- 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:
- The Excel sheet that draws equiangular spirals
now has Phi changed to F, the expansion factor for the curve.
Explanatory text has been added and another box to show the constant angle between the radius
(the line from the centre to the point on the curve)
and the direction of the curve at that point, which is constant for all points, hence the name Equiangular Spiral.
A further box computes the F for a given angle.
- A new Exact Fractions Calculator has been added to the Mathematical Magic of the Fibonacci Numbers page.
It converts any proper fraction into an exact decimal fraction, identifying the
fixed and recurring parts (if any).
- A new year is here so this Weblog file (you're reading it!) has been shortened by archiving the Weblog notes
for 2005 and 2006.
- 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.
© 1996-2008 Dr Ron Knott
Fibonacci Home Page