because my Surrey university email is not available at present and the Altavista POP email service is no longer free.
A new continued fraction investigation on fractions formed from neighbouring square numbers has been added to the Introduction to Continued Fractions page - with thanks to Anthony Shaw for first spotting these patterns.
Fernando Hirujo tells me that Donald Knuth's third edition of "Fundamental Algorithms" (volume 1 of The Art Of Computer Programming) has more correctly stated the full name of Al-Khwarizmi from whom the word algorithm is derived. So I've corrected my reference in the Algorithm section of the Fibonacci biography page to reflect this.
The table from 301 to 500, unfactorized but with prime Fibonacci numbers indicated, remains the same.
Carmichael's Theorem (see note for 2 Nov 2001) applies to the Lucas Numbers (except for Luc(6)=18).
The Factorization of the first 200 Lucas Numbers page has been updated and extended to include 101-200 and also now shows characteristic prime factors also.
- The Fibonacci Numbers up to Fib 500 are now colour coded: prime Fibonacci numbers are colour-coded and every Fibonacci number's unique prime factors that have not occured as a factor of any smaller Fibonacci number are shown in a separate colour too.
- These factors are shown in green up to Fib 200 and they are introduced in a new section on Fibonacci numbers and special prime factors on the Mathematics of the Fibonacci Numbers page.
- There is another new section on the same page pointing out that no Fibonacci number is next to a rpime (except for a couple of initial exceptions): No primes next to Fibonacci's!
- On the Easier Fibonacci Puzles page, yet another version of the Chairs In A Row puzzle has been included (and the 2 others have new names) called Chairs in a Row: The Antisocial Version.
Simon Singh presented the third of five weekly programmes today on Numbers on BBC Radio 4 (9.30am to 9.45am BST). The first two were on Zero and Pi and today's was on the Golden Ratio where you would have heard me making a contribution. The final two are on the complex number "i" (October 16) and finally, Infinity (October 23). You can listen to them live and online (anywhere in the world) by clicking on the "Listen to Radio 4 Live" button on the BBC Radio 4 web page.
A new Fibonacci Forgery: A simpler formula using Phi? that makes a nice application of logs.
Another relevant reference to the debate about Pi or Phi being used deliberately in the dimensions of the Great Pyramid has been added to the Phi and the Egyptian Pyramids? section.
Apologies that I still have lots of emails to reply to (I'm getting to yours soon!) not helped by the fact that I lost all emails sent during March and April! Sorry, but please can you resend your email if you sent one during that time and it'll be added to the queue awaiting a reply. Thanks!
There have been lots of small changes to add more references and update others, with two new awards added to the growing collection on the Home page.
A reference to Blair Kelly's excellent pages on the complete factorisation of all Fibonacci and Lucas numbers up to Fib(1000) and Lucas(1000) and partial results beyond has been added to the Fibonacci factors tables at this site.
Several minor changes have been made to other pages.
For those of you who have emailed me - thanks! Please accept my apologies if I have not yet replied to you. I have about 150 emails waiting for a reply at present going back to January 2000 :-( but don't let that stop you writing if you want to. Short emails get a fast response, often the same day. It's the longer ones or those with lots of detail that I have to find the time for - and I don't get paid for this now I'm no longer a lecturer! Thanks for your patience and I *do* appreciate all your emails.
New section on the Golden String page: The number of additions when computing f(n) by the recursive definition.
It picked up some dead links on the References page, the Art links and the Fibonacci in Nature page, all now corrected or removed.
The Fibonacci primes have been re-organised, and expanded on the Maths of the Fibonacci Series page.
The changes have been averaging no more than one or two per month recently.
The Google Search Engine is, in my view, the best on the Web! It always produces *just* the page
I was after as the first in its list, due to advanced searching algorithms based on the
popularity of a web page. You can now try it out both to search this site and to search the web, on the
Home Page.
Google now replaces the BeSeen search box.
WWW references to Eric's Treasure Trove of Mathematics have now been updated to go to the Wolfram site.
Also, a terrific demonstration of Geometer's Sketchpad facilities is now online, illustrating what happens when you dynamically alter the angle between seed on a seedhead and why the golden section angle gives the best seed packing. I developed this demonstration (with the aid of Sketchpad lecturer and expert: Annie Fetter) while the Math Forum for a Summer School in June 1998.
The page of Formulae for Fibonacci and Lucas numbers and Phi has been updated and is now available in PDF format.
Updated the seedPlotMAPLE file which plots the seed heads and animations so that it is compatible with the latest Maple version. Reduced the size of the Calculator gif file (185 bytes only now!) and altered the map of Pisa.
The Amazing Mathematical Object factor URL has been corrected on the first Puzzles Page.
has been added to the
(revised) Fibonacci, Phi and Lucas "rulers" used on many of the Web pages here. The rulers now appear uniformly
as:
|
|
|
Which do you find is the better searcher? Please do email me with your opinions.
This site was included in University of Wisconsin-Madison's Internet Scout Report for July 21st.
Added: A reference to the Rabbit constant evaluated to 330 dps on the Continued Fractions page.
Added: A reference to Phi to 10,000,000 decimal places on the Golden Section page.
!
