Gaon Around in Circles

V Gaon

The Haftorah of parshas Vayakhel, Shemos is from sefer Melachim ספר מלכים (Kings I) 7:23 describes the pool that was built in the house of שלמה המלך (King Solomon). The verse describes the pool as being circular with a diameter of 10 אמה (cubits) across and a circumference of 30 cubits around. This presents a difficulty for any student of math because the circumference of any circle with a diameter of 10 would be 10 x π (i.e. approximately 31.415 cubits).

So why does the verse describe the circumference as 30 cubits? Even if the verse were rounding it to the nearest cubit it would be 31 cubits and not 30 cubits. אפיקורסים (bible critics) took this as an example of a lack of mathematical sophistication.  דער װילנער גאון (The Vilna Gaon) explains that this verse shows an extraordinary level of mathematical sophistication. He explains that the Hebrew word for circumference is קו, in this verse the word קו, is spelled קוה. The ה in this case is silent and at first glance redundant.


Kings ed


The Vilna Gaon explains that the ratio of π / 3 (using 3.1415 for π).

3.1415 / 3 = 1.04716

He points out that the numerical value of the word קו, is 106.( ק = 100,ו= 6)

The numerical value of d קוה.is 111 .( ק = 100, ו= 6, ה= 5)

The ratio of 111/106 = 1.04716

The extra ה makes it clear that the Torah was aware of π to the 10,000th measure of π in the word for circumference.