Linear progressions and surface division by the same number are common in nature both geometrically and arithmetically. Multiplying each term by 1.618 or dividing by 0.618 can obtain the geometrical progressions:

1.0 x 1.618 = 1.618
Or
1.000 : 0.618 = 1.618
1.618 x 1.618 = 2.618
Or
1.618 : 0.618 = 2.618
2.618 x 1.618 = 4.236
Or
2.618 : 0.618 = 4.236

In the arithmetic progression each term is the sum of the preceding two terms:

0.618 + 1.000 = 1.618
1.000 + 1.618 = 2.618
1.618 + 2.618 = 4.236