Monday, August 24, 2020

PI Todays Daf

 

 



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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