Everything about golden ratio

-
The Golden Ratio (symbol is the Greek letter "phi" shown at left)
is a special number approximately equal to 1.618
It appears many times in geometry, art, architecture and other areas.

The Idea Behind It

We find the golden ratio when we divide a line into two parts so that:
the whole length divided by the long part
is also equal to
the long part divided by the short part
golden ratio (a+b)/a = a/b = 1.618...
parthenon golden ratio





Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece, but it is not really known if it was designed that way.

In nature most of the creatures anatomy follows golden ratio. Most of beautiful peoples faces follow golden ratio. 
And here is a surprise: when we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio.
In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:
A
B
 B/A
2
3
 1.5
3
5
 1.666666666...
5
8
 1.6
8
13
 1.625
...
...
 ...
144
233
 1.618055556...
233
377
 1.618025751...
...
...
 ...
We don't even have to start with 2 and 3, here I chose 192 and 16 (and got the sequence 192, 16, 208, 224, 432, 656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, ...):
A
B
 
B / A
192
16
 0.08333333...
16
208
 13
208
224
 1.07692308...
224
432
 1.92857143...

7408
11984
 1.61771058...
11984
19392
 1.61815754...



Comments

Post a Comment

Popular posts from this blog

View one layer

-
If you're working with multiple layers and you want to view one layer on its own, there's no need to hide all the others manually, simply hold down Alt and click the Eye icon of a layer to make every other layer invisible. Hold down Alt and click again to reveal them.
Read more

Photoshop shortcuts

-
Mastering these shortcuts will help you work smarter, save time. Cmd/Ctrl+Shift+Alt+E  will merge a copy of all Layers F  Cycle through workspace backgrounds X  Change your foreground and background colours D  Reset foreground and background colours to black and white ]  and  [  Change your brush tip size Cmd/Ctrl+J  Duplicate a layer or selection Space Bar  Hold Space and drag to navigate around the image TAB  Hides or shows all panels and tools Cmd/Ctrl+T  Transform a layer Cmd/Ctrl+E  Merge selected layer down, or merges several highlighted layers Cmd/Ctrl/Ctrl+Shift+Opt+S  Save for web & devices Cmd/Ctrl+L  Bring up levels box Cmd/Ctrl+T  Open Free Transform tool Cmd/Ctrl+M  Open Curves Cmd/Ctrl+B  Edit Colour Balance Cmd/Ctrl+Shift+Opt+C  Scale your image to your preferred state Cmd/Ctrl+Opt+G  Create clipping mask Cmd/Ctrl+0  Fit on screen Cmd/Ctrl+Shift+...
Read more

GST relief for home buyers, realtors warned

-
VISAKHAPATNAM: In major relief to property buyers, especially apartments, Goods and  Sales Tax  ( GST ) authorities have warned realtors and construction companies of punitive action if they do not pass on the benefits of input tax credit to the buyers by reducing the prices. N Srujan Kumar, GST commissioner, Vizag, told TOI that the  Central Board of Excise and Customs  at Delhi and its offices in various states have received several complaints that people who have booked flats and made part payment were asked to pay a higher tax for instalments paid after July 1, 2017. for more details https://timesofindia.indiatimes.com/city/visakhapatnam/gst-relief-for-home-buyers-realtors-warned/articleshow/62004279.cms
Read more