find some more Insights about Pi in our work on Eruvin 76b, go to http://www.dafyomi.co.il/eruvin/insites/ev-dt-076.htm .

I hope you find this helpful. Best wishes,

M. Kornfeld

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2)** THE VALUE OF "PI"**

**QUESTION**: The Gemara says that the circumference of a circle is three times greater than its diameter. How do we reconcile this Gemara with the known fact that the ratio of the circumference of a circle to its diameter is slightly more than three (Pi=3.14159...)?

(a) The **TOSFOS HA'ROSH** explains that the Gemara itself is addressing this issue. Why does the Gemara ask "from where do we learn" that the circumference of a circle is three times greater than the diameter? We do not need a verse to teach us a mathematical fact! The Gemara must be asking from where do we learn that we may use a slightly * inexact * value for determining the circumference of a circle. The Gemara learns from the verse that one may round off the relationship of the diameter of a circle to its circumference for all Halachic purposes, and assume it to be three. This is learned from the verse which describes the circumference of the Yam Shel Shlomo as * three * times its diameter.

Similarly, the **RAMBAM** (Perush ha'Mishnayos; see also Hil. Tum'as Mes 12:7) writes that Pi is actually an irrational number. "The exact relationship of the diameter to its circumference cannot be known and it is not possible to speak of it... and its actual value cannot be perceived." He writes that the value which is commonly used in calculations is 3 1/7 (3.142857...). The Tana'im of the Mishnah rounded this number and expressed it in terms of the nearest whole integer (3).

(c) It has been said in the name of the Vilna Ga'on (although there is no substantiation for that claim -- more reliably, it may be credited to one Matityahu ha'Kohen Munk (Frankfurt-London), who published the thought in "Sinai," Tamuz 1962, and "ha'Darom," 1967) that in the verse (Melachim I 7:23) that the Gemara cites, there is a Kri and a Kesiv; a word is pronounced differently than it is spelled. The word in the verse is written "v'Kaveh" (with a "Heh" at the end), but it is pronounced "v'Kav (with no "Heh"). The Gematria (numerical value) of the word "Kav" is 106, and the Gematria of the word "Kaveh" is 111. The ratio of the K'siv (111) to the K'ri (106), or 111/106, is 1.0471698. This value is an extremely close representation of the relationship of the real value for pi to 3 (111/106 = 3.1415094/3).

Hence, the difference between the actual value of pi and its practical value is expressed by the difference between the Kesiv (the actual, but unread word) and the Kri (the word as we use it) of the verse discussing pi!