**[To July 2018. For recent posts, see sidebar]**

**July 2018**

**[315] The Empty Set is Nothing to Worry About July 19, 2018**

**[314] Grandi’s Series: Divergent but Summable July 12, 2018**

**[313] Trigonometric Comfort Blankets on Hilltops July 5, 2018**

**June 2018**

**[312] Numbers with Nines June 28, 2018**

**[311] Optical Refinements at the Parthenon June 21, 2018**

**[310] “Dividends and Divisors Ever Diminishing” June 14, 2018**

**[309] Leopold Bloom’s Arithmetical Adventures June 7, 2018**

**May 2018**

**[308] Motifs: Molecules of Music May 31, 2018**

**[307] A Glowing Geometric Proof that Root-2 is Irrational May 24, 2018**

**[306] Mathematics at the Science Museum May 17, 2018**

**[305] Marden’s Marvel May 10, 2018**

**[304] Stan Ulam, a mathematician who figured how to initiate fusion May 3, 2018**

**April 2018**

**[303] Waves Packed in Envelopes**** April 26, 2018**

**[302] Geodesics on the Spheroidal Earth-II April 19, 2018**

**[301] Geodesics on the Spheroidal Earth – I April 12, 2018**

**[300] Fourier’s Wonderful Idea – II April 5, 2018**

**March 2018**

**[299] Fourier’s Wonderful Idea – I March 29, 2018**

**[298] Sophus Lie March 22, 2018**

**[297] Cubic Skulduggery & Intrigue March 15, 2018**

**[296] Subtract 0 and divide by 1 March 8, 2018**

**[295] Reducing R-naught to stem the spread of Epidemics March 1, 2018**

**February 2018**

**[294] The Evolute: Envelope of Normals February 22, 2018**

**[293] Galileo’s Book of Nature February 15, 2018**

**[292] Hardy’s Apology February 8, 2018**

**[291] Staying Put or Going with the Flow February 1, 2018**

**January 2018**

**[290] Kaprekar’s Number 6174January 25, 2018**

**[289] The Heart of Mathematics January 18, 2018**

**[288] Moebiquity: Ubiquity and Versitility of the Möbius Band January 11, 2018**

**[287] Energy Cascades in Van Gogh’s Starry Night January 4, 2018**

**December 2017**

**[286] Doughnuts and Tonnetze**

**[285] Darker Mornings, Brighter Evenings**

**[284] Vanishing Hyperballs**

**[283] The Star of Bethlehem … or was it a Planet?**

**November 2017**

**[282] Disentangling Loops with an Ambient Isotopy**

**[281] A Symbol for Global Circulation**

**[280] Slingshot Orbit to Asteroid Bennu**

**[279] More on Moduli**

**[278] Modular Arithmetic: from Clock Time to High Tech**

**October 2017**

**[277] Malfatti’s Circles**

**[276] Learning Maths has never been Easier**

**[275] Pedro Nunes and Solar Retrogression**

**[274] From Sailing on a Rhumb to Flying on a Geodesic**

**September 2017**

**[273] Building Moebius Bands**

**[272] Andrey Markov’s Brilliant Ideas are still a Driving Force **

**[271] Moessner’s Magical Method**

**[270] Euler and the Fountains of Sanssouci**

**August 2017**

** [269] Drawing Multi-focal Ellipses: The Gardener’s Method **

**[268] Locating the HQ with Multi-focal Ellipses **

** [267] Saros 145/22: The Great American Eclipse **

** [266] Fractions of Fractions of Fractions **

** [265] It’s as Easy as Pi **

**July 2017**

**[264] Who First Proved that C / D is Constant? **

**[263] Quadrivium: The Noble Fourfold Way **

** [262] Inertial Oscillations and Phugoid Flight**

** [261] Robert Murphy, a “Brilliant Meteor” **

**June 2017**

** [260] Patterns in Poetry, Music and Morse Code **

** [259] The Beer Mat Game**

** [258] Fractal Complexity of Finnegans Wake**

** [257] A Remarkable Pair of Sequences**

** [256] Beautiful Patterns in Maths and Music**

**May 2017**

** [255] Wavelets: Mathematical Microscopes **

**[254] Yves Meyer wins 2017 Abel Prize **

**[253] Hearing Harmony, Seeing Symmetry **

**[252] When Roughly Right is Good Enough**

**April 2017**

**[251] A Geometric Sieve for the Prime Numbers**

**[250] The Water is Rising Fast**

**[249] Torricelli’s Trumpet & the Painter’s Paradox**

**[248] The Improbability Principle**

**March 2017**

**[247] Treize: A Card-Matching Puzzle**

**[246] Numerical Coincidences**

**[245] A Life-saving Whirligig**

**[244] Brun’s Constant and the Pentium Bug **

**[243] Enigmas of Infinity**

**February 2017**

**[242] Topology in the Oval Office**

**[241] The Spire of Light **

**[240] Metallic Means **

**[239] Voronoi Diagrams: Simple but Powerful**

**January 2017**

**[238] The Beginning of Modern Mathematics **

**[237] The Library of Babel and the Information Explosion**

**[236] On Knots and Links**

**[235] The Citizens’ Assembly: Why do 10 Counties have no Members? **

**December 2016**

**[234] Unsolved: the Square Peg Problem **

**[233] Twenty Heads in Succession: How Long will we Wait?**

**[232] The Edward Worth Library: a Treasure Trove of Maths **

**[231] Raphael Bombelli’s Psychedelic Leap **

**[230] The Shaky Foundations of Mathematics **

**November 2016**

**[229] Taylor Expansions from India **

**[228] Marvellous Merchiston’s Logarithms **

**[227] Which is larger, e^pi or pi^e? **

**[226] A New Window on the World **

**October 2016**

**[225] That’s Maths Book Published Gill Books, 25 October.**

**[224] Thank Heaven for Turbulence Turbulent flow is everywhere**

**[223] Kepler’s Magnificent Mysterium Cosmographicum **

**[222] A Ton of Wonders An ode to the number 100
**

**September 2016**

**[221] Negative Number Names Historical baggage with terminology**

**[220] Venn Again’s Awake Diagrams for more than three sets**

**[219] The next Hamilton**** The chance effects of education**

**[218] Heron’s Theorem: a Tool for Surveyors No angles needed!**

**[217] The Tunnel of Eupalinos in Samos A remarkable engineering achievement
**

**August 2016**

**[216] Slicing Doughnuts Spiric sections**

**[215] Recreational Mathematics is Fun Enjoy it.**

**[214] A Toy Example of RSA Encryption Keeping us safe**

**[213] Can Mathematics Keep Us Secure? Let’s hope so.
**

**July 2016**

**[212] Random Harmonic Series Curious properties**

**[211] Computers Speaking in Irish Voice replacing text.**

**[210] Squircles A cool idea from Piet Hein**

**[209] Lateral Thinking in Mathematics Simpler from another angle**

**June 2016**

**[208] Lecture sans paroles: the factors of M67 Speechless**

**[207] Bending the Rules to Square the Circle Not Euclid’s way**

**[306] Bloom’s attempt to Square the Circle Seemed like a good idea**

**[205] Prime Generating Formulae Brilliant but useless**

**[204] Big Data: the Information Explosion It’s everywhere
**

**May 2016**

**[203] Mathematics Everywhere**** In Blackrock Station**

**[202] Andrew Wiles wins 2016 Abel Prize For Fermat**

**[201] Ramanujan’s Astonishing Knowledge of 1729 Near misses**

**[200] Modelling Rogue Waves New ideas on mechanism
**

**April 2016**

**[199] Sigmoid Functions: Gudermannian and Gompertz Curves**

**[198] The Inexorable Rise in Life Expectancy Live long and prosper**

**[197] The Power Tower Fractal Beauty in simple things**

**[196] The Search is on for Planet Nine Hold your breath
**

**March 2016**

**[195] The Imaginary Power Tower: Part II x^x^x^x…**

**[194] The Imaginary Power Tower: Part I x^x^x^x…**

**[193] Computus: Dating the Resurrection Easter Day**

**[192] Peano Music Axioms for natural numbers**

**[191] The Abel Prize The Nobel Prize for Mathematics**

**February 2016**

**[190] Bertrand’s Chord Problem Paradoxical**

**[189] Vanishing Zigzags of Unbounded Length Strange curves**

**[188] Franc-carreau or Fair-square Hard to win**

**[187] The Mathematics of Voting Not easy to be fair
**

**January 2016**

**[186] Prime Number Record Smashed Again Another Mersenne prime**

**[185] Entropy Piano Tuning It really works**

**[184]Twin Peaks The Entropy depends on the separation**

**[183] Richardson’s Forecast Factory A Marvellous Fantasy
**

**December 2015**

**[182] Squaring the Circular Functions Square Elliptic functions**

**[181] Factorial 52: A Stirling Problem Never the same hand twice**

**[180] How many Christmas Gifts? Pyramids of Baubles**

**[179] The Ping Pong Pendulum More rapid as it damps**

**[178] The Flight of a Golf Ball Dimples make the difference**

**November 2015**

**[177] Life’s a Drag Crisis Gustave Eiffel’s discovery**

**[176] Mathematics Solving Crimes Forensic mathematics**

**[175] Numbering the Family Tree Ahnentafel numbers**

**[174] Melencolia: An Enigma for Half a Millennium Dürer’s masterpiece**

**October 2015**

**[173] Mowing the Lawn in Spirals Almost Archimedean**

**[172]A Few Wild Functions When limits do not commute**

**[171] It’s a Small – Networked – World Graph theory everywhere**

**[170] Which Way did the Bicycle Go? Even Holmes nods**

**[169] New Tricks: No Clicks Noiseless CD recordings**

**September 2015**

**[168] Hamming’s Smart Error-correcting Codes SECDED removes errors**

**[167] The Ubiquitous Cycloid A historical curve**

**[166] Holbein’s Anamorphic Skull Deliberate distortion**

**[165] James Joseph Sylvester A Victorian mathematician**

**August 2015**

**[164] Thomas Harriot: Mathematician, Astronomer and Navigator Sailing with Sir Walter**

**[163] The Great American Eclipse: Put August 21, 2017 in your diary**

**[162] Buffon was no Buffoon Pins and Needles**

**[161] The Bridges of Paris A city stroll**

**July 2015**

**[160] Who Needs EirCode? A poor choice**

**[159] Bent Coins: What are the Odds? Don’t gamble on them**

**[158] RT60 and Acoustic Excellence Sabine’s great ideas**

**[157] Fun and Games on a Honeycombed Rhomboard. A popular game**

**[156] Pluto’s Unruly Family Far-away Chaos**

**June 2015**

**[155] Increasingly Abstract Algebra The growth of abstraction in mathematics.**

**[154] Emmy Noether’s beautiful theorem Connecting symmetry and conservation.**

**[153] Game Theory & Nash Equilibrium Game theory in the applied sciences.**

**[152] The Tragic Demise of a Beautiful Mind John Nash dies after receiving the Abel Prize.**

**May 2015**

**[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*.