exp(phi number)

Input

exp(ϕ)

Exact result

e^ϕ

Decimal approximation

5.04316564336002865131188218928542471032359017541384636030200019677778696091...

Property

e^ϕ is a transcendental number

Alternate form

e^(1/2 (1 + sqrt(5)))
e^(1/2 + sqrt(5)/2)

Number line

Number line

Continued fraction

[5; 23, 6, 294, 2, 1, 4, 1, 1, 1, 18, 1, 5, 1, 3, 1, 3, 1, 1, 1, 16, 1, 2, 4, 3, 1, 1, 18, 3, ...]

Alternative representation

e^ϕ = e^(-2 cos(216 °))
e^ϕ = e^(2 cos(π/5))
e^ϕ = exp(root of -1 - x + x^2 near x = 1.61803)
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POWERED BY THE WOLFRAM LANGUAGE