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11am GMT 26 July 2016
These pages on Mathematics are for those who don't like Mathematics or who hated maths at school
as well as for those at school (or who left school a long while ago) who want to see a fun
side of maths and who like to play with numbers. The level of mathematics required is
what would be taught up to GCSE (age 15) in UK schools and rarely does it need A-level skills (age 17, pre university).
What's special about the number 2016?
A page on fun maths facts and factoids for everyone, with puzzles all on the number
2016.
The Fibonacci Numbers
Fibonacci Numbers
a collection of information on Fibonacci numbers (0,1,1,2,3,5,8,13,21,...)
and the Golden section ( 0.61803... and 1.61803...)
This Fibonacci page was originally developed in 1995 and went live in 1996 so is one of the longest running pages on Mathematics on the web!
At the top it includes links to the pages shown here below. The whole site is hosted by the University of Surrey.
This page alone still gets more than 3000-5000 visits per day.
A simple way to reference this page is to use the automatic-redirection page
www.tinyurl.com/fibandphi.
Dr E Lawrence and myself, members of Surrey University Mathematics Department, were part of a large UK government
Teaching and Learning Technology Project (TLTP)
called Mathwise,
although now that name has been used by several other individuals and groups unassociated with this project.
It aimed to provide maths software to link school and university mathematics, involving
23 UK universities
developing activities and assessment on 40 topics in mathematics, ending in about 1995.
Mathwise never really reached its full potential because it was developed on a both PCs and Macs using
a variety of software, some of which soon became obsolete. The PC and Mac software was
never integrated into one unified and accessible system.
I developed this Fibonacci page after Mathwise to see if the (then new) internet
could be used to communicate maths, having the advantages that
it ran identically on many kinds of computer, both personal and desktop, PC and Mac
it was accessible everywhere
it would be easy to maintain as the web developed
it was free
It was designed as both a resource for teachers as well as for keen (and not-so-keen) students
who wanted to explore topics off the main school curriculum. Hence each webpage is longer than has now become the norm
on the web so that
each could be downloaded and viewed at leisure offline, dating from the days
when a wi-fi connection was still rare, costly and very slow.
This page gained many awards in its early days.
Other Recreational Mathematics topics
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 your browser on any PC, tablet or phone.
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.
UK School MATHEMATICS RESOURCES for GCSE and A-Level
that generates variations on 50 questions, marks, detects common errors, and shows the correct
answer and provides bar charts of your results. It was originally developed for
the Mathematics Enhancement Programme at Exeter University as a resource for Mathematics teachers.
One page on each of about 120 topics
for Mathematics A and AS Level developed for MEI and also available on their website.
Other topics and some Maths Jokes
If you like the TV programme Countdown, you'll love Got It!. Select some number
cards and it will generate a target number for you to make using the cards and +, -, × and ÷ in
30 seconds. You can select the level of difficulty from primary school level to Maths MasterMind. IF you get stuck or run out
of time, Got It will show you one way to get the target.
Herchel's Perpetual Calendar
which can not only find the day of the week for a given day, month and year, but
also tell you the years when your birthday falls on a Saturday, or which months in
a year have a "Friday 13th".
"Where do you go to get a degree in Apologies?" at the University
of Sorry (Surrey) (groan). Here's a collection
of similar "courses".
Visiting Fellow, Department of Mathematics,
formerly Lecturer in Mathematics and Computing Science Departments (1979-1998)
Faculty of Electronics and Physical Sciences, University of Surrey,
Email:
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, ... .
I now live in Bolton, near Manchester, UK.
Look out for these talks in the near future by Dr Knott
9 September 2016 University of Surrey (Guildford,UK) Open Days, Mathematics Department
as 24,25 June 2016
Recent talks, articles and events
24, 25 June 2016 University of Surrey (Guildford,UK) Open Days, Mathematics Department
Open to the general public, and free: three 15 minute mini-maths talks for those who don't think Maths can be Fun!
6 February 2016, Lancaster University Mathematics Masterclass, starts at 10am for those registered
2015 October 17 A repeat of the three talks given at the September University of Surrey Open Day, held in
the Mathematics Department on Level 04 (the top floor) of the AA Building:
2015 September 12 The University of Surrey Open Day: Three 15 minute mini-maths talks for the general public on How to share Pizzas and Inheritances - two puzzles and what the ancient Egyptians can teach us today; Dots and Flags or Proof By Pictures without any of that awkward algebra Numbers you can Eat: the Fibonacci numbers and the golden ratio
2015 March 21 Royal Institution Mathematics Masterclass "The Fibonacci Connection:The series, the number, the string" University of Surrey
2015 March 19 University of Surrey "Amazing Maths: The Fibonacci Connection:The series, the number, the string"
2015 March 14 Royal Institution Mathematics Masterclass "Forgotten Fractions" University of Surrey
2015 March 2 IMA NW Annual Sixth Form Lecture at Manchester Grammar School "Polygonal Numbers, Pictures and Proof"
2014 December 18: Florence Nightingale Day
at Lancaster University, schools talk promoting women to pursue mathematics; 18 December 2014, "Numbers you can Eat!"
2014 October: Article in IMA journal Mathematics Today
Vol 50, No 5, October 2014, pages 242-243 (Contents page)
an article on my Festival talk
"Fibonacci, Phi Food and Flowers" and my image chosen as one of the 50 Visions of Mathematics to celebrate the event.
See the image and explanation here
2014 July 14: "Puzzles, Pictures and Proofs" talk at the Fibonacci Numbers and Applications Conference 16 at Rochester, NY, USA
2014 July 3: IMA 50 Anniversary Festival of Maths and Its Applications, University of Manchester,
opening talk on "Fibonacci, Flowers, Phi, Food and Flowers"
2014 March 29: Manchester POPQUIZ talk: "Numbers You can Eat!"
2014 February 27: "Numbers You Can Eat" at Manchester College
2013 March 18: SciBAr (British Science Association, Didsbury, Manchester)
"Why Nature likes the Fibonacci Numbers"
2012 September 20: IMA NW Branch Student Teacher Lecture
on The Fascinating Fibonacci Numbers for beginning PGCE Students at Manchester Metropolitan University
and others.
2011 March 16: A Festival of Fractions, the IMA
Lancs and NW branch Annual Sixth Form lecture at Manchester Grammar School
2011 March 9: Online video conference with maths students at Meridian International School, Prague, Czech Republic
2011 February 9: Lichfield Schools talk on 'Flowers as Computers' or
The Fibonacci Numbers and the Golden Section in Nature and Mathematics, 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
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
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
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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 July 2016