But where the tech­ni­cal notation:

(1 + 0.618) × 0.618 = 1, or even x + x2 = 1,
would still seem not to help our immediate intuition, watch a simple ta­ble comparing just a few decimal steps, where the miracle takes shape.

0.1 ×1.1 =0.11 0.2 ×1.2=0.24
0.3 ×1.3=0.39 0.4 ×1.4=0.56
0.5 ×1.5= 0.75 0.6 ×1.6=0.96
0,6180399 × 1,6180399 = 1,00001321799201    
0.7 ×1.7=1.19 0.8 ×1.8 =1.44
0.9 ×1.9 =1.71
Both irrational num­bers derive from the ex­pres­sion (√5±1)÷2, where deserves to be noted how the two solutions of the reversed expression – (1±√5)÷2 to negative and positive results – essentially introduce a spa­ce-time back or forward, cen­tred around the point 0
This Proportion and even its equation's build on can be well and sim­ply re­presented /ob­tained through the ge­o­met­ric pro­cess - say using only straight­edge and com­pass - start­ing from a square with giv­en side = 2.