phi = (1+racine(5))/2
phi² = (1+racine(5))²/4 = (1+2racine(5)+5)/4
phi+1 = (1+racine(5))/2 + 1
si phi²=phi+1, alors:
(1+2racine(5)+5) - (1+racine(5)) - 1 = 0
----------------------- -----------------
4 2
(1+2racine(5)+5) - (2+2racine(5)) - 4 = 0
----------------------- ------------------ ----
4 4 4
(1+2racine(5)+5) - (2+2racine(5)) - 4 = 0
1 + 2racine(5) + 5 - 2 - 2racine(5) - 4 = 0
0 = 0
Les 2 membres sont égaux, donc la condition est bonne.
1 (1+racine(5))/2 - 1
--------------------- = --------------------------
(1+racine(5))/2 1
(1+racine(5))/2 * ( (1+racine(5))/2 - 1) = 1
