Golden Ratio and Fibonacci Sequence

Just been googling this in an idle moment.
Makes you think that we must have only scratched the surface of the mathematical rules that shape our environment.
Have a google...its mind boggling....not least for the questions it raises...how did the egyptians know it?!

 

er, why wouldn't the Egyptians know them? They are both very simple progressions
Golden ratio = 1+(1/(1+1/(1+1/(1..... ~1.618
Fibonacci 1,1,2,3,5,8,13,21 etc.....

Remember they didn't have much to do during the day so I suspect they could put more effort into maths than we do now. That is why most thing Mathematical were discovered by the Greeks, Egyptians, Babylonians etc some 2,5000 years ago. A lot of the proofs were done in the last 3 centuries, mainly by the French and English.

For any one interested in that sort of thing read 'Fermat's Last Theorum'

 

I think 'most thing(sic) Mathematical were discovered by the Greeks, Egyptians...' is probably unsupportable. I'm pretty sure the Egyptians didn't have a concept of infinite sequences, and although Archimedes had some concept of limits he didn't have the abstract tools to handle them.

Anyway the 'Golden Ratio' is easy to see. If you take a rectangle and partition it into a square and another rectangle and the sides of the two rectangles have the same ratio then it's 'Golden'. If a rectangle is AxB (and A is larger than B) then it is 'Golden' if

A/B = B/(A-B)

for convenience B could be '1'...

A = 1/(A-1)

or

A(A-1) = 1

A is the 'Golden Ratio' of about 1.618.

A couple of highly recommended books about easy maths history,

A History of Pi and Zero: The Biography of a Dangerous Idea.

Paul

 

On a hifi note, what do people think of the use of 'golden ratios' by Cardass for cabling and I believe for the ideal listening room?

(details on the cardass website)

 

Who knows - there may be something in it re the listening room, I suspect not re the cables. My guess is that they don't care or know themselves - but from a marketing perspective it sounds suitably mathematico-mystical and pythagorean to make folks think that they know someting we don't.

 

I don't see any good reason for the ideal room to be rectangular.

Paul

 

It should be yellow, black & rectangular.

 

Like a wasp in a box?

 

No, wedge shapes inside. I see them everywhere.

 

The ideal listening room is infinite.

 

There there. Back on the couch.

 

Infinite wedges?

 

Ouch. Not. Time for you to do some work perhaps. Taxpayers' money and all that.

 

It has kind of wedge shapes inside.

 

cheese in a tin?

 

Oh, what does it mean?

 

Cheese in a tin is more resilliant to mould? maybe?

 

Oh, I see them everywhere,

Everywhere, do you hear me?

 

I see the voices, i dont hear them, i see them.
They tell me to jump, but i ignore them.

 

What you have been seeing everywhere you look are those yellow and black signs used to indicate a fallout shelter in buildings.