[151] Maps on the Web Web Mercator is valuable but has limitations.
[150] Mercator’s Marvellous Map had profound influence on our world-view.
[149] Eccentric Pizza Slices A curious puzzle with an infinite family of solutions.
[148] Modelling the Markets The Black-Scholes equation can give misleading predictions.

April 2015

[147] Brouwer’s Fixed-Point Theorem Useful throughout mathematics.
[146] Tap-tap-tap the Cosine Button A simple example of a fixed point.
[145] For Good Comms, Leaky Cables are Best Counter-intuitive implication of electrical resistance.
[144] The Hodograph Hamiltons clever construction.
[143] Mode-S: Aircraft Data improves Weather Forecasts A simple example of vector analysis.

March 2015

[142] Golden Moments There are 44 golden moments every day.
[141] You Can Do Maths We all think in a mathematical way. You can do it!
[140] A King of Infinite Space: Euclid I. Euclid organized and systematized geometry.
[139] Café Mathematics in Lvov: The Scottish Cafe.

February 2015

[138] The Birth of Functional Analysis: Stefan Banach and his spaces.
[137] MGP: Tracing our Mathematical Ancestry: Find your famous forebears.
[136] The Klein 4-Group: The symmetry of a paperback book.
[135] Perelman’s Theorem: Who Wants to be a Millionaire? The Poincare conjecture proved.

January 2015

[134] The Steiner Minimal Tree: Optimising network connections.
[133] Plateau’s Problem and Double Bubbles: Surfaces meet at 120º.
[132] Barcodes and QR Codes: Zebra stripes and leopard spots.
[131] Seifert Surfaces for Knots and Links: Surprising surfaces bounded by knots.
[130] The MacTutor Archive: A valuable historical resource.
[129] 2014 in review: January 1, 2015, WordPress review of blog.

December 2014

[128] Fermat’s Christmas Theorem: A result in additive number theory.
[127] Information Theory: The wide implications of Claude Shannon’s work.
[126] New Curves for Old: Inversion produces new curves.
[125] The Year of George Boole: Boole’s centenary celebrated at UCC.

November 2014

[124] Falling Bodies [2]: Philae falling slowly to a space-rock.
[123] Earth’s Shape and Spin Won’t Make You Thin: Oranges and lemons.
[122] Falling Bodies [1]: Sky-diving: Slowing down as you fall farther.
[121] El Niño likely this Winter: Indications are for a warming ocean.

October 2014

[120] Light Weight (*): Bending of light according to Newton and Einstein.
[119] Waring’s Problem & Lagrange’s Four-Square Theorem.
[118] Old Octonions may rule the World: Numbers discovered by Graves and Cayley.
[117] Triangular Numbers: EYPHKA: Gauss’s enigmatic diary entry.
[116] Algebra in the Golden Age: How ancient knowledge was preserved and extended.

September 2014

[115] Curves with Singularities: Kinky and loopy curves.
[114] How Big was the Bomb? G I Taylor’s brilliant dimensional analysis.
[113] Cartoon Curves: Draw your favourite Walt Disney character with maths.
[112] The Biggest Harp in Ireland: Music on a Liffey Bridg

August 2014

[111] Temperamental Tuning: Musical structure and the Circle of Fifths.
[110] Biomathematics: the New Frontier: Biological sciences become more quantitative.
[109] Do you remember Venn? The power of a simple picture.
[108] “Come See the Spinning Globe”: Foucault’s amazing experiment causes pendulum fever

July 2014

[107] Degrees of Infinity: Cantor’s “paradise” of infinite quantities.
[106] Invention or Discovery? Conjecture: Definitions are invented. Theorems are discovered.
[105] Digital Dentistry: A system with maths, computing and engineering combined.
[104] Gauss’s Great Triangle and the Shape of Space: Do the three angles add to pi?
[103] Beauty is the First Test: Aesthetic aspects of mathematics

June 2014

[102] Balancing a Pencil: Maybe rocket science, but not quantum physics.
[101] When did Hammurabi reign? Ancient chronology and climate change.
[100] Biscuits, Books, Coins and Cards: Massive Hangovers: How slowly the harmonic numbers grow.
[99] Sunflowers and Fibonacci: Models of Efficiency: Patterns in nature.

May 2014
[98] The High-Power Hypar: Architecture, climate models and tennis balls.
[97] The Chaos Game: Beautiful patterns from simple algorithms.
[96] The Future of Society: Prosperity or Collapse? A simple model of societal development.
[95] Predator-Prey Models: Vito Volterra’s integrable nonlinear model.
[94] The Faraday of Statistics: Gosset and Student’s t-test.

April 2014
[93] Breaking Weather Records: Another application of harmonic numbers.
[92] Clothoids Drive Us Round the Bend: Beautiful mathematical motorways.
[91] Rollercoaster Loops: Thrilling vertical loops.
[90] The Predictive Power of Maths: The remarkable capacity of mathematics to anticipate physical phenomena.

March 2014

[89] Solar System Perturbations: Almost all the mass is in the Sun.
[88] The Unity of Mathematics: Tendency to fragment is offset by dramatic synthesis.
[87] The Langlands Program: Sweeping unification through surprising connections.
[86] Simulating the Future Climate: Computer models: benefits and drawbacks.

February 2014

[85] The Prime Number Theorem: How many primes less than n ?
[84] Euclid in Technicolor: Oliver Byrne’s amazing edition of Euclid.
[83] Speed Cubing & Group Theory: Cubophiles can solve the problem in 5 seconds.
[82] French Curves and Bézier Splines: Matnematical ways of drawing graceful corves.

January 2014

[81] Bézout’s Theorem: How many times do polynomials intersect?
[80] Pythagorean triples: 3, 4 and 5 give the sides of a right triangle. What else does?
[79] Robots & Biology: The interplay between mechanics and biological systems.
[78] White Holes in the Kitchen Sink: A simple observation with deep dynamics.
[77] Interesting Bores: Hydraulic jumps provide sporting opportunities.

December 2013

[76] Experiment and Proof: Proof is the gold-standard of maths
[75] Santa’s Fractal Journey: We estimate the dimension of his route
[74] Ireland’s Fractal Coastline: Two estimates with different methods agree
[73] Population Projections: Where is the world population heading?

November 2013

[72] A Simple Growth Function: Different kinds of growth
[71] The Antikythera Mechanism: An amazing Computer from ancient Greece
[70] The Watermelon Puzzle: A counter-intuitive result.
[69] Euler’s Gem: V – E + F = 2. It turns up everywhere.

October 2013

[68] Hyperbolic Triangles and the Gauss-Bonnet Theorem: Linking geometry and topology
[67] Poincare’s Half-plane Model (bis): More on hyperbolic geometry
[66] Geometry in and out of this World: Non-Euclidean geometry
[65] Poincaré’s Half-plane Model: Hyperbolic geometry in the half-plane
[64] The Simpler the Better: The simplex method in linear programming

September 2013

[63] A Mathematical Dynasty: The remarkable Bernoullis
[62] Sonya Kovalevskaya: A brilliant mathematician
[61] New Estimate of the Speed of Light: Light-hearted comment
[60] Irish Maths Week 2013: A Key annual mathematical event in Ireland

August 2013

[59] A Hole through the Earth: Falling to the antipodes
[58] Ternary Variations: Cantor’s surprising ternary set.
[57] Travelling under Pressure: The Atmospheric Railway
[56] The remarkable BBP Formula: Arbitrary (hex) digits of pi
[55] Admirably Appropriate: Symbiosis between pure and applied mathematics

July 2013
[54] Paddling Uphill: Apparent uphill flow of River Shannon.
[53] Matholympic Heroes: The IMO in Santa Marta, Colombia.
[52] Hailstone Numbers: A challenging problem in number theory.
[51] The School of Athens: Projective geometry and the mathematics of perspective.

June 2013

[50] Senior Wranglers: Wranglers and the Mathematical Tripos.
[49] Normal Numbers: Surprising properties of Champernowne’s Number.
[48] Joyce’s Number: Maximum number using three 9s.
[47] Prime Secrets: Two exciting results in prime number theory.

May 2013

[46] Gauss’s Oversight: Gauss misses a crucial connection.
[45] The Sholders of Giants: The mathematician John Wallis.
[44] Kelvin Wakes: Beautiful ship-wave patterns.
[43] Loaves & Fishes: The Banach-Tarski Theorem.
[42] Monster Symmetry: The monster group and symmetry in physics.

April 2013
[41] Spots & Stripes: Reaction-diffusion processes and pattern generation.
[4-] The Dozenal System: Base-twelve arithmetic.
[39] Pythagoras goes Global: Pythagoras’ Theorem on the sphere.
[38] Bayes Rules OK: Many implications of Bayes’ Theorem.

March 2013
[37] Peaks, Pits & Passes: Some properties of maps and charts.
[36] The Pitch-drop Experiment: A long-running physics experiment.
[35] Happy Pi-Day: 3/14, a cause for celebration.
[34] CAT Scans: Medical imaging and the Radon transform.
[33] More Equal than Others: Robert Recorde and the “=” sign.

February 2013
[32] The Swingin’ Spring: Complex dynamics of a simple mechanical system.
[31] SVD: The invaluable Singular Value Decomposition.
[30] Computer Maths: Will computers ever be able to do mathematical research?

January 2013
[29] Chess Harmony: Some properties of the harmonic series.
[28] The Lambert W-function: An interesting special function.
[27] Topology Underground: The geometry and topology of subway systems.
[26] The Power Tower: Surprising convergence of iterated exponents.
[25] Archimedes Uncovered: The Archimedes Palimpsest.

December 2012
[24] Pons Asinorum: A startling geometric proof.
[23] Santa’s Challenge: Santa Claus and the travelling salesman problem.
[22] Sharing a Pint: An amusing puzzle for the pub.
[21] Ramanujan’s Lost Notebook: Ramanujan’s papers found in the Wren Library.

November 2012
[20] Taxi-cab Geometry: Where circles are square and pi equals 4.
[19] Surreal Numbers: Conway’s ingenious transfinite numbers.
[18] Where in the World: GPS and relativity.
[17] Shackleton’s Spectacular: An amazing feat of navigation.
[16] A Mersennery Quest: GIMPS and the search for Mersenne primes.

October 2012
[15] The Popcorn Function: A function with extraordinary continuity properties.
[14] Carving up the Globe: Many ways to dissect the sphere.
[13] The Falling Slinky: The bottom stays still!
[12] Contagion: Modelling infectious diseases.

September 2012
[11] The End of Small-pox: Daniel Bernoulli and innoculation.
[10] The Kahn Academy: A revolution on maths education.
[9] The Beautiful Game: Golden section nowhere to be seen.
[8] Packing & Stacking: From Kepler to Hales.
[7] No Maths Involved: Aspects of Sudoku.
August 2012
[6] Sproutology: Another clever invention of John Conway.
[5] Analemmatic Sundials: You are the gnomon (pointer).
[4] Napier’s Nifty Rules: Spherical trigonometry made simple.
[3] PageRank: How Google finds things fast.

July 2012
[2] The Two Cultures: Beethoven and Gauss.
[1] That’s Maths: Articles in The Irish Times.