# 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.