Posts to October 2016. For latest posts, see sidebar
 That’s Maths Book Published Gill Books, 25 October.
 Thank Heaven for Turbulence Turbulent flow is everywhere
 Kepler’s Magnificent Mysterium Cosmographicum
 A Ton of Wonders An ode to the number 100
 Negative Number Names Historical baggage with terminology
 Venn Again’s Awake Diagrams for more than three sets
 The next Hamilton The chance effects of education
 Heron’s Theorem: a Tool for Surveyors No angles needed!
 The Tunnel of Eupalinos in Samos A remarkable engineering achievement
 Random Harmonic Series Curious properties
 Computers Speaking in Irish Voice replacing text.
 Squircles A cool idea from Piet Hein
 Lateral Thinking in Mathematics Simpler from another angle
 Lecture sans paroles: the factors of M67 Speechless
 Bending the Rules to Square the Circle Not Euclid’s way
 Bloom’s attempt to Square the Circle Seemed like a good idea
 Prime Generating Formulae Brilliant but useless
 Big Data: the Information Explosion It’s everywhere
 Mathematics Everywhere In Blackrock Station
 Andrew Wiles wins 2016 Abel Prize For Fermat
 Ramanujan’s Astonishing Knowledge of 1729 Near misses
 Modelling Rogue Waves New ideas on mechanism
 Sigmoid Functions: Gudermannian and Gompertz Curves
 The Inexorable Rise in Life Expectancy Live long and prosper
 The Power Tower Fractal Beauty in simple things
 The Search is on for Planet Nine Hold your breath
 The Imaginary Power Tower: Part II x^x^x^x…
 The Imaginary Power Tower: Part I x^x^x^x…
 Computus: Dating the Resurrection Easter Day
 Peano Music Axioms for natural numbers
 The Abel Prize The Nobel Prize for Mathematics
 Bertrand’s Chord Problem Paradoxical
 Vanishing Zigzags of Unbounded Length Strange curves
 Franc-carreau or Fair-square Hard to win
 The Mathematics of Voting Not easy to be fair
 Prime Number Record Smashed Again Another Mersenne prime
 Entropy Piano Tuning It really works
Twin Peaks The Entropy depends on the separation
 Richardson’s Forecast Factory A Marvellous Fantasy
 Squaring the Circular Functions Square Elliptic functions
 Factorial 52: A Stirling Problem Never the same hand twice
 How many Christmas Gifts? Pyramids of Baubles
 The Ping Pong Pendulum More rapid as it damps
 The Flight of a Golf Ball Dimples make the difference
 Life’s a Drag Crisis Gustave Eiffel’s discovery
 Mathematics Solving Crimes Forensic mathematics
 Numbering the Family Tree Ahnentafel numbers
 Melencolia: An Enigma for Half a Millennium Dürer’s masterpiece
 Mowing the Lawn in Spirals Almost Archimedean
A Few Wild Functions When limits do not commute
 It’s a Small – Networked – World Graph theory everywhere
 Which Way did the Bicycle Go? Even Holmes nods
 New Tricks: No Clicks Noiseless CD recordings
 Hamming’s Smart Error-correcting Codes SECDED removes errors
 The Ubiquitous Cycloid A historical curve
 Holbein’s Anamorphic Skull Deliberate distortion
 James Joseph Sylvester A Victorian mathematician
 Thomas Harriot: Mathematician, Astronomer and Navigator Sailing with Sir Walter
 The Great American Eclipse: Put August 21, 2017 in your diary
 Buffon was no Buffoon Pins and Needles
 The Bridges of Paris A city stroll
 Who Needs EirCode? A poor choice
 Bent Coins: What are the Odds? Don’t gamble on them
 RT60 and Acoustic Excellence Sabine’s great ideas
 Fun and Games on a Honeycombed Rhomboard. A popular game
 Pluto’s Unruly Family Far-away Chaos
 Increasingly Abstract Algebra The growth of abstraction in mathematics.
 Emmy Noether’s beautiful theorem Connecting symmetry and conservation.
 Game Theory & Nash Equilibrium Game theory in the applied sciences.
 The Tragic Demise of a Beautiful Mind John Nash dies after receiving the Abel Prize.
 Maps on the Web Web Mercator is valuable but has limitations.
 Mercator’s Marvellous Map had profound influence on our world-view.
 Eccentric Pizza Slices A curious puzzle with an infinite family of solutions.
 Modelling the Markets The Black-Scholes equation can give misleading predictions.
 Brouwer’s Fixed-Point Theorem Useful throughout mathematics.
 Tap-tap-tap the Cosine Button A simple example of a fixed point.
 For Good Comms, Leaky Cables are Best Counter-intuitive implication of electrical resistance.
 The Hodograph Hamiltons clever construction.
 Mode-S: Aircraft Data improves Weather Forecasts A simple example of vector analysis.
 Golden Moments There are 44 golden moments every day.
 You Can Do Maths We all think in a mathematical way. You can do it!
 A King of Infinite Space: Euclid I. Euclid organized and systematized geometry.
 Café Mathematics in Lvov: The Scottish Cafe.
 The Birth of Functional Analysis: Stefan Banach and his spaces.
 MGP: Tracing our Mathematical Ancestry: Find your famous forebears.
 The Klein 4-Group: The symmetry of a paperback book.
 Perelman’s Theorem: Who Wants to be a Millionaire? The Poincare conjecture proved.
 The Steiner Minimal Tree: Optimising network connections.
 Plateau’s Problem and Double Bubbles: Surfaces meet at 120º.
 Barcodes and QR Codes: Zebra stripes and leopard spots.
 Seifert Surfaces for Knots and Links: Surprising surfaces bounded by knots.
 The MacTutor Archive: A valuable historical resource.
 2014 in review: January 1, 2015, WordPress review of blog.
 Fermat’s Christmas Theorem: A result in additive number theory.
 Information Theory: The wide implications of Claude Shannon’s work.
 New Curves for Old: Inversion produces new curves.
 The Year of George Boole: Boole’s centenary celebrated at UCC.
 Falling Bodies : Philae falling slowly to a space-rock.
 Earth’s Shape and Spin Won’t Make You Thin: Oranges and lemons.
 Falling Bodies : Sky-diving: Slowing down as you fall farther.
 El Niño likely this Winter: Indications are for a warming ocean.
 Light Weight (*): Bending of light according to Newton and Einstein.
 Waring’s Problem & Lagrange’s Four-Square Theorem.
 Old Octonions may rule the World: Numbers discovered by Graves and Cayley.
 Triangular Numbers: EYPHKA: Gauss’s enigmatic diary entry.
 Algebra in the Golden Age: How ancient knowledge was preserved and extended.
 Curves with Singularities: Kinky and loopy curves.
 How Big was the Bomb? G I Taylor’s brilliant dimensional analysis.
 Cartoon Curves: Draw your favourite Walt Disney character with maths.
 The Biggest Harp in Ireland: Music on a Liffey Bridg
 Temperamental Tuning: Musical structure and the Circle of Fifths.
 Biomathematics: the New Frontier: Biological sciences become more quantitative.
 Do you remember Venn? The power of a simple picture.
 “Come See the Spinning Globe”: Foucault’s amazing experiment causes pendulum fever
 Degrees of Infinity: Cantor’s “paradise” of infinite quantities.
 Invention or Discovery? Conjecture: Definitions are invented. Theorems are discovered.
 Digital Dentistry: A system with maths, computing and engineering combined.
 Gauss’s Great Triangle and the Shape of Space: Do the three angles add to pi?
 Beauty is the First Test: Aesthetic aspects of mathematics
 Balancing a Pencil: Maybe rocket science, but not quantum physics.
 When did Hammurabi reign? Ancient chronology and climate change.
 Biscuits, Books, Coins and Cards: Massive Hangovers: How slowly the harmonic numbers grow.
 Sunflowers and Fibonacci: Models of Efficiency: Patterns in nature.
 The High-Power Hypar: Architecture, climate models and tennis balls.
 The Chaos Game: Beautiful patterns from simple algorithms.
 The Future of Society: Prosperity or Collapse? A simple model of societal development.
 Predator-Prey Models: Vito Volterra’s integrable nonlinear model.
 The Faraday of Statistics: Gosset and Student’s t-test.
 Breaking Weather Records: Another application of harmonic numbers.
 Clothoids Drive Us Round the Bend: Beautiful mathematical motorways.
 Rollercoaster Loops: Thrilling vertical loops.
 The Predictive Power of Maths: The remarkable capacity of mathematics to anticipate physical phenomena.
 Solar System Perturbations: Almost all the mass is in the Sun.
 The Unity of Mathematics: Tendency to fragment is offset by dramatic synthesis.
 The Langlands Program: Sweeping unification through surprising connections.
 Simulating the Future Climate: Computer models: benefits and drawbacks.
 The Prime Number Theorem: How many primes less than n ?
 Euclid in Technicolor: Oliver Byrne’s amazing edition of Euclid.
 Speed Cubing & Group Theory: Cubophiles can solve the problem in 5 seconds.
 French Curves and Bézier Splines: Matnematical ways of drawing graceful corves.
 Bézout’s Theorem: How many times do polynomials intersect?
 Pythagorean triples: 3, 4 and 5 give the sides of a right triangle. What else does?
 Robots & Biology: The interplay between mechanics and biological systems.
 White Holes in the Kitchen Sink: A simple observation with deep dynamics.
 Interesting Bores: Hydraulic jumps provide sporting opportunities.
 Experiment and Proof: Proof is the gold-standard of maths
 Santa’s Fractal Journey: We estimate the dimension of his route
 Ireland’s Fractal Coastline: Two estimates with different methods agree
 Population Projections: Where is the world population heading?
 A Simple Growth Function: Different kinds of growth
 The Antikythera Mechanism: An amazing Computer from ancient Greece
 The Watermelon Puzzle: A counter-intuitive result.
 Euler’s Gem: V – E + F = 2. It turns up everywhere.
 Hyperbolic Triangles and the Gauss-Bonnet Theorem: Linking geometry and topology
 Poincare’s Half-plane Model (bis): More on hyperbolic geometry
 Geometry in and out of this World: Non-Euclidean geometry
 Poincaré’s Half-plane Model: Hyperbolic geometry in the half-plane
 The Simpler the Better: The simplex method in linear programming
 A Mathematical Dynasty: The remarkable Bernoullis
 Sonya Kovalevskaya: A brilliant mathematician
 New Estimate of the Speed of Light: Light-hearted comment
 Irish Maths Week 2013: A Key annual mathematical event in Ireland
 A Hole through the Earth: Falling to the antipodes
 Ternary Variations: Cantor’s surprising ternary set.
 Travelling under Pressure: The Atmospheric Railway
 The remarkable BBP Formula: Arbitrary (hex) digits of pi
 Admirably Appropriate: Symbiosis between pure and applied mathematics
 Paddling Uphill: Apparent uphill flow of River Shannon.
 Matholympic Heroes: The IMO in Santa Marta, Colombia.
 Hailstone Numbers: A challenging problem in number theory.
 The School of Athens: Projective geometry and the mathematics of perspective.
 Senior Wranglers: Wranglers and the Mathematical Tripos.
 Normal Numbers: Surprising properties of Champernowne’s Number.
 Joyce’s Number: Maximum number using three 9s.
 Prime Secrets: Two exciting results in prime number theory.
 Gauss’s Oversight: Gauss misses a crucial connection.
 The Sholders of Giants: The mathematician John Wallis.
 Kelvin Wakes: Beautiful ship-wave patterns.
 Loaves & Fishes: The Banach-Tarski Theorem.
 Monster Symmetry: The monster group and symmetry in physics.
 Spots & Stripes: Reaction-diffusion processes and pattern generation.
[4-] The Dozenal System: Base-twelve arithmetic.
 Pythagoras goes Global: Pythagoras’ Theorem on the sphere.
 Bayes Rules OK: Many implications of Bayes’ Theorem.
 Peaks, Pits & Passes: Some properties of maps and charts.
 The Pitch-drop Experiment: A long-running physics experiment.
 Happy Pi-Day: 3/14, a cause for celebration.
 CAT Scans: Medical imaging and the Radon transform.
 More Equal than Others: Robert Recorde and the “=” sign.
 The Swingin’ Spring: Complex dynamics of a simple mechanical system.
 SVD: The invaluable Singular Value Decomposition.
 Computer Maths: Will computers ever be able to do mathematical research?
 Chess Harmony: Some properties of the harmonic series.
 The Lambert W-function: An interesting special function.
 Topology Underground: The geometry and topology of subway systems.
 The Power Tower: Surprising convergence of iterated exponents.
 Archimedes Uncovered: The Archimedes Palimpsest.
 Pons Asinorum: A startling geometric proof.
 Santa’s Challenge: Santa Claus and the travelling salesman problem.
 Sharing a Pint: An amusing puzzle for the pub.
 Ramanujan’s Lost Notebook: Ramanujan’s papers found in the Wren Library.
 Taxi-cab Geometry: Where circles are square and pi equals 4.
 Surreal Numbers: Conway’s ingenious transfinite numbers.
 Where in the World: GPS and relativity.
 Shackleton’s Spectacular: An amazing feat of navigation.
 A Mersennery Quest: GIMPS and the search for Mersenne primes.
 The Popcorn Function: A function with extraordinary continuity properties.
 Carving up the Globe: Many ways to dissect the sphere.
 The Falling Slinky: The bottom stays still!
 Contagion: Modelling infectious diseases.
 The End of Small-pox: Daniel Bernoulli and innoculation.
 The Kahn Academy: A revolution on maths education.
 The Beautiful Game: Golden section nowhere to be seen.
 Packing & Stacking: From Kepler to Hales.
 No Maths Involved: Aspects of Sudoku.
 Sproutology: Another clever invention of John Conway.
 Analemmatic Sundials: You are the gnomon (pointer).
 Napier’s Nifty Rules: Spherical trigonometry made simple.
 PageRank: How Google finds things fast.