In a number of *Mishnayot* discuss the relationship between the
circumference of a circle and its diameter is mentioned. In mathematics,
this relationship is defined by an irrational constant (3.14159…). The
Greek letter *Pi* (π) has been popularised due to its adoption to
represent that value.

Having a mathematic and engineering background, the adoption of three in
the *Mishnah* and *Gemara* had been at first surprising. Matters are
further complicated as the *Gemara* (*Eiruvin* 14a) brings a *pasuk*
from *Melachim* (I 7:23) in support of this position:

And [

Shlomo HaMelech] made the pool of cast metal tenamotfrom rim to rim circular all around and fiveamotwas its height and a line of thirtyamotwould encircle it all around.

The *Rambam* (*Eiruvin* 1:5) notes that *Pi* is irrational and cannot be
known. He adds that in his time ^{22}/~~7~~ (3.1429…) was the well accepted
approximation. The *Rambam* explains that since the number is irrational
the *Chachamim* took a large figure, the nearest integer, as a
satisfactory approximation.

In this manner, the *Rosh* (*Teshovot* 2:19) answered the *Rashba’s*
question of why it was necessary to bring a *pasuk* in support of a
matter than can be solved scientifically. He explains that the source
was required to teach that an approximation of three is sufficient for
legal matters. In fact the *Aruch HaShulchan* (*Orach Chaim* 363:22)
rules that this is indeed a divine decree that three is used for all
legal questions.

Conversely, the *Tashbetz* (1:165) explains that the *Chachamim* did
have accurate approximations and used them for practical applications.
Nonetheless they followed the principle that “One should always teach
his student in a brief manner” (*Pesachim* 3b) and the approximation of
three achieved this end.

A person shared with me an insight in the name of the Vilna Gaon on this
issue. The source brought for the relationship being three is from the
*Yam Shel Shlomo*; a ‘sea’ that was one of the utensils constructed by
*Shlomo* *HaMelech* in the *Beit Ha’Mikdash*. It is described in two
places in *Tanach*: in *Melachim* (1 7:23) and *Divrei Ha’Yamim* (2
4:2). In *Melachim* however there appears to be a ‘spelling mistake’ -
the word for line (קָו) is written קוה. In other words the line that is
taken and multiplied by three, as stated in the *pasuk*, is distorted.
Taking the numerical value (*gematria*) of קוה (111) and dividing by the
numerical value of קו (106) and then multiply by three as stated, the
result is 3.141509... far more accurate than ^{22}/~~7~~ that I grew up
with!^{41}

To be honest I do not remember the conclusion and I have since heard
different endings from the above exercise. Nonetheless, it appears to
support everything stated above. The *Navi* is conveying that the value
3 is suitable for all intents and purpose – whether for teaching alone
or even practical applications. Nonetheless we find, albeit encoded, a
far more accurate value that aligns so perfectly with the meaning of the
text. It appears to be recognition that three, or any other such value
adopted for practical purpose, is just an approximation.^{42}

^{41} Note that engineers use approximation to four or five decimal
place.

^{42} As an aside the Guinness record for reciting the digits of Pi
from memory is 67,890 taking him 24 hours and 4 minutes. *Baruch
sh’natan Torah l’amo Yisrael!*

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