Replies

1. 
   Jimma | Apr 05, 2003 08:44pm | #1

   It is a series of numbers any two of which add up to the next number. For example: 1-1=2, 2-3=5, 3-4=7 etc. I know of no application to the Golden Mean, which is a ratio of 1:1.618 or thereabouts.

1. 
   roninfante | Apr 07, 2003 01:09pm | #6

   Assuming that the sequence starts 1, 1, 2,.... then the ratio of two terms, the n+1th term divided by the nth term is a pretty good approximation to the golden ratio. In fact the limit (as n goes to infinity) of these ratios is the golden ratio. The n doesn't have to be too large. For instance 8/5 = 1.6.

2. 
   DonaldCBrown | Apr 05, 2003 08:50pm | #2

   http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

3. 
   TomS | Apr 05, 2003 08:54pm | #3

   Fibonacci series is that each number is the sum of the previous two.

   1, 1, 2, 3, 5, 8, 13... etc. 

   This series can be employed as a method ofr pleasing proportions when designing furniture ('Shaping Wood' by Lonnie Bird pg 37)

   He also illustrates the Golden Mean of 1:1.618 and Hambidge rectangles based on arcs drawn from the previous sized drawer.

   It is an interesting book I got from the library.  I might even buy this one.

   TomS

1. 
   nikkiwood | Apr 05, 2003 09:08pm | #4

   I understand now that the series is built on the sum of the previous two numbers, but how do you start?

   For instance, if I am going to build a dresser, how can I use the Fibonacci series to determine height, width, and pleasing proportion for, say five drawers of different heights?

1. 
   MHargrove | Apr 07, 2003 09:04am | #5

   Start the sequence with whatever dimension you like. To an example (a five-drawer "pyramidal" chest), make the first width dimension any size you like.  Let's call that dimension A.  In a true Fibonacci series, the second drawer would be the same dimension (but let's give it a different name and call that dimension B).  The third drawer would have dimension C, which is the sum of A + B.  Drawer four has dimension D, which is B + C, and drawer 5 has dimension E, which is C + D.

   A crude graphic:

               A |----------|

               B |----------|

   C  = A + B |----------|----------|

   D  = B + C |-------------------|----------|

   E  = C + D |------------------------------|--------------------|

   Obvioiusly, you could turn this "sideways" and use the dimensions as depths instead of widths.  I just couldn't find a way to make that look good on a posting :-)

   Make sense?

   Edited 4/7/2003 2:08:14 AM ET by MarkH

   Edited 4/7/2003 2:08:36 AM ET by MarkH