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#988659 - Sat Jun 15 2013 04:43 PM Golden Ratio
gracious1 Offline
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Registered: Tue May 01 2012
Posts: 714
Loc: New York USA
If the Golden Ratio phi is irrational, why is it called the Golden Ratio? confused


Edited by gracious1 (Sat Jun 15 2013 04:43 PM)

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#988759 - Sun Jun 16 2013 08:29 AM Re: Golden Ratio [Re: gracious1]
JanIQ Offline
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Registered: Thu Jul 09 2009
Posts: 587
Loc: Antwerp<br>Belgium
The Golden Ratio is basically a ratio between two given numbers. If this ratio happens to be the irrational number 1.6180339887 etc, the ratio is called the Golden Ratio.
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#989805 - Thu Jun 20 2013 10:26 PM Re: Golden Ratio [Re: gracious1]
nautilator Offline
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Registered: Mon Jan 09 2012
Posts: 267
Loc: Pennsylvania USA
Because the definition is any pair of numbers that satisfiess the ratio a/b = b/(a+b).

Solving it (taking a=1) does get an irrational result though. (1+sqrt[5])/2.

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#989812 - Thu Jun 20 2013 11:19 PM Re: Golden Ratio [Re: gracious1]
kevinatilusa Offline
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Registered: Fri May 17 2002
Posts: 315
Loc: Riverside, CA, USA        
One of the first places the golden ratio appeared was as part of the Golden Rectangle (a rectangle that can be divided into a square plus a smaller copy of the original rectangle -- see the picture at right in the link).

Golden rectangles can come in any size: if you double all the sides of a golden rectangle, you'll be left with a (bigger) golden rectangle. What's important is the ratio between length and width. And that ratio is the golden ratio.

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