Tag Archives: Mathematics

Secrets of Pi

This week’s conjoined Torah portions of Vayak’hel and Pekudei conclude the description of the Mishkan’s construction. The Haftarah for Pekudei is a passage from the seventh chapter of I Kings (the exact verses vary by community) describing King Solomon’s construction of the Jerusalem Temple. One of the most breathtaking structures standing in front of the Temple was the “Molten Sea”, a large bathtub for the kohanim to immerse in (as per Rashi and II Chronicles 4:6). The Tanakh describes that the bath was circular, sitting upon a base of twelve oxen statues, and had a total depth of five cubits, roughly ten feet. It held a volume of alpayim bat, “two thousand baths” of water (I Kings 7:26). In fact, the Hebrew bat (בת) is likely the etymology for the English word “bath”!

Illustration of the First Jerusalem Temple, or Solomon’s Temple, with the Molten Sea on the right.

What’s most perplexing in the description is that we are told the diameter of the circular tub was 10 cubits, yet its circumference was 30 cubits. Throughout history, many have pointed out that this seems to be an error! We all know that the ratio of a circle’s circumference to its diameter is π or Pi, which is 3.1415926 (and so on). So, the Tanakh should have said that the diameter was 10 cubits and the circumference was 31 or 31 and a half cubits. How do we solve this puzzle, and what deeper significance does Pi hold in the Torah?

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Mind-Blowing Gematriot

In this week’s parasha, Ha’azinu, Moses cautions the people in his final song to carefully fulfil “all the words of this Torah, for it is not an empty thing for you” (Deuteronomy 32:46-47). The Ba’al HaTurim (Rabbi Yakov ben Asher, 1269-1343) comments here that, on a deeper level, the words “for it is not an empty thing for you” are referring to gematriot, the numerical calculations and mathematical codes embedded in the Torah, that emanate from the divinity and precision of the Hebrew language. The general public often disparages gematria as being unreal or artificial in some way, a soup where anyone can find anything they are looking for. This couldn’t be further from the truth. While some have certainly abused gematria in unnatural ways, there is a legitimate foundation and system to it. Continue reading

The Meaning of Tiferet

In the parasha of Ki Tavo, we read:

And God has affirmed today that you are His treasured people, as He promised, who shall observe His commandments, and He shall place you above the nations that He has made, for fame, renown, and glory, and you shall be a holy nation unto Hashem, your God, as He promised.

The unique word for “glory” here, tiferet (תפארת), appears just three times in the whole Torah, and another 26 times or so in the rest of the Tanakh (not including the related tiferah). That it appears specifically three times in the Torah is no coincidence, for Tiferet is the third of the lower Sefirot, and is always associated with the number 3. It sits at the centre of the mystical Tree of Life, and is the only Sefirah interlinked with all the others. In Kabbalistic texts, Tiferet holds tremendous significance, and is discussed perhaps more than any other Sefirah. It is the Sefirah of the Torah, and of Israel, and the one associated with the very Name of God, the Tetragrammaton (יהוה). What is so special about Tiferet and why is it so important? Continue reading