Comments on Puzzle #22397: It is Golden
By Rob in Japan (rgmjp)
peek at solution solve puzzle
quality: 
difficulty: 
solvability: line logic only
peek at solution solve puzzle
quality: difficulty: solvability: line logic only
Puzzle Description:
The Golden Ratio roughly 1.61803398875
#1: Jota (jota) on Jul 19, 2013
Phi!#2: JoDeen Mozena (ozymoe) on Jul 19, 2013
Semper Phi! lol#3: Norma Dee (norm0908) on Jul 19, 2013
Hi phi.#4: Thomas Genuine (Genuine) on Jul 19, 2013
This is the REAL Golden Rate.#5: Joe (infrapinklizzard) on Jul 19, 2013 [SPOILER]
Why?
If x=[SQR(5)+1]/2 then 1/x=x-1
or
Make a Fibonacci-serie with ANY two beginning element! The rate of the two last element will iterate to this Golden rate!
Here's how to construct the Golden Ratio: http://postimg.cc/image/63r6dh3sx/full/#6: Kristen Vognild (kristen) on Jul 20, 2013
It was drawn in Sketchup and the arc is a bit sketchy. So the numbers are mathematically generated and not taken from the drawing.
Make a square 1x1. From the midpoint of one side, make a radius to an opposite corner. Length radius = [sqrt(0.5^2 + 1^2)] = 1.1180339887498948482045868343656
Extend the arc to the baseline of the square. The excess equals [radius - 0.5] = 0.61803398874989484820458683436564
The total length of the rectangle = [1 + excess] or [radius + 0.5] = 1.6180339887498948482045868343656
The proportion of the length of the rectangle to the length of the square is [1.61803398874989484820458683436564 / 1] or 1.61803398874989484820458683436564 - the value of phi.
The Golden Ratio was used in a LOT of classical paintings.
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