DAF YOMI
עירובין יד
מאת בן אחותי הרה"ג ר' אברהם אשי דיק שליט"א
In today's daf we learn about the ratio
between the circumference (עיגול) and diameter (קו) of a circle as
it relates to a קורה and the pool of Shlomo.
The gemara quotes the possuk in מלכים א ז כג :
וַיַּ֥עַשׂ אֶת־הַיָּ֖ם מוּצָ֑ק עֶ֣שֶׂר בָּ֠אַמָּה מִשְּׂפָת֨וֹ
עַד־שְׂפָת֜וֹ עָגֹ֣ל ׀ סָבִ֗יב וְחָמֵ֤שׁ בָּֽאַמָּה֙ קוֹמָת֔וֹ וקוה
[וְקָו֙] שְׁלֹשִׁ֣ים בָּֽאַמָּ֔ה יָסֹ֥ב אֹת֖וֹ סָבִֽיב׃
"Then he made the pool of cast metal, 10 cubits across from
rim to rim, rounded, and it was 5 cubits high, and it measured 30
cubits in circumference".
Some have scorned the Torah by pointing out that the ratio
identified here is inaccurate. Mathematicians have proven that the
actual ratio is Pi, or 3.1415....
This means that the ratio of 1:3 identified in the possuk and the
gemara is off by about 4.5 percent.
Now, the term for circumference in the possuk is קו. However, for
some reason the כתיב has it spelled קוה.
Explains the גר"א: the גמטריה of קו is 106. The גמטריה of קוה
is 111. The ratio of 106 to 111 is the same as the ratio of 3 to Pi
/ 3.1415.... (106/111 = .9549..., and 3/3.1415 = .9549...)
This can be illustrated by the following equation: 3 ×
(111/106) = 3.1415.
3.1415 is Pi down to four decimals!!!
Some have explained that in general the קרי is an expression how we
apply the Torah into our lives. Sometimes, it must vary from
the כתיב, when the latter, as a
manifestation the absolute truth, is beyond our ability
to apply.
Although one could get very technical and say that the above
calcultion works only down to four decimals, as Pi is
3.14159265.... and 3 × 111/106 is 3.14150943....
However this tiniest discrepancy is not an issue; because in fact,
Shlomo could not make a perfectly scientific circle down to such a
minute measure. Every human made circle must be at least very
slightly oval, thus slightly diminishing the length of the
circumference in ratio to the (longer) diameter of the
oval.
Thus, in reality, it is perfectly possible that the
circumference was actually 30 × 111/106 and
not exactly 10 × pi.
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