Rupert (W.Yorkshire) wrote:
"K" wrote in message
...
"Rupert (W.Yorkshire)" writes
"K" wrote in message
...
"Rupert (W.Yorkshire)" writes
"K" wrote in message
...
Broadback writes
Not being an artistic sort of chap, I can admire well designed gardens
but
lack the vision to design them. I am planning on an island rose bed,
what
would be a pleasing shape, is an oval or oblong with circular short
ends
best? Also what proportion of length to breadth, is 2:1 pleasing to
the
eye?
Shouldn't the Golden Ratio come in here? (Square root of 5) divided by
2
if I remember rightly.
The answer is about 1.6 so summat is wrong. Looked it up (1+sqrt5)/2.
Architect man spent ages wiffling away about this to me last week (at
vast
expense).

Yep. It's the solution to a = 1/(1+a). Keep substituting for a in the
rhs
and you get the 'continued fraction 1/(1+1/(1+1/(1+....))). Of no use to
man nor beast but a pretty mathematical form.

And doesn't the Fibonacci series link into this somehow too?
--
Kay
snip

So what exactly is the link to Fibonacci - is it that the ratio of
successive terms tends to .618?


That's good enough for me and is explained here
http://www.mcs.surrey.ac.uk/Personal...at.html#golden

For those who think we are drifting OT - the Fibonacci series turns up

all over nature. Each term is the sum of the two previous, starting 0 1,
so:
0 1 1 2 3 5 8 13 21 35 56 91 ....

and whenever you see a set of spirals - sunflower, that spirally
cauliflower, cacti, fircones - counting the spirals in one direction then
counting the spirals in the direction crossing the first, gives you two
successive terms of the Fibonacci series.



Kay


Thank you all for your help and useful suggestions.