Phi and the Square Root of 5.

Phi equals the square root of 5, plus 1, all divided by 2.

In Wikipedia and in Dr Ron Knott's website and in other places one sees this equation.
 I wondered WHY it was so.  No-one seemed to be able to really explain it,

So I looked at it,  and looked at it, and worked around it,
and came to an idea that may explain why.......

It really works out to 1.618033.......etc.  Absolutely astounding,  and it was known in the time of Plato, apparently.


It only works when sides are 1 and 2 and hypotenuse is square root of 5
=  1.618033.........

Otherwise the golden relationship gives a different but consistent value.

*****  Even 1 / phi =  Sq root of hyp -(minus) adjacent, all divided by  opposite.

Please click on images to enlarge them and be able to read them properly.  Thank you.

What does it all mean?  I have absolutely no idea.
It looks as if "Phi"  plateaus out at 1.793 604.......
who knows what it looks like at much higher numbers.

You can use this relationship where the square root of the hypotenuse is F(n+2) plus the adjacent side F(n) divided by the opposite side equals "Phi".
When the values are square root of 5    plus  1   divided by 2   the result is 1.61803........
otherwise the anatomy of "phi"  goes to 1.793604......

Please see "Anatomy of Phi" graph in previous post,  Refinding Phi Part 1,  6/13/2013



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I have found out that you can type the symbol for Phi, using character map.  Go to Start, all programs (or run), accessories, system tools and then character map,  where one then clicks on font needed, select, copy,  then go to Windows document.....edit....paste.  However sometimes it does not work when pasted on my blog.   I need to type it all out, print then scan it and use the result as an Image.   As above.

*******There is a great story by Sugata Mitra on You Tube or Ted Talks on NPR.org
regarding his million dollar idea for the "School in the Clouds".  He put a computer in a hole in the wall in a slum street in India,  and waited and watched (remotely).  Some time later he spoke with the children there.  They had taught themselves English, using character map!  Plus they said they'd like a better processor and a mouse!  The children taught each other!  It shows that  a group of children is potentially a Super Organism.  We might be dumbing down our people too much. 
Another wonderful Speaker on Ted is Arvind Gupta who makes toys out of trash.
In truth, there are spectacularly good Speakers on all kinds of subject.  It is awesome.
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