Golden Ratio in Judaism: God’s Signature in Creation

Hello, I’d like to ask about the concept of the golden ratio — also known as the divine proportion, which appears in nature across many fields, and also seems to appear in the Torah in approximate form, both in Noah’s Ark and the Ark of the Covenant. What does the Torah say about this kind of “proof” of divine design, and are there other examples? Also, regarding mathematics, why is the number π (pi) rounded to 3 in the Talmud?

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Indeed, the golden ratio is a fascinating phenomenon that many have pointed to as “the fingerprint of God” in creation, or “God’s signature” in the universe. Unfortunately, there are not enough articles on this important subject, which can teach us about the divine planning behind all of creation.

As Wikipedia summarizes: “According to some theories, the golden ratio was first discovered by a student of Pythagoras. It was described in Euclid’s Elements about 2,300 years ago. In those days, it was called the ‘extreme and mean ratio.’ Luca Pacioli, an Italian Renaissance mathematician, dedicated an entire book to it and called it The Divine Proportion. The ratio represents many dimensions and patterns in nature, and from classical Greece onward, it was also used in art and architecture.”

The golden ratio appears (or is claimed to appear) in:

• Geometry: pentagrams, pentagons, golden rectangles, golden triangles.

• Botany: leaf arrangements on stems, seed placement in apples, pine cones, sunflower heads, rose petals.

• Crystallography: quasicrystals with fivefold symmetry, such as the discovery by Professor Dan Shechtman, who received the 2011 Nobel Prize in Chemistry.

• Animals: deer antlers, the ratio of bees in a hive.

• Human creativity: art, architecture, and even certain aspects of psychology.

Pi in the Talmud

Regarding pi, it is mentioned by the sages in the Talmud (Eruvin 14a): “Any circle that has a circumference of three handbreadths has a width (diameter) of one handbreadth. From where do we know this? Rabbi Yochanan said: it is derived from the verse: ‘And he made the Sea of cast metal, ten cubits from brim to brim, round in shape, five cubits high, and a line of thirty cubits encircled it all around’ (Kings I 7:23).”

From this, the Talmud records that the ratio of a circle’s circumference to its diameter — what we call pi, is 3.

It has been explained that it is precisely because the number is not exact that the sages needed to cite the verse. The point was to teach that halachah (Jewish law) does not demand mathematical precision beyond the whole number of 3. If Jewish law had required full accuracy, there would have been no need for a verse to justify the value; they would have stated the precise decimal.

The golden ratio — also called the divine proportion, is indeed a remarkable phenomenon that suggests divine order and harmony in the universe. Similarly, the way pi is treated in the Talmud reflects how Torah law often values practical, applicable guidance over absolute mathematical precision.