Dictionary of Mathematics 5e Companion Website ARCHIVE
Mathematics
Web Links
Here is a list of recommended web links, arranged alphabetically by the relevant dictionary entries.
Archived Web Links: 4th Edition
A B C D E F G H I J K L M N P R S T U
abacus
http://abacus.etherwork.net/Lee/
A description of how one abacus works.
adders
http://computer.howstuffworks.com/boolean2.htm
An article demonstrating how a simple adder works.
ambiguous case
http://yteach.co.uk/index.php/resources/sine_rule_low_sines_...
An animation showing the construction of the two possible solutions.
analysis of variance
http://www.bmj.com/cgi/content/full/312/7044/1472
A description of the analysis and its interpretation in a medical context (subscription).
Apollonius' circle
http://www.jimloy.com/cindy/apoll.htm
An interactive web page where you can alter the ratio to see how the circle changes.
Archimedean solid
http://www.scienceu.com/geometry/facts/solids/
Links to the thirteen Archimedean solids, which can be manipulated to see the shapes fully.
Archimedean spiral
http://www.mathematische-basteleien.de/spiral.htm
An animation showing the Archimedean spiral.
Arrow’s impossibility theorem
http://www.sjsu.edu/faculty/watkins/arrow.htm
An illustration of the theorem.
bisection method
http://archives.math.utk.edu/visual.calculus/1/bisection.3/i...
An interactive page which demonstrates the method for finding a root of a cubic equation.
blinding
http://www.bmj.com/cgi/content/full/321/7259/504
A full discussion of the ethics and principles of blinding in clinical trials (subscription).
bridges of Königsberg
http://nrich.maths.org/public/viewer.php?obj_id=2327
An interactive page in which you can construct your own problem like the bridges of Königsberg.
bubble sort algorithm
http://www.sorting-algorithms.com/bubble-sort
A demonstration of the bubble sort in action.
Buffon's needle
http://www.mste.uiuc.edu/reese/buffon/bufjava.html
A simulation of Buffon's needle experiment.
Cantor set
http://www.mathacademy.com/pr/prime/articles/cantset/
A visual representation of the Cantor set.
catenary
http://www-history.mcs.st-andrews.ac.uk/Java/Catenary.html
An interactive exploration of the shape of a catenary.
Central Limit Theorem
http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html
An applet that lets you define the population and then take multiple samples of different sizes to explore the behaviour of the Central Limit Theorem.
Classification Theorem for Surfaces
http://www.maths.ed.ac.uk/~aar/surgery/zeeman.pdf
A well-illustrated description of some types of surfaces.
coefficient of determination
http://nestor.coventry.ac.uk/~nhunt/regress/Discus72a.xls
An interactive spreadsheet which allows you to change data values and see how r2 and its component calculations change for a linear model.
compound interest
http://www.moneychimp.com/calculator/compound_interest_calcu...
A compound interest calculator.
conic, conic section
http://www.shodor.org/interactivate/activities/ConicFlyer/
An interactive demonstration of a conic section.
contour line
http://raider.mountunion.edu/~mcnaugma/topographic%20maps/co...
An illustrated explanation of contour lines.
control chart
http://www.sqconline.com/control-chart-variables-enter.html
Construct a control chart for your own choice of parameters.
critical path analysis
http://www.mindtools.com/critpath.html
An article including an example of critical path analysis.
cuboctahedron
http://www.scienceu.com/geometry/facts/solids/java/cubeocta....
A cuboctahedron which can be manipulated to see its shape fully.
damped oscillations
http://www.lon-capa.org/~mmp/applist/damped/d.htm
An applet exploring the effects of changing parameters on damped oscillations.
discrete (finite) Fourier transform
http://www.jhu.edu/signals/fourier2/index.html
A discrete Fourier transform tool in which choosing different options from the signal menu illustrates a number of signals and the approximating function using a specified number of Fourier coefficients.
du Sautoy, Marcus
http://people.maths.ox.ac.uk/~dusautoy/
Marcus du Sautoy's website at Oxford University.
dynamic programming
http://20bits.com/articles/introduction-to-dynamic-programming/
A detailed introduction to the method with examples.
eccentricity
http://www.math.odu.edu/cbii/calcanim/#defel
Two animations of ellipses with different eccentricities.
elastic collision
http://www.walter-fendt.de/ph14e/collision.htm
An applet allowing elastic collisions of objects of different masses and initial speeds to be explored, showing the behaviour of velocity, momentum, and kinetic energy of the two objects.
equiangular spiral
http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/KURSATg...
Animations of related curves, and an interactive manipulation of the spiral in Geometer's Sketchpad.
escape speed
http://highered.mcgraw-hill.com/olcweb/cgi/pluginpop.cgi?it=...
An interactive tool allowing you to choose a rocket launch speed and then see how a rocket fired vertically and another fired horizontally (from some distance above the Earth) would behave.
Euclid
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Eucl...
A fuller biography of Euclid.
exploratory data analysis
http://www.statgraphics.com/eda.htm
Explanations with visual representations of many of the standard tools of exploratory data analysis.
exponential decay
http://www.edumedia-sciences.com/a100_l2-radioactive-decay.html
An animation showing the physical decay and corresponding graph of three radioactive isotopes (subscription).
exponential growth
http://bcs.whfreeman.com/thelifewire/content/chp54/5402001.html
An interactive demonstration of exponential growth is included; click under the tab labelled 'Graph'.
feasible region
http://people.richland.edu/james/ictcm/2006/wpshade.html
An interactive demonstration leading the user through steps to create the feasible region given a number of inequalities.
Fibonacci number
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
A site with examples of Fibonacci numbers in nature and the relationship to the golden section.
Fibonacci sequence
http://www.mathacademy.com/pr/prime/articles/fibonac/index.asp
A site with more on the Fibonacci sequence and links with Pascal's triangle.
Fields Medal
http://www.mathunion.org/general/prizes/fields/details/
The website of the awarding body of the Fields medal.
forced oscillations
http://www.acoustics.salford.ac.uk/feschools/waves/shm3.htm
Animations and videos of forced oscillation and resonance.
Four Colour Theorem
http://serendip.brynmawr.edu/playground/fourcolor/
A Shockwave file allowing you to create your own map and colour it in, or see an automated solution with no more than four colours.
Fourier transform
http://www.relisoft.com/science/Physics/sound.html
An illustrated discussion of the Fourier transform and its applications.
fractal
http://sprott.physics.wisc.edu/fractals.htm
Examples of colourful fractal images.
gambler's ruin
http://probability.ca/jeff/java/gambler.html
A Java applet showing the gambler's ruin problem.
geometric sequence
http://www.articlesforeducators.com/dir/mathematics/sequence...
Stories illustrating the dramatic behaviour of geometric sequences.
golden ratio, golden rectangle
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci...
Shows the golden ratio in biology and the relationship to Fibonnaci numbers.
golden section
http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm
Examples of the golden section in art and architecture.
Halley, Edmond FRS
http://csep10.phys.utk.edu/astr161/lect/comets/halley.html
Pictures of Halley's comet and related information.
Heisenberg's uncertainty principle
http://www2.warwick.ac.uk/fac/sci/physics/current/teach/modu...
An applet illustrating Heisenberg's uncertainty principle.
helix
http://www.math.mcmaster.ca/gabardo/Pictures/animation01a.gif
An animation of a helix.
Hilbert, David
http://aleph0.clarku.edu/~djoyce/hilbert/
The 23 mathematical problems of Hilbert.
histogram
http://www.autograph-math.com/inaction/td/frequency_density.htm
An illustration of the construction of a histogram.
Hooke's law
http://webphysics.davidson.edu/applets/animator4/demo_hook.html
An interactive illustration of Hooke's law.
index
http://www.netcomuk.co.uk/~jenolive/sindexes.html
Examples of calculations of index numbers.
Julia set
http://homepages.inf.ed.ac.uk/wadler/mandelbrot-maps/mmaps.html
A Java applet which allows visualizations of Mandelbrot and Julia sets.
Kepler's laws of planetary motion
http://astro.unl.edu/naap/pos/animations/kepler.swf
Animation which illustrates all three laws.
Klein bottle
http://www.kleinbottle.com/whats_a_klein_bottle.htm
A fuller description and images of Klein bottles.
Koch curve
http://www.miqel.com/fractals_math_patterns/visual-math-iter...
Animation of a Koch curve.
Leonardo da Vinci
http://www.mos.org/leonardo/
An online exhibition about da Vinci.
life tables
http://www.ons.gov.uk/ons/taxonomy/index.html?nscl=Interim+L...
Gives access to the latest life tables.
magic square
http://www.vtaide.com/png/3x3-E.htm
An interactive 3 x 3 magic square.
Mandelbrot set
http://homepages.inf.ed.ac.uk/wadler/mandelbrot-maps/mmaps.html
A Java applet which allows visualizations of Mandelbrot and Julia sets.
Markov chain
http://people.hofstra.edu/Stefan_Waner/markov/markov.html
An interactive simulation for up to four states with user-defined transition matrix.
Mathemapedia
http://www.ncetm.org.uk/mathemapedia
The home page of Mathemapedia.
Mersenne prime
http://www.mersenne.org/
Home page of the Great Internet Mersenne Prime Search.
Millennium Prize problems
http://www.claymath.org/millennium/
The Millennium Prize problems home page.
Möbius band
http://www.popmath.org.uk/sculpmath/pagesm/mb.html
The Möbius band in art.
moving average
http://stockcharts.com/school/doku.php?id=chart_school:techn...
Illustrations of the moving average from financial markets.
National Centre for Excellence in the Teaching of Mathematics
http://www.ncetm.org.uk/
The NCETM home page.
parabola
http://www.calculus.org/Contributions/animations.html
Properties of the parabola with links to animated illustrations.
parabolic spiral
http://curvebank.calstatela.edu/parabolafermat/parabolaferma...
An animation of a parabolic spiral.
Pascal's triangle
http://www.mathsisfun.com/pascals-triangle.html
An illustration of some of the patterns in Pascal's triangle.
pedal curve
http://mathworld.wolfram.com/PedalCurve.html
An animation of a pedal curve.
perfect number
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Perfe...
A brief history of perfect numbers.
predator-prey equations
http://home.messiah.edu/~deroos/CSC171/PredPrey/PPIntro.htm
Simulations of fox and rabbit populations.
prisoner's dilemma
http://serendip.brynmawr.edu/playground/pd.html
Play the prisoner's dilemma against the computer.
relativity theory
http://www.allaboutscience.org/theory-of-relativity.htm
An article about relativity with a related video.
resonance
http://www.acoustics.salford.ac.uk/feschools/waves/shm3.htm
Animations and videos of forced oscillation and resonance.
retail price index
http://www.ons.gov.uk/ons/rel/cpi/consumer-price-indices/ind...
Gives access to the latest indices on price inflation, including the RPI values since June 1947.
sieve of Eratosthenes
http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm
An interactive animation of the sieve of Eratosthenes used to obtain prime numbers.
Simpson's paradox
http://www.retailmedia.org/2008/10/retail-media-and-simpsons...
Examples of Simpson's paradox.
slide rule
http://www.sliderule.ca/
Descriptions of various slide rules and how they work.
sorting algorithms
http://www.cs.ubc.ca/~harrison/Java/sorting-demo.html
Demonstrations of a variety of sorting algorithms in operation.
stereographic projection
http://www.math.union.edu/~dpvc/math/4D/stereo-projection/we...
A full description of stereographic projection with two videos to illustrate how it looks.
tangent field
http://www.autograph-maths.com/inaction/td/de(a).htm
A Flash demonstration of tangent fields in Autograph.
tessellation
http://gwydir.demon.co.uk/jo/tess/index.htm
Tessellations with various grids and interactive design tools.
Tower of Hanoi
http://www.mazeworks.com/hanoi/
An interactive applet for different numbers of discs, with animated solutions.
twin primes
http://primes.utm.edu/top20/page.php?id=1
More information on twin primes, including a list of the twenty largest pairs identified.
Universal Product Code
http://www.howstuffworks.com/upc.htm
More details of how UPC works, including a video case study of their use in tracking parcels.
