spring-of-mathematics:

Golden Ratio φ = (1+sqrt(5))/2 = 1.6180339887498948482…
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0. Two quantities a and b are said to be in the golden ratio φ if
(a+b)/a = a/b = φ
One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ:
(a+b)/a = 1+ b/a = 1+1/φ
Therefore: 1+1/φ = φ  Multiplying by φ gives: φ^2 - φ - 1 = 0
Using the quadratic formula, two solutions are obtained:: 
φ = (1- sqrt(5))/2 or φ = (1+sqrt(5))/2
Because φ is the ratio between positive quantities φ is necessarily positive:
φ = (1+sqrt(5))/2 = 1.6180339887498948482…
See more at Golden Ratio.
Image: Phi (golden number) by Steve Lewis.

spring-of-mathematics:

Golden Ratio φ = (1+sqrt(5))/2 = 1.6180339887498948482…

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0. Two quantities a and b are said to be in the golden ratio φ if

(a+b)/a = a/b = φ

One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ:

(a+b)/a = 1+ b/a = 1+1/φ

Therefore: 1+1/φ = φ 
Multiplying by φ gives: φ^2 - φ - 1 = 0

Using the quadratic formula, two solutions are obtained::

φ = (1- sqrt(5))/2 or φ = (1+sqrt(5))/2

Because φ is the ratio between positive quantities φ is necessarily positive:

φ = (1+sqrt(5))/2 = 1.6180339887498948482…

See more at Golden Ratio.

Image: Phi (golden number) by Steve Lewis.

Chrome Pirate

This western Russian river empties, fused into the Barants Sea, a powerful, unyielding display of natures enduring truth. River meets it’s mother ocean. A deafening roar bellows from the rivers life force, heralding the path home into tundra and taiga, the interior of the Kola Peninsula. An army of invaders, festooned in chrome and fins, eagerly staged at the rivers entrance, about to return from one, maybe even four campaigns lasting years out at sea. The Atlantic Salmon of the Yokanga are formidable. Marauders of the open sea, they move through the powerful gates of the Yokanga like belligerent pirates raiding their home port. These Atlantic Salmon of the Yokanga show no mercy as only they are capable of moving up and over impossible waterfalls. A well presented fly is accepted as an equitable challenge fit for a returning warrior and the angler who has been called to meet face to face with a destiny forged by an unyielding desire…