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based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


is the golden ratio , with numerical value .
  • Mathematical constant treated as numeric by NumericQ and as a constant by D.
  • GoldenRatio can be evaluated to any numerical precision using N.
Numerical value:
Numerical value:
Click for copyable input
Evaluate to any precision:
Do exact computations:
Simplify GoldenRatio expressions:
TraditionalForm formatting:
Golden ratio rectangle:
Make a phyllotaxis pattern ("simulated sunflower head"):
Compute the Fibonacci numbers:
Corners of an icosahedron:
Position of 1s in a Fibonacci substitution system :
Compute the effective "inverse" of the Fibonacci numbers:
Simulated palm tree trunk:
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