Golden ratio

The golden ratio is the positive root of the quadratic x^2 = x + 1, equal to about 1.618. It gives the proportion in which a line or rectangle is divided so that the whole is to the larger part as the larger part is to the smaller.

\varphi = \frac{1+\sqrt{5}}{2}

What the symbols mean

the golden ratio, a dimensionless number approximately equal to 1.618
the principal square root of 5

About this formula

  • FieldMathematics
  • TopicIrrational numbers and constants
  • LevelHigh school
  • Also calledgolden mean, golden section, phi, golden ratio formula, phi equals one plus root five over two, golden ratio value
  • SourceWikidata Q41690

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