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The golden line / rectangle is for the eye the best ratio. You find this ratio in nature and in the best designs.
Golden  ratio line
What is the Golden Ratio?

The golden ratio is an irrational mathematical constant.

phi= 1.6180339887
phi= 0.6180339887

Explanation Golden ratio line:

Golden  ratio line

Point (S) on the line A to B divided the line in two
"Golden Sections"

The golden line ratio A to S to B.
*S1 is mirror point from S Golden  ratio line

Golden  ratio line

In this website the golden ratio is denoted by the Greek lowercase letter phi (phi): 1.6180339887, while its inverse, (1/phi), which is also equal to (phi-1), or 0.6180339887... is denoted by the uppercase variant Phi phi.

The figure on the right illustrates the geometric relationship that defines this constant. Expressed algebraically:

phi

This equation has one positive solution in the algebraic irrational number

phi
Golden ratio conjugate

phi

The negative root of the quadratic equation for φ(the "conjugate root") is 1/Φ = 1- Φ = -0.618.
The absolute value of this quantity (=0.618) corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, b/a), and is sometimes referred to as the golden ratio conjugate.It is denoted here by the capital Phi (Φ):

Explanation Golden ratio Rectangle:

phi

Golden rectangle construction:
1) Construct a square (green).
2) Draw a cirle from the midpoint M opposite corner C and R.
3) Extend line A,S to B.
4) Defines the long dimension of the rectangle point B.

Explanation Golden ratio Eye point:

phi

Next to the square shows up a new golden rectangle. You see a endlessly repeating.


Golden place:


phi

The ideal place in the golden rectangle for example a person.



What is the Golden Ratio?
Calculator
Calculate your golden line&rectangle
Input line:  
Placed on (page background):
Align Golden rectangle:
Rotate background page:
Results
Border problem: Right Footer

*The preview example is 300% from a pixel ratio:
Golden rectangle: W:100 x H:61.803 pixels.
Placed on: none W:1 x H:1 pixels.



*The golden rectangle example is 300% from:
a pixel ratio W:100 x H:61.8 pixels.

0
Y
X
C
A
B
S
S1
M
E1
E2
none W1 X H1
E1
E2
E3
E4
P1
P2
P3
P4
Line: E1/3
Line: P1/3
Line: P2/4
Line: E2/4
Golden rectangle W100 X H61.803

Align Golden Rectangle is Golden Rectangle to none

Top: Y 0
Left: X 0
Right: X -99
Footer: Y-60.803

Page background is:

Width: 1 X Height: 1

The golden line:


Golden ratio line
100
38.2
61.8

The Golden Rectangle:

Width(AB): 100 X Height(AC): 61.803


S vpoint from A : 61.803 INT: 61.8
S point from B : 38.197 INT: 38.2

Golden ratio rectangle
61.8
30.9
30.9
38.2
61.8
69.1
100
69.1
38.2
7.3
23.6
61.8

Rectangle: sizes

A to M= 30.902 INT: 30.9
A to S1= 38.197 INT: 38.2
A to S= 61.803 INT: 61.8
A to B= 100 INT: 100
A to C= 61.803 INT: 61.8

M to A= 30.902 INT: 30.9
M to S1= 7.295 INT: 7.3
M to S= 30.902 INT: 30.9
M to B= 69.098 INT: 69.1

M to R (radius) = 69.098 INT: 69.1

S1 to A= 61.803 INT: 61.8
S1 to M= 7.295 INT: 7.3
S1 to S= 23.607 INT: 23.6
S1 to B= 61.803 INT: 61.8

S to A= 61.803 INT: 61.8
S to M= 30.902 INT: 30.9
S to S1= 23.607 INT: 23.6
S to B= 38.197 INT: 38.2

B to A= 100 INT: 100
B to M= 69.098 INT: 69.1
B to S1= 61.803 INT: 61.8
B to S= 38.197 INT: 38.2

C to B= 117.557 INT: 117.6



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Kind regards,

Bas Kostelijk

Creative • Developer • Entrepreneur
Thanks for visiting The Golden Ratio Calculator I hope you will enjoy. Get inspired and share it to the world!