Endiaferousa kai h paratirisi tou Manoli Fanourgaki:

φ^2 - φ - 1 = 0

Δ=sqrt(1+4) = sqrt(5)

φ = ( 1 + - sqrt(5) ) / 2

Δεχόμαστε τη λύση με +.

Παρατηρώ ότι η λύση με το - ειναι το 1/φ

Mia akoma paratirisi einai kai oti o logos duo sunexomenwn orwn tis akolouthias Fibonacci (estw x kai y o epomenos) y/x teinei sto φ otan oi oroi teinoun sto apeiro. Malista an kanoume ena grafima, me tin akolouthia ston orizontio kai ton logo duo sunexomenwn ston katheto, to sxima proseggizei auto tis aposvenomenis talantwsis, me eutheia aposvesis to φ.

Án pali paroume ton antistrofo logo, x/y, to apotelesma tha proseggizei to θ, pou mallon (den exw apodeiksi) isoutai me 1/φ.

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