**[To December 2022. For recent posts, see** sidebar]

**December 2022**

**[547] Spiric curves and phase portraits December 29, 2022****[546] Closeness in the 2-Adic Metric December 22, 2022****[545] Convergence of mathematics and physics December 15, 2022****[544] Curvature and Geodesics on a Torus December 8, 2022****[543] Low-pass Filtering and the Remarkable Integrals of Borwein and Borwein December 1, 2022**

**November 2022**

**[542] What’s the Next Number? November 24, 2022****[541] The Rich Legacy of Indian Mathematics November 17, 2022****[540] Mercury’s Mercurial Orbit November 10, 2022****[539] The Power of the 2-gon: Extrapolation to Evaluate Pi November 3, 2022**

**October 2002**

**[538] Dropping Pebbles down a Mine-shaft October 27, 2022****[537] From Sub-atomic to Cosmic Strings October 20, 2022****[536] Finding the Area of a Field October 13, 2022****[535] CND Functions: Curves that are Continuous but Nowhere Differentiable October 6, 2022**

**September 2022**

**[534] Topological Calculus: away with those nasty epsilons and deltas September 29, 2022****[533] The 3-sphere: Extrinsic and Intrinsic Forms September 22, 2022****[532] Making Sound Pictures to Identify Bird Songs September 15, 2022****[531] Dynamic Equations for Weather and Climate September 8, 2022****[530] Curl Curl Curl September 1, 2022**

**August 2022**

**[529] X+Y and the Special Triangle****August 25, 2022****[528] The Navigational Skills of the Marshall Islanders August 18, 2022****[527] Space-Filling Curves, Part II: Computing the Limit Function August 11, 2022****[526] Space-Filling Curves, Part I: “I see it, but I don’t believe it” August 4, 2022**

**July 2022**

**[525] Poincare’s Square and Unbounded Gomoku July 28, 2022****[524] Fields Medals presented at IMC 2022 July 21, 2022****[523] Goldbach’s Conjecture and Goldbach’s Variation July 14, 2022****[522] The Size of Sets and the Length of Sets July 7, 2022**

**June 2022**

**[521] Can We Control the Weather? June 30, 2022****[520] The Arithmetic Triangle is Analytical too June 23, 2022****[519] ICM 2022 — Plans Disrupted but not Derailed June 16, 2022****[518] Swingin’-Springin’-Twistin’-Motion June 9, 2022****[517] Parity of the Real Numbers: Part I June 2, 2022**

**May 2022**

**[516] Fairy Lights on the Farey Tree May 26, 2022****[515] Image Processing Emerges from the Shadows May 19, 2022****[514] Parity and Partition of the Rational Numbers. Part II: Density of the Three Parity Classes May 12, 2022****[513] Parity and Partition of the Rational Numbers. Part I: The Three Parity Classes May 5, 2022**

**April 2022**

**[512] A Finite but Unbounded Universe April 28, 2022****[511] The Whole is Greater than the Part — Or is it? April 21, 2022****[510] Following the Money around the Eurozone April 14, 2022****[509] Mamikon’s Visual Calculus and Hamilton’s Hodograph April 7, 2022**

**March 2022**

**[508] Infinitesimals: vanishingly small but not quite zero March 31, 2022****[507] The Chromatic Number of the Plane March 24, 2022****[506] The Improbability Principle and the Seanad Election March 17, 2022****[505] Hyperreals and Nonstandard Analysis March 10, 2022****[504] A Prescient Vision of Modern Weather Forecasting March 3, 2022**

**February 2022**

**[503] Why Waffle when One Wordle Do? February 24, 2022****[502] Sources and Scenes of Mathematical Inspiration February 17, 2022****[501] Where is the Sun? February 10, 2022****[500] Mathematical Equations are our Friends February 3, 2022**

**January 2022**

**[499] Gaussian Primes January 27, 2022****[498] Letters to a German Princess: Euler’s Blockbuster Lives On January 20, 2022****[497] Euler’s Journey to Saint Petersburg January 13, 2022****[496] Some Characteristics of the Mathematical Psyche January 6, 2022**

**December 2021**

**[495] De Branges’s Proof of the Bieberbach Conjecture December 30, 2021****[494] Number Partitions: Euler’s Astonishing Insight December 23, 2021****[493] Bernoulli’s Golden Theorem and the Law of Large Numbers Dec. 16, 2021****[492] Set Density: are even numbers more numerous than odd ones? Dec. 9, 2021****[491] Buffon’s Noodle and the Mathematics of Hillwalking December 2, 2021**

**November 2021**

**[490] Chiral and Achiral Knots November 25, 2021****[489] Émilie Du Châtelet and the Conservation of Energy November 18, 2021****[488] Cantor’s Theorem and the Unending Hierarchy of Infinities Nov. 11, 2021****[487] Topsy-turvy Maths: Proving Axioms from Theorems November 4, 2021**

**October 2021**

**[486] How to Write a Convincing Mathematical Paper October 28, 2021****[485] Mathematical Scandals and Scoundrels October 21, 2021****[484] The Square Root Spiral of Theodorus October 14, 2021****[483] A Grand Unification of Mathematics October 7, 2021**

**September 2021**

**[482] The Spine of Pascal’s Triangle September 30, 2021****[481] Embedding: Reconstructing Solutions from a Delay Map Sept. 23, 2021****[480] Earth System Models simulate the changing climate September 16, 2021****[479] The Signum Function may be Continuous September 9, 2021****[478] The Social Side of Mathematics September 2, 2021**

**August 2021**

**[477] Real Derivatives from Imaginary Increments August 26, 2021****[476] Changing Views on the Age of the Earth August 19, 2021****[475] Carnival of Mathematics August 12, 2021****[474] Phantom traffic-jams are all too real August 5, 2021**

**July 2021**

**[473] Simple Models of Atmospheric Vortices July 29, 2021****[472] Finding Fixed Points July 22, 2021****[471] All Numbers Great and Small July 15, 2021****[470] Approximating the Circumference of an Ellipse July 8, 2021****[469] Kalman Filters: from the Moon to the Motorway July 1, 2021**

**June 2021**

**[468] Gauss Predicts the Orbit of Ceres June 24, 2021****[467] Seeing beyond the Horizon June 17, 2021****[466] Al Biruni and the Size of the Earth June 10, 2021****[465] The Simple Arithmetic Triangle is full of Surprises June 3, 2021**

**May 2021**

**[464] Hanoi Graphs and Sierpinski’s Triangle May 27, 2021****[463] Multi-faceted aspects of Euclid’s Elements May 20, 2021****[462] A Model for Elliptic Geometry May 13, 2021****[461] Improving Weather Forecasts by Reducing Precision May 6, 2021**

**April 2021**

**[460] Can You Believe Your Eyes? April 29, 2021****[459] The Size of Things April 22, 2021****[458] Entropy and the Relentless Drift from Order to Chaos April 15, 2021****[457] Circles, polygons and the Kepler-Bouwkamp constant April 8, 2021****[456] Was Space Weather the cause of the Titanic Disaster? April 1, 2021**

**March 2021**

**[455] The Dimension of a Point that isn’t there March 25, 2021****[454] Making the Best of Waiting in Line March 18, 2021****[453]Differential Forms and Stokes’ Theorem March 11, 2021****[452] Goldbach’s Conjecture: if it’s Unprovable, it must be True March 4, 2021**

**February 2021**

**[451] Mamikon’s Theorem and the area under a cycloid arch February 25, 2021****[450] Machine Learning and Climate Change Prediction February 18, 2021****[449] Apples and Lemons in a Doughnut February 11, 2021****[448] Complexity: are easily-checked problems also easily solved? February 4, 2021**

**January 2021**

**[447] Euler’s Product: the Golden Key January 28, 2021****[446] Euler: a mathematician without equal and an overall nice guy January 21, 2021****[445] The Basel Problem: Euler’s Bravura Performance January 14, 2021****[444] We are living at the bottom of an ocean January 7, 2021**

**December 2020**

**[443] Derangements and Continued Fractions for e December 31, 2020****[442] Arrangements and Derangements December 24, 2020****[441] On what Weekday is Christmas? Use the Doomsday Rule December 17, 2020****[440] Will RH be Proved by a Physicist? December 10, 2020****[439] Decorating Christmas Trees with the Four Colour Theorem December 3, 2020**

**November 2020**

**[438] Laczkovich Squares the Circle November 26, 2020****[437] Ireland’s Mapping Grid in Harmony with GPS November 19, 2020****[436] Aleph, Beth, Continuum November 12, 2020****[435] Weather Forecasts get Better and Better November 5, 2020**

**October 2020**

**[434] The p-Adic Numbers (Part 2) October 29, 2020****[433] The p-Adic Numbers (Part I) October 22, 2020****[432] Terence Tao to deliver the Hamilton Lecture October 15, 2020****[431] From Impossible Shapes to the Nobel Prize October 8, 2020****[430] Mathematics and the Nature of Physical Reality October 1, 2020**

**September 2020**

**[429] Doughnuts and Dumplings are Distinct: Homopoty-101 September 24, 2020****[428] Will mathematicians be replaced by computers? September 17, 2020****[427] TeX: A Boon for Mathematicians September 10, 2020****[426] Suitable Names for Large Numbers September 3, 2020**

**August 2020**

**[425] Jung’s Theorem: Enclosing a Set of Points August 27, 2020****[424] Is There Anyone Out There? The Drake Equation gives a Clue August 20, 2020****[423] Think of a Number: What are the Odds that it is Even? August 13, 2020****[422] Resolution of Paradox: a Gateway to Mathematical Progress August 6, 2020**

**July 2020**

**[421] Berry’s Paradox and Gödel’s Incompleteness Theorem July 30, 2020****[420] Does Numerical Integration Reflect the Truth? July 23, 2020****[419] Cornelius Lanczos – Inspired by Hamilton’s Quaternions July 16, 2020****[418] Buridan’s Ass July 9, 2020****[417] The Ever-growing Goals of Googology July 2, 2020**

**June 2020**

**[416] The Online Encyclopedia of Integer Sequences June 25, 2020****[415] The Geography of Europe is Mapped in our Genes June 18, 2020****[414] Dimension Reduction by PCA June 11, 2020****[413] Pooling Expertise to Tackle Covid-19 June 4, 2020**

**May 2020**

**[412] The Monte-Carlo Method May 28, 2020****[411] Changing the way that we look at the world May 21, 2020****[410] A New Perspective on Perspective May 14, 2020****[409] John Casey: a Founder of Modern Geometry May 7, 2020**

**April 2020**

**[408] Order in the midst of Chaos April 30, 2020****[407] John Horton Conway: a Charismatic Genius April 23, 2020****[406] Exponential Growth must come to an End April 16, 2020****[405] The Ross-Littlewood Paradox April 9, 2020****[404] The Mathematics of Fair Play in Video Games April 2, 2020**

**March 2020**

**[403] Bang! Bang! Bang! Explosively Large Numbers March 26, 2020****[402] Covid-19: Modelling the evolution of a viral outbreak March 19, 2020****[401] Samuel Haughton and the Twelve Faithless Hangmaids March 12, 2020****[400] Samuel Haughton and the Humane Drop March 5, 2020**

**February 2020**

**[399] Zhukovsky’s Airfoil February 27, 2020****[398] How many numbers begin with a 1? More than 30%! February 20, 2020**

**[397] A Ring of Water Shows the Earth’s Spin February 13, 2020****[396] Using Maths to Reduce Aircraft Noise February 6, 2020**

**January 2020**

**[395] The Rambling Roots of Wilkinson’s Polynomial January 30, 2020****[394] Adjoints of Vector Operators January 23, 2020****[393] The “extraordinary talent and superior genius” of Sophie Germain January 16, 2020****[392] Grad, Div and Curl on Weather Maps: a Gateway to Vector Analysis January 9, 2020****[391] The knotty problem of packing DNA January 2, 2020**

**December 2019**

**[390] Divergent Series Yield Valuable Results December 26, 2019****[389] Having your Christmas Cake and Eating it December 19, 2019****[388] The Intermediate Axis Theorem December 12, 2019****[387] A New Mathematical Discovery from Neutrino Physics December 5, 2019**

**November 2019**

**[386] Archimedes and the Volume of a Sphere November 28, 2019****[385] Airport Baggage Screening with X-Ray Tomography November 21, 2019****[384] Elliptic Trigonometry: Fun with “sun”, “cun” and “dun” November 14, 2019****[383] The Vastness of Mathematics: No One Knows it All November 7, 2019**

**October 2019**

**[382] An Attractive Spinning Toy: the Phi-TOP October 31, 2019****[381] Some Fundamental Theorems of Maths October 24, 2019****[380] Maths and Poetry: Beauty is the Link October 17, 2019****[379] The Wonders of Complex Analysis October 10, 2019****[378] Emergence of Complex Behaviour from Simple Roots October 3, 2019**

**September 2019**

**[377] Zeroing in on Zeros September 26, 2019****[376] George Salmon, Mathematician & Theologian September 19, 2019****[375] Spiralling Primes September 12, 2019****[374] An English Lady with a Certain Taste September 5, 2019**

**August 2019**

**[373]***ToplDice*is Markovian August 29, 2019**[372] The curious behaviour of the Wilberforce Spring. August 22, 2019****[371] The Brief and Tragic Life of Évariste Galois August 15, 2019****[370] Stokes’s 200th Birthday Anniversary August 8, 2019****[369] Algorithms: Recipes for Success August 1, 2019**

**July 2019**

**[368] Billiards & Ballyards July 25, 2019****[367] Learning Maths without even Trying July 18, 2019****[366] Boxes and Loops July 11, 2019****[365] What did the Romans ever do for Maths? July 4, 2019**

**June 2019**

**[364] Cumbersome Calculations in Ancient Rome June 27, 2019****[363] Simple Curves that Perplex Mathematicians and Inspire Artists June 20, 2019****[362] Bernard Bolzano, a Voice Crying in the Wilderness June 13, 2019****[361] Spin-off Effects of the Turning Earth June 6, 2019**

**May 2019**

**[360] Symplectic Geometry May 30, 2019****[359] Chase and Escape: Pursuit Problems May 23, 2019****[358] The Rise and Rise of Women in Mathematics May 16, 2019****[357] Bouncing Billiard Balls Produce Pi May 9, 2019****[356] Kepler’s Vanishing Circles Hidden in Hamilton’s Hodograph May 2, 2019**

**April 2019**

**[355] K3 implies the Inverse Square Law. April 25, 2019****[354] Closing the Gap between Prime Numbers April 18, 2019****[353] Massive Collaboration in Maths: the Polymath Project April 11, 2019****[352] A Pioneer of Climate Modelling and Prediction April 4, 2019**

**March 2019**

**[351] A Chirping Elliptic Rocker March 28, 2019****[350] Joseph Fourier and the Greenhouse Effect March 21, 2019****[349] The Kill-zone: How to Dodge a Sniper’s Bullet March 14, 2019****[348] Hokusai’s Great Wave and Roguish Behaviour March 7, 2019**

**February 2019**

**[347] Don’t be Phased by Waveform Distortions February 28, 2019****[346] Multiple Discoveries of the Thue-Morse Sequence February 21, 2019****[345] Folding Maps: A Simple but Unsolved Problem February 14, 2019****[344] Rambling and Reckoning February 7, 2019**

**January 2019
**

**[343] Our Dearest Problems January 31, 2019****[342] From a Wide Wake to the Width of the World January 24, 2019****[341] Discoveries by Amateurs and Distractions by Cranks January 17, 2019****[340] Really, 0.999999… is equal to 1. Surreally, this is not so! January 10, 2019****[339] Trappist-1 & the Age of Aquarius January 3, 2019**

**December 2018**

**[338] Gaussian Curvature: the Theorema Egregium December 27, 2018**

**[337] Consider a Spherical Christmas Tree December 20, 2018**

**[336] The 3 : 2 Resonance between Neptune and Pluto December 13, 2018**

**[335] Random Numbers Plucked from the Atmosphere December 6, 2018**

**November 2018**

**[334] The Two Envelopes Fallacy November 29, 2018**

**[333] Gravitational Waves & Ringing Teacups November 22, 2018**

**[332] The “Napoleon of Crime” and The Laws of Thought November 15, 2018**

**[331] Listing the Rational Numbers III: The Calkin-Wilf Tree November 8, 2018**

**[330] Johannes Kepler and the Song of the Earth November 1, 2018**

**October 2018**

**[329] Saving Daylight with Hip-hop Time: a Modest Proposal October 25, 2018**

**[328] Who Uses Maths? Almost Everyone! October 18, 2018**

**[327] Listing the Rational Numbers II: The Stern-Brocot Tree October 11, 2018**

**[326] The Many Modern Uses of Quaternions October 4, 2018**

**September 2018**

**[325] Listing the Rational Numbers: I. Farey Sequences September 27, 2018**

**[324] Tom Lehrer: Comical Musical Mathematical Genius September 20, 2018**

**[323] A Trapezoidal Prism on the Serpentine September 13, 2018**

**[322] Face Recognition September 6, 2018**

**August 2018**

**[321] A Zero-Order Front August 30, 2018**

**[320] The Flight of the Bumble Bee August 23, 2018**

**[319] The Miraculous Spiral on Booterstown Strand August 16, 2018**

**[318] Euler’s “Degree of Agreeableness” for Musical Chords August 9, 2018**

**[317] Tides: a Tug-of-War between Earth, Moon and Sun August 2, 2018**

**July 2018**

**[316] Grandi’s Series: A Second Look July 26, 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*.