jc:

Have a look at this table below (somewhat corrupted when viewed in plain text) I did on what I understand the series to be:


Golden Ratio                                                    	
                                                        	
                                                Ratio           Angle (degrees)
Iteration       Side A  Side B  (A/B)           (arctan A/B)
1               1               1               1               45
2               1               2               0.5             26.56505118
3               2               3               0.666666667             33.69006753
4               3               5               0.6             30.96375653
5               5               8               0.625           32.00538321
6               8               13              0.615384615             31.60750225
7               13              21              0.619047619             31.75948008
8               21              34              0.617647059             31.70142967
9               34              55              0.618181818             31.72360296
10              55              89              0.617977528             31.71513352
11              89              144             0.618055556             31.71836855
12              144             233             0.618025751             31.71713288
13              233             377             0.618037135             31.71760487
14              377             610             0.618032787             31.71742458
15              610             987             0.618034448             31.71749344
16              987             1597            0.618033813             31.71746714
17              1597            2584            0.618034056             31.71747719
18              2584            4181            0.618033963             31.71747335
19              4181            6765            0.618033999             31.71747482
20              6765            10946           0.618033985             31.71747426
21              10946           17711           0.61803399              31.71747447
22              17711           28657           0.618033988             31.71747439
23              28657           46368           0.618033989             31.71747442
24              46368           75025           0.618033989             31.71747441
25              75025           121393          0.618033989             31.71747441
26              121393          196418          0.618033989             31.71747441
27              196418          317811          0.618033989             31.71747441
28              317811          514229          0.618033989             31.71747441
29              514229          832040          0.618033989             31.71747441
30              832040          1346269         0.618033989             31.71747441
31              1346269         2178309         0.618033989             31.71747441
32              2178309         3524578         0.618033989             31.71747441

Note that it pretty quickly settles out on a ratio of 0.618 (though it does show up as 0.61835 and 0.625 early on) and the angle is 31.72 degrees (or 31.7174744...).

I think someone made mention of the idea that maybe this series is one that approaches a given ration when the calculation is carried out a large number of times--the table above shows that it does.

I've also attached the calculations as an Excel spreadsheet.  Excel is a favorite tool of mine for repetitive calculations.

I note that the ratio of 1/1.618 is 0.618...

Interesting, but my mind is getting fried on this whole business.  

Do you want Golden Fries with that?

BM

P.S. I again refer you to the item I googled which has some high fallutin' derivations and constructions on the subject:

http://jwilson.coe.uga.edu/emt669/Student.Folders/Frietag.Mark/Homepage/Goldenratio/goldenratio.html


-----Original Message-----
From: Pre-patinated plastic gumby block w/ coin slot
[mailto:[log in to unmask]]On Behalf Of John
Callan
Sent: Thursday, February 03, 2005 9:21 AM
To: [log in to unmask]
Subject: [BP] Golden


Cuyler,

I may be doing something wrong, but I keep coming up with 1-1/4".  When
I went through the A/C=B/A routine I came up with .61538xxx and
.625xxx.  We are talking about a difference of 0.01+/-.  At this scale,
3"+/-, its a difference a craftsperson, can deal with it, probably with
sandpaper.  If I needed to work at microscopic level, I might want to
figure out how to increase the accuracy.  If I'm working on the
preliminary design for an airport this might be too much accuracy.