Pavimenti

May 31, 2010 in formulas, seminars

“Pavimenti romani lacunosi in opus tessellatum:
classificazione dei meccanismi compositivi e variazioni di scala”
Alessandra Carlini
Facoltà di Architettura, Università Roma Tre

“Pavimenti islamici, studio sulla composizione”
Elisa Conversano
Facoltà di Architettura, Università Roma Tre

Il seminario illustra il progetto di ricerca che da anni impegna matematici ed architetti del laboratorio “Formulas” su possibili applicazioni della teoria delle tassellazioni piane allo studio di pavimenti.
Il primo risultato sistematico, pubblicato in diversi contesti scientifici e portato in mostra presso il Festival dela Scienza di Genova e il Festival della Matematica di Roma, riguarda l’analisi e la ricostruzione virtuale dei mosaici delle tabernae ai Marcati di Traiano (Roma) a partire dai frammenti in loco (Responsabile scientifico: L.Tedeschini Lalli; Consulenza archeologica: L.Ungaro).
Il seminario si articola in due interventi che illustrano gli sviluppi della ricerca.
Il primo “Pavimenti lacunosi in opus tessellatum: classificazione dei meccanismi compositivi e cambiamenti di scala”, si concentra sui pavimenti romani in bianco/nero, allargando il campo d’indagine storica e geometrica.
Il secondo, “Pavimenti islamici: studio sulla composizione”, recupera la parte dei risultati della tesi di laurea “Composizioni modulari: il caso delle cupole islamiche” (Realtore: L.Tedeschini Lalli; Correlatore: N.Rizzi; 2006) relativa allo studio della composizione dei pavimenti islamici.

Martin Gardner, Puzzler and Polymath, Dies at 95

May 24, 2010 in formulas, news

Douglas Martin, New York Times

Martin Gardner, who teased brains with math puzzles in Scientific American for a quarter-century and who indulged his own restless curiosity by writing more than 70 books on topics as diverse as magic, philosophy and the nuances of Alice in Wonderland, died Saturday in Norman, Okla. He was 95.

Martin Gardner was a prolific and wide-ranging writer.

He had been living in an assisted-living facility in Norman, his son James said in confirming the death.

Mr. Gardner also wrote fiction, poetry, literary and film criticism, as well as puzzle books. He was a leading voice in refuting pseudoscientific theories, from ESP to flying saucers. He was so prolific and wide-ranging in his interests that critics speculated that there just had to be more than one of him.

His mathematical writings intrigued a generation of mathematicians, but he never took a college math course. If it seemed the only thing this polymath could not do was play music on a saw, rest assured that he could, and quite well.

“Martin Gardner is one of the great intellects produced in this country in the 20th century,” said Douglas Hofstadter, the cognitive scientist.

W. H. Auden, Arthur C. Clarke, Jacob Bronowski, Stephen Jay Gould and Carl Sagan were admirers of Mr. Gardner. Vladimir Nabokov mentioned him in his novel “Ada” as “an invented philosopher.” An asteroid is named for him.

Mr. Gardner responded that his life was not all that interesting, really. “It’s lived mainly inside my brain,” he told The Charlotte Observer in 1993.

His was a clarifying intelligence: he said his talent was asking good questions and transmitting the answers clearly and crisply. In “Annotated Alice” (1960), Mr. Gardner literally rained on the parade of his hero, Lewis Carroll.

Carroll writes of a “golden afternoon” in the first line of “Alice’s Adventures in Wonderland,” a reference to an actual day rowing on the Thames. Mr. Gardner found that the day, July 4, 1862, was, in truth, “cool and rather wet.”

Mr. Gardner’s questions were often mathematical. What is special about the number 8,549,176,320? As Mr. Gardner explained in “The Incredible Dr. Matrix” (1976), the number is the 10 natural integers arranged in English alphabetical order.

The title of a book he published in 2000 was calculated to tweak religious fundamentalists — “Did Adam and Eve Have Navels?” — suggesting that the first man and woman had had umbilical cords. This time he gave no answer.

“Gardner has an old-fashioned, almost 19th-century, Oliver Wendell Holmes kind of American mind — self-educated, opinionated, cranky and utterly unafraid of embarrassment,” Adam Gopnik wrote in The New York Times Book Review in 1999.

Martin Gardner was born Oct. 21, 1914, in Tulsa, Okla., where his father, a petroleum geologist, started an oil company. As a boy he liked magic tricks, chess, science and collecting mechanical puzzles.

Unbeknownst to his mother at the time, he learned to read by looking at the words on the page as she read him L. Frank Baum’s Oz books. As an adult, he wrote a sequel to Baum’s “Wonderful Wizard of Oz” called “Visitors From Oz,” in which Dorothy encounters characters from the “Alice” books and Geraldo Rivera.

Mr. Gardner majored in philosophy at the University of Chicago, from which he graduated in 1936. In 1937 he returned to Oklahoma to be assistant oil editor of The Tulsa Tribune at $15 a week. Quickly bored, he returned to the University of Chicago, where he worked in press relations and moonlighted selling magic kits.

He joined the Navy and served on a destroyer. While doing night watch duty, he thought up crazy plots for stories, including “The Horse on the Escalator,” which he sold to Esquire magazine.

After a stint as editor of Humpty Dumpty, a children’s magazine, Mr. Gardner began a long relationship with Scientific American with an article in 1956 on hexaflexagons, strips of paper that can be folded in certain ways to reveal faces besides the two that were originally on the front and back. When the publisher suggested that he write a column about mathematical games, he jumped at the chance.

By his account, Mr. Gardner then rushed out to secondhand bookstores to find books about math puzzles, an approach he used for years to keep just ahead of his monthly deadline. “The number of puzzles I’ve invented you can count on your fingers,” he told The Times last year.

Dr. Hofstadter, who succeeded Mr. Gardner at Scientific American, said Mr. Gardner achieved elegant results by drawing on fields from logic to the philosophy of science to literature. He conveyed “the magical quality of mathematics,” Dr. Hofstadter said.

Mr. Gardner, who lived in Hastings-on-Hudson, N.Y., for most of the years he wrote for Scientific American, resigned from the magazine in 1981. Two years later he began a column in Skeptical Inquirer, “Notes of a Fringe Watcher,” which he continued to write until 2002. He had already begun beating this drum, debunking psuedoscience, in his book “Fads and Fallacies in the Name of Science.” He helped found the Committee for the Scientific Investigation of Claims of the Paranormal.

In The New York Review of Books in 1982, Stephen Jay Gould, the evolutionary biologist, called Mr. Gardner “the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.”

There was much more, including his annotated editions of “Casey at the Bat” and “The Night Before Christmas.” In his philosophical writing Mr. Gardner rejected speculative metaphysics because it could not be proved logically or empirically. He wrestled with religion in essays and in a novel that described his personal journey from fundamentalism, “The Flight of Peter Fromm” (1973). He ultimately found no reason to believe in anything religious except a human desire to avoid “deep-seated despair.” So, he said, he believed in God.

After retiring from Scientific American, Mr. Gardner lived for many years in Hendersonville, N.C. His wife, the former Charlotte Greenwald, died in 2000. Besides his son James, of Norman, he is survived by another son, Thomas, of Asheville, N.C., and three grandchildren. For all Mr. Gardner’s success in refuting those who take advantage of people’s gullibility, he sometimes could not help having fun with it himself. In one Scientific American column, he wrote that dwelling in pyramids could increase everything from intelligence to sexual prowess. In another he asked readers to remember the holiday that begins the month of April.

“I just play all the time,” he said in an interview with Skeptical Inquirer in 1998, “and am fortunate enough to get paid for it.”

New Chair of Financial Mathematics appointed – Kings College London

May 17, 2010 in formulas, news

Dr Damiano BrigoThe School of Physical Sciences & Engineering at King’s has appointed Dr Damiano Brigo to the Gilbart Chair of Financial Mathematics. Dr Brigo is currently Visiting Professor of Mathematical Finance at Imperial College and Managing Director and Global Head of the Quantitative Innovation team at Fitch Solutions.

Dr Brigo is a specialist in stochastic mathematical models in finance, signal processing, filtering and control. Two of his main works are ‘Interest Rate Models – Theory and Practice’, with F. Mercurio, and a new book on ‘Credit Models and the Crisis’, with A. Pallavicini and R. Torresetti. He has published more than 50 articles in top journals for Mathematical Finance, Systems Theory, Probability and Statistics. Dr Brigo is Managing Editor of the International Journal of Theoretical and Applied Finance, he is a member of the Fitch Academic Advisory Board and is part of scientific committees for academic conferences occurring at MIT and other academic and industry institutions.

Record of innovation

Dr Brigo is listed as the most popular author and second most prolific credit author in defaultrisk.com and waslisted as the most cited author in Risk Magazine in 2006. He has also been a charter member of Risk Who’s Who since 2007. His current interests include valuation and pricing, risk measurement, credit and default modelling, counterparty risk, stochastic dynamical models for commodities and inflation, the interaction between the exponential statistical manifold and the dynamic features of stochastic processes laws, nonlinear stochastic filtering, and stochastic processes consistent with mixtures of distributions.

He obtained a PhD in stochastic filtering with differential geometry in 1996 from the Free University of Amsterdam, following a BSc in Mathematics with honors from the University of Padua.

Chris Mottershead, Vice-Principal (Research & Innovation), welcomed Dr Brigo’s appointment, saying: ‘I am delighted that Damiano is joining the Financial Mathematics group at King’s. He brings massive experience and a record of innovation in credit risk and interest rate modelling that perfectly complements the group’s interests.’

Notes to editors

About the Chair
The Professorship is named after the distinguished English banker and author James William Gilbart (1794-1863). JW Gilbart was the first General Manager of the London and Westminster Bank. His principal works on banking were Practical Treatise on Banking (1827), The History and Principles of Banking (1834); The History of Banking in America (1837); Lectures on the History and Principles of Ancient Commerce (1847); Logic for the Million (1851); and Logic of Banking (1857). He was elected a Fellow of the Royal Society in 1846. The Gilbart Lectures on Banking were an annual institution at King’s dating back to 1872, and more recent speakers included Eddie George (1996), Howard Davies (1998).

About Financial Mathematics
The King’s Financial Mathematics Group was founded in 2000 and now numbers two full professors, one visiting professor, one reader and two lecturers, in addition to visiting and temporary staff, and eight PhD students. The group runs a large weekly seminar attended by academics and City of London practitioners, and a world-renowned MSc in Financial Mathematics with around 50 students.

King’s College London
King’s College London is one of the top 25 universities in the world (Times Higher Education 2009) and the fourth oldest in England. A research-led university based in the heart of London, King’s has nearly 23,000 students (of whom more than 8,600 are graduate students) from nearly 140 countries, and some 5,500 employees. King’s is in the second phase of a £1 billion redevelopment programme which is transforming its estate.

King’s has an outstanding reputation for providing world-class teaching and cutting-edge research. In the 2008 Research Assessment Exercise for British universities, 23 departments were ranked in the top quartile of British universities; over half of our academic staff work in departments that are in the top 10 per cent in the UK in their field and can thus be classed as world leading. The College is in the top seven UK universities for research earnings and has an overall annual income of nearly £450 million.

King’s has a particularly distinguished reputation in the humanities, law, the sciences (including a wide range of health areas such as psychiatry, medicine and dentistry) and social sciences including international affairs. It has played a major role in many of the advances that have shaped modern life, such as the discovery of the structure of DNA and research that led to the development of radio, television, mobile phones and radar. It is the largest centre for the education of healthcare professionals in Europe; no university has more Medical Research Council Centres.

King’s College London and Guy’s and St Thomas’, King’s College Hospital and South London and Maudsley NHS Foundation Trusts are part of King’s Health Partners. King’s Health Partners Academic Health Sciences Centre (AHSC) is a pioneering global collaboration between one of the world’s leading research-led universities and three of London’s most successful NHS Foundation Trusts, including leading teaching hospitals and comprehensive mental health services. For more information, visit: www.kingshealthpartners.org.

2010 Jamaican Mathematical Olympiad Awards

May 12, 2010 in formulas

The 2010 Jamaican Mathematical Olympiad was a national mathematical competition open to all high school students in Jamaica. This competition was implemented by The University of the West Indies in association with Sterling Asset Management Limited. The students who entered competed for a selection as a National Mathematics Champion at their grade level. In addition, they competed to be one of the top overall performers who met the age requirements of the competition. The three who are been selected will travel to Mayaguez, Puerto Rico this month to compete in the 12th Centro 2010 Regional Mathematical Olympiad against other competing countries from across the globe.

The awards ceremony was held on Saturday May 8, 2010 at the Mona Visitors’ Lodge and Conference Centre, UWI. There, the top three students of each category were given their awards. The 2010 Jamaican Mathematical Olympiad Team is comprised of the three highest ranked students, as well as two alternatives.

The awardees in the seventh grade category were: Mellisa Douglas (1st place of St. Andrew High School), Orville Kirkland (2nd place of St Mary High School) and Danielle Notice (3rd place of Bishop Gibson High School).

The awardees in the eight grade category were: Anphernee Wilson (1st place of Herbert Morrison Technical High School), Marc-Ann Allen (2nd place of Immaculate Conception High School) and Sherika Anderson (3rd place of Immaculate Conception High School).

The awardees in the ninth grade category were: Nicholas McFarlane (1st place of Ardenne High School), Shanika Wright (2nd place of Holy Childhood High School) and Janielle Walters (3rd place of Glenmuir High School).

The awardees in the tenth grade category were: Aaron Johnson (1st place of Campion College), Daniel Chin (2nd place of Glenmuir High School) and Sanjae King (3rd place of Glenmuir High School)

The awardees in the eleventh grade category were: Tamrah Brown (1st place of Immaculate Conception High School), Shannon DaCosta (2nd place of Immaculate Conception High School) and Andre Thompson (3rd place of Glenmuir High School).

The members of the 2010 Jamaican Mathematical Olympiad Team are: Aaron Johnson, Nicholas McFarlane and Daniel Chin, with Sanjae King and Jhanelle Thomas as the first and second alternatives respectively. These students will participate in the 2010 Central American and Caribbean Regional Mathematical Olympiad which will be held from May 26 to June 1, 2010.

Simple connectedness in the New York Review of Books

May 10, 2010 in formulas, news

“A diagram showing ‘simple connectedness,’ a topological property allowing for, in this example, a rubber band around the surface of a sphere to be shrunk to no more than a point. This property was long known to characterize two-dimensional spheres and has now been shown to characterize three-dimensional spheres as well by Perelman’s proof of the Poincaré Conjecture.” — caption from Paulos’ review; image credit: Richard Morris/Wikipedia.
John Allen Paulos’ review of a new book about Grisha Perelman (New York Review of Books, April 29, 2010) gives him the opportunity to teach the Review’s readers some topology. The book is “Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century” by Masha Gessen (Houghton-Mifflin-Harcourt); and according to Paulos it is “a fascinating biography of … the fearsomely brilliant and notoriously antisocial Russian mathematician.” Paulos starts with a lightning summary of the principal episodes in Perelman’s life, and then spends an awkward couple of paragraphs mulling Gessen’s suggestion that Perelman may have Asperger’s syndrome; Paulos refers to the British psychologist Simon Baron-Cohen who “maintains that there is some neurological reason for the strong correlation between mathematical talent and Aspberger’s syndrome. Whether true or not, mathematicians do score consistently higher on what he calls his AQ (autism-spectrum quotient) test …” And he tells us the old joke about the definition of an extroverted mathematician: the one who looks at your feet while he’s talking.

The second half of the review focuses on the actual mathematics in unusual, and unusually correct, detail. First a definition of topology (“the branch of geometry concerned with the basic properties of geometric figures that remain unchanged when they are stretched and shrunk, deformed and distorted, or subjected to any ‘smooshing,’ as long as they’re not ripped or punctured.”) Then some examples of topological properties: knotting, separation, dimension, boundaries, genus (the doughnut and the coffee cup, of course) and simple connectedness: “imagine stretching a rubber band around the surface of a ball”, etc., with reference to the picture reproduced above. “Poincaré was aware of the fact that a two-dimensional sphere–the topological term for the two-dimensional surface of a three-dimensional ball–could be defined by this property of simple connectivity. That is, any simply connected two-dimensional closed surface … is topologically equivalent to the surface of a ball. He wondered if simple connectedness might characterize three-dimensional spheres as well. The statement that it does so is the Poincaré Conjecture.” After working at giving the NYRB readers some clue as to what a 3-dimensional sphere might be (“… can’t be visualized except in cross-sections–or, it is said, by a very few mathematicians like William Thurston of Cornell University …”) Paulos sketches the history of the problem including the Ricci flow (“Think of blowing hot air into a crinkled-up balloon.”), the problem of singularities (“places where the process breaks down and part of the shape starts to stretch on and on, beyond bound–a little like dividing by zero”), how to correct them (“a repair must be made using a controlled process of grafting on pieces of other shapes that topologists call ‘surgery'”), the fundamental problem (“there was no guarantee that repairs could be made for every type of singularity and for every recurrence of the same type”), Perelman’s solution (“…dazzlingly showed that all possible singularities were reparable, and … demonstrated how to do the requisite surgeries and put all the stringy and lumpy pieces of the blob together”) and the subsequent turmoil in the mathematical world. A tremendous amount of good information in a very small space.

Seminario: Punti distanti e cammini minimi su poliedri

May 10, 2010 in formulas, seminars

Martedi 25 maggio, aula Sirleto ore 14.00

“Punti distanti e cammini minimi su poliedri”

Paola Magrone

Facoltà di Architettura, Università Roma Tre

Cercando problemi (da proporre agli allievi architetti) riguardanti i percorsi minimi su poliedri attraverso lo studio dello sviluppo piano, si possono incontrare interessanti problemi matematici aperti o di recente soluzione. Ad esempio la questione dei punti distanti sui poliedri. Anche su un oggetto semplice come una scatola, non è ovvio capire se il punto più lontano da uno dato sia, o meno, in posizione antipodale, oppure quale sia la lunghezza massima possibile per una geodetica sul tetraedro. Questo problema si traduce anche in una questione di analisi nonlineare: ricerca e studio delle geodetiche su insiemi detti “varietà coniche”. Verranno illustrate le linee principali di questo tipo di approccio.