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“The history of π is a quaint little mirror of the history of man. It is the story of Archimedes of Syracuse, whose method of calculating π defied substantial improvement for some 1900 years, and it is also the story of a Cleveland businessman, who published a book in 1931 announcing the grand discovery that π was exactly […]
I have been uninspired by current events lately, but thought this would make a decent post, so here goes: Read More View Post
“The commuters with faint effort maneuvered onto the onramps of the 5 and 405 freeways and melded into the hundreds and thousands of other vehicles destined for Anaheim, Costa Mesa, Huntington Beach, Long Beach, Torrance, Los Angeles and beyond. The lifeblood of the greater southern California heart being fed every morning with chrome fiberglass, and rubber blood cells. Every cell with a purpose — a destination in the greater host organism to perform, shine, bluster, bully, hide-out, survive, commiserate, and exchange information in their eight-hour, stress-laden, boredom-laden slice of time in their collective, deceptively un-choreographed effort to keep the sprawling city-state alive.”
The excerpt above is from another unfinished novel that I started several years ago.
I write a weekly book review for the Daily News of Galveston County. (It is not the biggest daily newspaper in Texas, but it is the oldest.) My review normally appears Wednesdays. When it appears, I post the review on Ricochet on the following Sunday. Read More View Post
In one of the less-reputable areas of Ricochet – you know, the areas your mother warns you about – a conversation went something like this… (Spoiler alert, this post gets nerdy so fast, all the other posts will threaten to take your lunch money just for reading the next sentence.)
Person 1: What races do you usually play in Dungeons & Dragons? (See? Told ya. Cough up that money.)
…before it flies apart? Theory Read More View Post
I am not a mathematician. I’m not qualified to comment on the complex (or maybe even simple) mathematical functions, formulas, proofs and theorems produced by Srinivasa Ramanujan that have challenged, continue to challenge and now are being used by mathematicians, physicists and other scientists today (over 90 years after Ramanujan’s death) to understand and make […]
So for years, like all of you, I’ve been idly wondering if it’s true that For every ε > 0, there are only finitely many triples of coprime positive integers a + b = c such that c > d1+ε, where d denotes the product of the distinct prime factors of abc. I figure that’s a question that occurs to everyone in the small hours of the morning, now and again. Once, when I was stuck in the métro during a wildcat strike, I reckoned I’d figured out a marvellous little proof. But I scribbled it down on the back of a pack of Gitanes, shoved it into the Pile of Papers, and never found it again.
Anyway, in 2012, Shinichi Mochizuki had one of those restless nights, then quietly posted 2,000 pages of scribblings on his website:
I want to take note of John Nash’s death this weekend. Nash was a pivotal figure in several disciplines, and was the subject of the movie A Beautiful Mind. He was a man who suffered mental illness, and at times the suffering was severe.
I came across his work by studying game theory, in which his theory of “Nash equilibrium” is a basic building block. His equilibrium is what allows us to predict rational behavior (although it can’t predict whether the players are rational). The short version is that there are situations in which a person is rational to choose a particular strategy, regardless of what the other players do. That’s what makes that strategy predictable.
Here is an excerpt from a common core 9th grade mathematics textbook, from the chapter Modeling and Using Exponential Functions: It can be amazing how many different historical events are connected in one way or another. For example, there are some environmentalists who claim that the increase in the world’s population has led to an […]
Two or more years ago I stumbled upon the Numberphile channel on YouTube. While catching up on their videos, I discovered an interesting one on “How big is a billion?”. It got me to thinking about how Obama could use this to appear to be reducing the debt. The summary of the video is that there […]
Mathematics is often said to be a game for the young. The Fields Medal, the most prestigious prize in mathematics, is restricted to candidates 40 years or younger. While many older mathematicians continue to make important contributions in writing books, teaching, administration, and organising and systematising topics, most work on the cutting edge is done by those in their twenties and thirties. The life and career of Harold Scott MacDonald Coxeter (he usually went by the name “Donald”) (1907–2003), the subject of this superb biography, is a stunning and inspiring counter-example. Coxeter’s publications (all of which are listed in an appendix to this book) span a period of eighty years, with the last, a novel proof of Beecroft’s theorem, completed just a few days before his death.
Coxeter was one of the last generation to be trained in classical geometry, and he continued to do original work and make striking discoveries in that field for decades after most other mathematicians had abandoned it as mined out or insufficiently rigorous, and it had disappeared from the curriculum not only at the university level but, to a great extent, in secondary schools as well. Coxeter worked in an intuitive, visual style, frequently making models, kaleidoscopes, and enriching his publications with numerous diagrams. Over the many decades his career spanned, mathematical research (at least in the West) seemed to be climbing an endless stairway toward ever greater abstraction and formalism, epitomised in the work of the Bourbaki group. (When the unthinkable happened and a diagram was included in a Bourbaki book, fittingly it was a Coxeter diagram.) Coxeter inspired an increasingly fervent group of followers who preferred to discover new structures and symmetry using the mind’s powers of visualisation. Some, including Douglas Hofstadter (who contributed the foreword to this work) and John Horton Conway (who figures prominently in the text) were inspired by Coxeter to carry on his legacy. Coxeter’s interactions with M. C. Escher and Buckminster Fuller are explored in two chapters, and illustrate how the purest of mathematics can both inspire and be enriched by art and architecture (or whatever it was that Fuller did, which Coxeter himself wasn’t too sure about—on one occasion he walked out of a new-agey Fuller lecture, noting in his diary “Out, disgusted, after ¾ hour” [p. 178]).