"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

0.618 is the solution which is also part of the Golden rule thing.

Golden rule thing is that if you take a rectangle whose sides are 1 and
1+a, then chop off a 1 x 1 square from one end, the remaining piece is a
rectangle whose sides are in the same ration as the rectangle you
started with. That's where the equation comes from. You're right, the
solution is a=.618, which means the long side of the original rectangle
is 1.618.

I only
got that from Googling Fibonacci:-)

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

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.

e to the power i (pie) = -1 where i = sqrt -1
substitute j for i (if you are younger than me)
Also a bit of useless information but could explain the existence of a
God:-)



--
Kay