21 November 2006
The problem with files ending ".txt" given an "Access denied" error page has been
remedied by removing the ".txt" from the file names for the present which Surrey University's
techies investigte the problem. Apologies to those who have not been able to access
10,000 dps of Phi, 25,000 bits of Phi
and Maple program to plot seed head patterns.
11 November 2006
A new section on the Silver Means has been added to
the Introduction to Continued Fractions page.
14 August 2006
The Calculator for counting the number of
sets of Fibonacci numbers with a given sum has been extended to find all numbers
or the first in a given range with a specific number of Fibonacci sets (find n given R(n)).
26 July 2006
OOps! I put the Phi4 spiral
(r=Phi4 theta) in the Excel spreadsheet instead of the Phi spiral
(r=Phitheta) - now corrected. That section
has been split into The Fibonacci Squares Spiral
and The Golden (or Phi) Spiral and the
relationship between the two clarified.
The 12th Fibonacci Conference was fanastic with many new results presented, some of which will find their
way onto this site in the coming weeks and months!
11 July 2006
An Excel spreadsheet together with instructions for generating a Golden Spiral
using a spreadsheet is now included in the Golden Spiral
section of the 2D Geometry page.
25 May 2006
When giving the talk below (May 12 2006) - which was about
what Robert Langdon might have given in his lecture(s) on Symbolism In Art Class
at Harvard, as given in the brief summary in chapter 20 on Dan Brown's "The Da Vinci Code"
- I noticed several golden sections in the huge tapestry at the East end of Coventry Cathedral
and checked them out on a print of Sutherand's huge work.
What I found is detailed in a new section:
Graham Sutherland's Tapestry in Coventry Cathedral on
Fibonacci Numbers and The Golden Section in Art, Architecture and Music
12 May 2006
An FRIDAY MAY 12th 2006 at
Do You Believe In The Da Vinci Code?
where I talked about The Fibonacci Numbers and The Golden Section in Dan
Brown's The Da Vinci Code'
and other speakers addressed other issues raised by this popular book.
12 December 2005
Phi to 10,000 decimal places and to 25,000 binary places, computed using Maple, in separate text files
with links to them from the Golden Section and Geometry page.
24 October 2005
After the section which shows that F(n)/F(n-1) tends to Phi as n gets larger, there is now a
new section finding the ratios of F(n)/F(n-2), F(n)/F(n-3), ... and these ratios tend to
Phi2, Phi3 etc.
16 August 2005
AAgh! The final section of the new the Fibonomials page is now included!
The large brackets are now rendered in a way that still allows Text Increase but should be visible now on all browsers.
6 August 2005
A new page! Finding recurrence relationships between the squares, cubes and all powers of Fibonacci numbers leads us to
a table of numbers in many ways similar to Pascal's Triangle and the Binomal numbers (coefficients): they are called
28 May 2005
20 new formulae have been added to the Fibonacci and Phi Formulae page taking it to
almost 240 formulae in total. The new ones are from
A T Benjamin and J J Quinn's
Proofs That Really Count (2003)
and all the relevant Fib, Phi etc formula from that book are references on the new updated Formulae page.
Benjamin's and Quinn's book proves each formula in a neat and fun way, using counting arguments based on
25 February 2005
Well in time for the next Pythagrean Triple Date (4/3/05), the Pythagorean
Triples page has been updated with more sections, a calculator with very fast counting algorithms and
a new Puzzles and Problems section.
8 February 2005
Two new pages:
The Fibonacci Sequence Visualiser is now online.
It was designed for Casey Mongoven
to use for his music composition and plots a series of numbers in a graph-like form.
Also, the Pythagorean Triangles
page has been extended with two sophisticated calculators (no plug-ins or downloads
7 January 2005
The sections on
Pentagrams and Pentagons in the
Two-dimensional Geometry and the Golden section
or Fantastic Flat Phi Facts page have been simplified and updated.
© 1996-2008 Dr Ron Knott