Mystical systems
Golden Ratio
Direct answer
Golden Ratio: The golden ratio is the number about 1.618, one plus the square root of five divided by two, which cuts a line so that the whole is to the longer part as the longer is to the shorter.
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At a glance
- Also called
- golden section, golden mean, divine proportion, phi 1.618
- Found in
- Mystical Systems
- Related
- Sacred Geometry, Fibonacci Sequence, Platonic Solids, Vesica Piscis
The golden ratio is the number about 1.618, one plus the square root of five divided by two, which cuts a line so that the whole is to the longer part as the longer is to the shorter.
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What is the golden ratio in simple terms?
The golden ratio is a fixed number, about 1.618, often written with the Greek letter phi. A line is cut in the golden ratio when the whole line is to its longer part as the longer part is to the shorter. Its exact value is one plus the square root of five, all divided by two. A rectangle with sides in this ratio can have a square cut from it and leave a smaller rectangle of the same shape, and the diagonal and side of a regular pentagon stand in the ratio too.
A great deal of legend has gathered round the number. It is said to rule the Parthenon, the pyramids, the human face and the nautilus shell. Careful measurement supports few of these claims. The mathematics needs no such help: the ratio is real, exact and easy to draw.
On the tree of the hidden arts: Sacred geometry.
What sets Golden Ratio apart
What sets this number apart is a property no other positive number has: its square is itself plus one, and its reciprocal is itself minus one. That is why a golden rectangle sheds a square and leaves a smaller copy of itself, again and again without end, and why the ratio cannot be written as any fraction of whole numbers. It is, in a precise sense, the hardest of all numbers to approach by fractions, which is the reason it turns up where plants space their seeds.
- Exact value: one plus the square root of five, divided by two; about 1.6180339887
- Defined by: Euclid, Elements, about 300 BCE, as the cut in extreme and mean ratio
- Named golden: Martin Ohm, 1835, in German as goldener Schnitt
- Letter phi: proposed about 1909 by Mark Barr, after the sculptor Phidias
- Truly present: in the regular pentagon, where diagonal and side stand in this ratio
- Not shown: in the Parthenon, by any measurement not chosen to show it; the Great Pyramid fits, as a plain rule of slope also does
Often mistaken for something else: The Fibonacci sequence is a list of whole numbers; the golden ratio is the single number their neighbouring ratios approach and never reach.
The story behind Golden Ratio
Luca Pacioli called it the divine proportion in a book of 1509 that Leonardo da Vinci illustrated. The name golden section first appears in a German textbook by Martin Ohm in 1835, and the letter phi was proposed about 1909. Adolf Zeising, in the 1850s, spread the idea that it was a universal law of beauty.
Why Golden Ratio matters
Golden Ratio is the best known number in sacred geometry, and the clearest case of true mathematics carrying untrue claims.
How to read Golden Ratio
Draughtsmen and designers treat it as one pleasing proportion among several; a reader can draw it with compasses and test any claim made for it.
Golden Ratio in practice: an example
A reader who measures a bank card finds its sides near 1.59 to 1, close to the golden ratio and not equal to it.
Where readings of Golden Ratio go wrong
Most claims that it governs buildings, bodies and paintings depend on where the measuring starts. It has no power over anything.
Sources and editorial method
This entry summarizes the tradition in the Almanac's own words; where no source is listed, it is an editorial summary rather than a primary text, and symbolic readings are named as the tradition's, not as fact.
What they are held to mean is a tradition, and many popular claims of the golden ratio in buildings, bodies and paintings do not survive measurement.
- Source
- The Great Almanac Dictionary
- Category
- Mystical Systems
- Aliases
- golden section, golden mean, divine proportion, phi 1.618, golden ratio meaning
- Last updated
- 2026-09-26
See Golden Ratio in your personal almanac
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Common questions
What is the golden ratio in simple terms?
It is the number about 1.618. Cut a line so that the whole is to the longer piece as the longer piece is to the shorter, and the two pieces are in the golden ratio.
Is the golden ratio really in the Parthenon?
Not by any measurement that was not chosen to find it. The published figures depend on which steps and edges are counted, and no ancient source says the builders worked by it.
How is the golden ratio linked to Fibonacci numbers?
Divide a Fibonacci number by the one before it and, past the first few, the answer lies near 1.618. The further along the sequence, the closer it comes, though it never arrives.
