What's New on Dr Ron Knott's Fibonacci and Phi Web site?

24 June 2011
Updates to the Pythagorean Triangles page now includes a section on the three excircles and how the Fibonacci method of generating pythagorean triangles makes several formulae simpler, together with more on primes in pythagorean triples
13 May 2011
More images of Alexis Monnerot-Dumaine's rabBIT Fractal and mine, with detailed instructions of how to make them.
20 April 2011
Major update and extention with new sections added to The RabBIT Sequence (the Golden string) and a new comprehensive calculator.
A new section covers patterns that can and cannot occur in the Golden String (10110101101....), where they occur and some surprising results on these matchings. Another new section discusses the recently-found stones-and-pots game (mancala-type) that gives the spectrum of Phi. Finally, a new fractal curve based on the golden string is also included.
18 April 2011
Updates to the Pythagorean Triangles page with new sections on another simple fraction method of generating Pythagorean triples and the Calculators on this page now have buttons to lengthen or shorten the results area which makes the calculators more usable on mobile phones and iPad which do not provide scroll buttons on internal sections sometimes
4 February 2011
Some new formula for higher powers added to the Fib and Phi Formulae page
28 December 2010
Several small updates on several pages and some additional results about areas of Pythagorean triangles are included, as well as some interesting facts about Fibonacci numbers and Pythagorean triangle areas.
4 October 2010
The Continued Fraction Calculator has had three new functions added to use in input: Fibonacci: F(n), Lucas L(n) and General FIbonacci G(a,b,n);
Two new buttons manipulate the CF : to reverse it and to take its reciprocal
The second results area can be collapsed to make more room for the main Results.
1 October 2010
The old Farey Fractions page has been extended and renamed to fareySB.html with a new title: Fractions in the Farey Sequences and the Stern-Brocot Tree. It now a new section and calculator on the Stern-Brocot Tree of Fractions.
22 September 2010
A new section debunking the myths about the positions of hands on a clock forming golden rectangles has been added to the Fibonacci Numbers and The Golden Section in Art, Architecture and Music page.
23 July 2010 The Fibonacci Quarterly has now been scanned electronically and made available online except that the latest editions are only accessible to those who subscribe to the journal.
5 May 2010
Several people have asked me for an explanation of the 63=64 puzzle so I have added a "spoiler" button which will reveal a diagram showing the answer.
18 January 2010
More formulae added to the Fibonacci and Phi Formula page, in particular, almost all of the Hoggatt (1969) formulae are now included, along with a change of style (formatting) of the formulae and references. This is to facilitate distinguishing I2 from 12 in formula references because Hoggatt's formulae names all begin with I not 1.
11 January 2010
More Vajda formulae added and corrected the second form of Johnson-11 on the Fibonacci and Phi Formula page
9 December 2009
Some updates to the section on reversed CFs on An Introduction to Continued Fractions
28 September 2009
The URL of this site has now changed from
www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci
to
www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci

The original URL will redirect to the new site automatically for the foreseeable future.
My contact page and details of all my Maths web sites is still the same at www.ronknott.com.

23 September 2009
We're back - with apologies for the 6 days when this site was inaccessible due to major updates to Surrey University website computers.
If it ever happens again try this:
  • use Google and search for "Fibonacci" to find the URL to this FIbonacci website at www.mcs.surrey.ac.uk/...
  • then use Google's Cached link to retrieve a copy.
  • Animations, links, movies should all work but links to other pages at the Surrey Fibonacci site will not; follow the above procedure to access them individually.
You will need to do this for my other pages at MCS at Surrey too until the site is back online.
9 August 2009
Large tables have been made scrollable on the Pythagorean Triangles page;
New section on Smallest Denominators of Egyptian Fractions.
9 July 2009
More on the Pythagorean triples formed by prefixing an extra digit on the front such as 5 12 13 with a "1" on the front gives the (valid) triple 15 112 113
29 June 2009
Two corrections to the Fibonacci and Phi Formulae page plus some more Generating Functions.
23 June 2009
A New section on Generating Functions for various Fibonacci, Lucas and Generalised Fibonacci series has been added to the Fibonacci and Phi Formulae page; the PDF version has been updated too.
6 June 2009
A new puzzle Another one! of the rods variety (compositions of integers).
8 March 2009
Penrose Tilings has a new animation Dissecting the Sharp and Flat Triangles.
27 February 2009
New graphs of the numbers of primitive and all Pythagorean triangles
1 February 2009
Updated and revised Pythagorean Triangles page:
27 January 2009
A new section on Continued Fractions connecting π, Φ and e also refers to the latest revised and updated edition (the 6th) of Hardy and Wright's classic book Introduction to the Theory of numbers.
9 January 2009
A new section on an irregular tiling similar to the Penrose tilings, but even simpler: Another Irregular tiling using Phi: the Amman Chair
30 December 2008
Happy New Year!
The mark a New Year, there is now a new panel on the Home page with links to my other Maths pages.
The Runsums Calculator has been updated and extended.
7 November 2008
The Fibonacci2 Base system has been added to the Fibonacci Bases page and has a new Calculator.
31 July 2008
Photos from the 13th International Conference on Fibonacci Numbers and Applications held at Patras, Greece, 5-12 July 2008
3 July 2008
A new section on the Introduction to Continued Fractions page on a nice method of converting a continued fraction to a simple fraction
30 June 2008
The Fibonacci Representations page has some a new section Using only the Negatively Indexed Fibonacci numbers. The Some names have been changed and
17 June 2008
An email from John Bibby gave me the idea of a new Fibonacci magic trick using the Fibonacci (or Zeckendorf) representations of number. It is a Think Of A Number trick and an online calculator will produce the cards you need for the trick.
3 June 2008
The Two fractions method of generating all Pythagorean triangles is now included, with a calculator
19 May 2008
Many updates and more new sections on the Pythagorean Triangles page
28 April 2008
More on Pythagorean dissections added
18 April 2008
A new section on visual proofs (proof without words or look-and-see proofs) of Pythagoras' Theorem has been added to the Pythagorean Triangles page. Also, a primary student from Australia, Penny Drastik, has found some new and smaller solutions to one of the Pythagorean Triangles Jigsaw (dissection) puzzles!
14 April 2008
The Pythagorean Triangles page has been expanded with many new features.
11 February 2008
The Egyptian Fractions page has been updated with extended calculators and a complete list of the 2/n table of 4000 years ago as in the Rhind Mathematical Papyrus, with comments on that list.
4 February 2008
A new Calculator to find all the best fractions that approximate a given value is now on the Introduction to Continued Fraction page.
17 January 2008
Pythagorean triangles updates:
8 January 2008
Two new goodies and a clear-up for the New Year:
26 December 2007
S Vajda's wonderful book Fibonacci and Lucas numbers, and the Golden Section: Theory and Applications, is now back in print in a Dover reprint.
21 December 2007
A new Phigits (Base Phi) Calculator converts from decimal (whole numbers) to base Phi and vice-versa.
6 December 2007
A new section on Remainders after division or Fibonacci MOD n also called the Pisano Periods is on the The Mathematical Magic of the Fibonacci Numbers page with a new Calculator so you can investigate these cycle-lengths for yourself.
29 November 2007
I was on Melvyn Bragg's In Our Time on BBC Radio 4 today (November 29, 2007) when we discussed "The Fibonacci Numbers". Click on the link if you want to Listen Again or to download the 45 minute programme as a podcast.
5 November 2007
There is now an even simpler proof that Phi is irrational.
A new section on Fixed Length Egyptian Fractions has been added to the Egyptian Fractions page and the online calculator in that section now finds fractions of a given length.
1 October 2007
A new section on a formula for the number of primitive Pythagorean triangles with a given inradius is on the Pythagorean Triples page.
29 September 2007
Another minor update to the Pythagorean Triple Generator and Fast Count Calculator.
The FibLog entries for 2003 and 2004 archived (in a separate file).
27 September 2007
The Pythagorean triangles page has been updated with more information on Pythagorean triangles with a given inradius, and a bug in the Triple Generator and Fast Count Calculator (computing total counts now works) has been corrected.
26September 2007
The Easier Puzzles page has been rearranged to regroup the puzzles. Most puzzles now have a mathematical note following them saying how the problem in desribed in more formal mathematical terms. It is surprising the wide variety of areas of mathematics (graph theory, number theory, permutations, compositions, strings, etc) where the Fibonacci Numbers appear!
25 September 2007
And yet another new Easier Fibonacci puzzle! This is based on finding matchings in a path graph of n vertices, or Chairs in a Row: The Chatty version. Note that the links and titles of the other puzzles in the Seating Arrangements section have been renamed.
24 September 2007
Another new puzzle has been added to the Easier Fibonacci Puzzles page: Chess Match Seating. The snail of 20 Sept 07 is now Fibonacci's Ravenous Rabbit! This is the problem of finding a perfect matching in P(2)xP(n) - a lattice on 2n points.
20 September2007
A new puzzle has been added to the Easier Fibonacci Puzzles page: Fibonacci's Rabbits and the Two Lettuce Rows inspired by the latest copy of the Fibonacci Quarterly. This is the problem of finding non-intersecting walks that "never look back" in a P(2)xP(n) lattice.
4 August 2007
After a very enjoyable trip to the Eden Project in Cornwall at the end of July, there are new photos of the Education Centre (the Core) and the sculpture at its heart (the Core) as well as some innovative applications of the Fibonacci Numbers to the design of quilts shown to me by two Falmouth ladies present at my talk there. photos
6 June 2007
More on convergents to continued fractions and new sections: a simple geometrical interpretation and a quick and easy method of calculating convergent fractions further explains why the convergents are "best" fractional approximations and why nature uses the Fibonacci ratios to best approximate the irrational value of Phi.
The Continued Fraction Calculator now has a button to compute all the best approximations (up to an accuracy of 0.00001).
30 May 2007
Several updates to the Introduction to Continued Fractions page:
a new CF for e has been added; a new section on other "best" approximations; more on cogs and orreries.
More pictures of the 4 and 7 spirals in the recently added Always Fibonacci? section;
Some emails I have received now cast doubt on whether the golden section does occur in Beethoven's Fifth symphony and this is mentioned now on the Art and Music page.
10 May 2007
a new section on the first page (Fibonacci Numbers in Nature) shows pictures of flowers and plants where the Fibonacci numbers do not appear.
2 May 2007
Several new interactive demonstrations of seedheads showing why phi (0.6180339...) seeds-per-turn is the ideal packing for seeds on a seedhead including an Excel spreadsheet and several links to Mathematica's Demonstration Project animations (you don't need to have Matheamtica to see them).
6 March 2007
A new section on Vajda's formulae for the factors of F(kt) and L(kt) has been added to the Fibonacci and Phi Formulae page
5 March 2007
A new sunflower picture with 34 and 55 spirals as been added to the Fibonacci Numbers in Nature page.
27 February 2007
Two new sections have been added to the Introduction to Continued Fractions page: More Silver mean Properties and Fibonacci-Related Continued Fractions on CFs of the form [1,1,1,...,1,a], which was reported in the latest Fibonacci Quarterly of August 2006.
22 February 2007
A new diagram in the Leaves Per Turn section of the Fibonacci Numbers in Nature page shows that the sunflower leaves of an actual sunflower are almost exactly where they should be if each leaf is 0.618 of a turn further round than the previous leaf.
16 February 2007
The Two Dimensional Geometry and the Golden Section page has been reorganised to make it more accessible and ordered by shape (the links to the sections have not been changed) and a new section has been added: Phi and Right-Angled Triangles.
13 February 2007
Two new Fibonacci Puzzles have been added to the Simple Fibonacci Puzzles page and a new formula for F(n) in terms of any generalised Fibonacci series G(n) on the Fibonacci and Phi Formulae page. Dead links have been updated across the site.
The Fiblog for 2005 and 2006
The FibLog for 2003 and 2004
The FibLog for 1999 to 2002
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