Ron Knott's web pages on Mathematics:
- Fibonacci Numbers
a huge award-winning collection of information on Fibonacci numbers (0,1,1,2,3,5,8,13,21,...)
and the Golden section ( 0.61803... and 1.61803...) which gets more than 5000
visits per day to the index (first) page alone!
- Egyptian Fractions explains how the
Egyptians and Babylonians of 3000 BC represented fractions and how they used them.
In some ways, their method is better than the decimal system! There are now some online calculators on this page to take some
of the work out of generating these fractions.
- An Introduction to Continued Fractions
links their use in explaining the patterns on seedheads and flowers and their usefulness in mathematics too.
- There is an online Continued Fraction Calculator
so you can experiment for yourself. No download is needed -- it is all accomplished on the web page!
- An accurate
Fractions Calculator to convert ordinary fractions to and from decimal fractions
to any number of decimal places accuracy.
The web page does not need an extra software, just a Script-enabled browser.
- Pythagorean Triangles - those integer-sided, right-angled triangles
such as the triangle with sides of 3, 4 and 5. Includes a formula for generating them all and calculator which
shows you how. These triangles were extensively studied by the Babylonians of
5000 years ago and some of the oldest mathematical writings (clay tablets) contain tables of such triangles.
The page includes several online interactive Calculators so you can experiment for yourself.
- Runsums
are sums of consecutive numbers, e.g. 4+5 is a runsum for 9, as is 2+3+4.
An on-line calculator computes all the runsums for a given number and finds numbers
with a specific number of runsums (e.g. under "2" would be 9 because 9 has just 2 runsums
shown above). Runsums are the difference between two Triangle Numbers, and this
is also explained on the web page.
- I have several pages on the CountOn
site which continues the work of Maths Year 2000, the UK government sponsored site for schools
which started in the International Year of Mathematics in 2000:
- A Perpetual Calendar
which can not only find the day of the week for a given day, months and year, but
also tell you the years when your birthday falls on a Saturday, or which months in
a year have a "Friday the 13th".
- Interactive Tests (one page per topic)
for Mathematics A and AS Level for MEI.
- "Where do you go to get a degree in Apologies?" at the University
of Sorry (Surrey) (groan). Here's a collection
of similar "courses".
Dr Ron Knott
Ph.D, M.Sc, B.Sc (Pure Maths), C.Math, FIMA, C.Eng, MBCS, CITP
Visiting Fellow, Department of Mathematics,
Faculty of Electronics and Physical Sciences,
University of Surrey,
Email: 
I now live in Bolton, near Manchester, UK.
I was a lecturer in the Departments of Mathematics and Computing Science
at the University of Surrey, Guildford, UK, for 19 years
until September 1998 when I left to start working for
myself making web pages for maths education sites.
I now give mathematics talks to students at schools and universities
as well as to general audiences, teachers' conferences, Science Festivals as well as
schools and universities on topics reflected in the topics of the web pages above:
especially the Fibonacci Numbers and why they occur so often in plants,
Fun with Fractions, As Easy As Pi, ... .
Recent talks, among others, include the following:
- 2012: IMA NW Branch Student Teacher Lecture
on The Fascinating Fibonacci Numbers for beginning PGCE Students at Manchester Metropolitan University
and others.
- 2011: A Festival of Fractions, the IMA
Lancs and NW branch Annual Sixth Form lecture at Manchester Grammar School,
16 March 2011
- 2011: Online video conference with maths students at Meridian International School, Prague, Czech Republic, 9 March 2011
- 2011: Lichfield Schools talk on 'Flowers as Computers' or
The Fibonacci Numbers and the Golden Section in Nature and Mathematics, 9 February 2011, Friary School, Lichfield
- 2010: Mathematical Experiments using the Fibonacci Numbers, Keele University Maths Dept (school talk), 8 July 2010
- 2010: Investigations with the Fibonacci Numbers, talk at the IMA 12th Young Mathematicians Conference, University of Newcastle, 15 May 2010
- 2010: Flowers as Computers with Fibonacci and Phi, talk to
the Lichfield Science and Engineering Society, 16 March 2010
- 2009: British Association Science Festival, Guildford, September 2009 on Flowers as Computers
- 2008,2007: The Eden Project: 26 July 2007, 22 May 2008 on Numbers in Plants
- 2007: BBC Radio 4 Melvyn Bragg's
In Our Time
November 29, 2007 when we discussed "The Fibonacci Numbers".
Click on the link to
Listen Again or to download the 45 minute programme as a podcast.
- 2007: Cambridge Science Festival, 17 March 2007
- 2006: Coventry Cathedral's "Da Vinci Code" evening: 12 May 2006
- 2005: Fibonacci Numbers and Phi: New and News, talk at TSM 11 Technology for Secondary Mathematics
, 11 July 2005
- 2004: Fibonacci Fibonacci and Phi for Fun: Facts and Fallacies, IMA NW Branch meeting, 6 October 2004
- 2002: BBC Radio 4 "Numbers" series: Phi, I 29 November 2002
- 1998, 2000: Orkney Science Festival: 1998, 2000 on Patterns and Numbers in Plants
- 1998: BBC Radio Scotland: 1998 interview for the Orkney Science Festival talks
Please contact me by initially by email at
if you want to enquire about a talk at your school or society or Science Festival suitable for
a general audience or for mathematics students.
updated: 22 February 2013