Einstein notation - Wikipedia In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity. As part of mathematics it is a notational subset of Ricci calculus; however, it is often used in applications in physics that do not distinguish between tangent and cotangent spaces. It was introduced to physics by Albert Einstein in 1916.
Wonders of Math - The Game of Life What is the Game of Life? by Paul Callahan Rules of the Game of Life Life is played on a grid of square cells--like a chess board but extending infinitely in every direction. A cell can be live or dead. Discovery of classic pi formula a ‘cunning piece of magic’ : NewsCenter While most people associate the mathematical constant π (pi) with arcs and circles, mathematicians are accustomed to seeing it in a variety of fields. But two University scientists were still surprised to find it lurking in a quantum mechanics formula for the energy states of the hydrogen atom. “We didn’t just find pi,” said Tamar Friedmann, a visiting assistant professor of mathematics and a research associate of high energy physics, and co-author of a paper published this week in the Journal of Mathematical Physics. “We found the classic seventeenth century Wallis formula for pi, making us the first to derive it from physics, in general, and quantum mechanics, in particular.” The Wallis formula—developed by British mathematician John Wallis in his book Arithmetica Infinitorum—defines π as the product of an infinite string of ratios made up of integers.
Math Monday: Hula Hoop Geometry, Part 1 By Glen Whitney for the Museum of Mathematics Math Mondays have so far featured a wide array of different items from which one can make a tremendous variety of geometric constructions, but there has not yet been one on hula hoops. This week and next we’ll remedy that oversight.
En el Día de Pi, 10 curiosidades sobre el número irracional El matemático griego Arquímedes fue uno de los primeros en aproximar su valor. Para aquellos que deseen conocer cuánto mide, solo deberán calcular el perímetro de una circunferencia y dividirlo por su diámetro. Blogthinkbig.com | Cada 14 de marzo se celebra en todo el mundo el Día de Pi, una conmemoración que trata de promover la divulgación sobre el número π en particular y acercar las matemáticas a la sociedad. What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree Clever student: I know! Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong! Mathematical Beauty: A Q&A with Fields Medalist Michael Atiyah Despite Michael Atiyah’s many accolades — he is a winner of both the Fields and the Abel prizes for mathematics; a past president of the Royal Society of London, the oldest scientific society in the world (and a past president of the Royal Society of Edinburgh); a former master of Trinity College, Cambridge; a knight and a member of the royal Order of Merit; and essentially Britain’s mathematical pope — he is nonetheless perhaps most aptly described as a matchmaker. He has an intuition for arranging just the right intellectual liaisons, oftentimes involving himself and his own ideas, and over the course of his half-century-plus career he has bridged the gap between apparently disparate ideas within the field of mathematics, and between mathematics and physics. Penrose had been trying to develop his “twistor” theory, a path toward quantum gravity that’s been in the works for nearly 50 years. “I thought, ‘Oh, my God,’” Penrose said. Courtesy of Michael Atiyah
Exploring Multivariable Calculus And then relaunch Chrome. Instructors: If you are an instructor using this project in any way, please send me an email to let me know of your interest. I would love to see more people using the materials from this project, and it is important that I be able to report how the project is doing to the NSF. Math Mystery: Shinichi Mochizuki and the Impenetrable Proof Sometime on the morning of August 30 2012, Shinichi Mochizuki quietly posted four papers on his website. The papers were huge—more than 500 pages in all—packed densely with symbols, and the culmination of more than a decade of solitary work. They also had the potential to be an academic bombshell. In them, Mochizuki claimed to have solved the abc conjecture, a 27-year-old problem in number theory that no other mathematician had even come close to solving. If his proof was correct, it would be one of the most astounding achievements of mathematics this century and would completely revolutionize the study of equations with whole numbers. Mochizuki, however, did not make a fuss about his proof.
Math Learning Disabilities By: Kate Garnett (1998) While children with disorders in mathematics are specifically included under the definition of Learning Disabilities, seldom do math learning difficulties cause children to be referred for evaluation. In many school systems, special education services are provided almost exclusively on the basis of children's reading disabilities. Even after being identified as learning disabled (LD), few children are provided substantive assessment and remediation of their arithmetic difficulties. This relative neglect might lead parents and teachers to believe that arithmetic learning problems are not very common, or perhaps not very serious. However, approximately 6% of school-age children have significant math deficits and among students classified as learning disabled, arithmetic difficulties are as pervasive as reading problems.
The Golden Ratio: Design's Biggest Myth In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Greats like Le Corbusier and Salvador Dalí have used the number in their work. The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple logo are all said to incorporate it. It's bullshit.
Matlet Una raccolta scelta e assistita di programmini, denominati applets, da usare online. Per permetterci di migliorare la nostra offerta, chiediamo cortesemente ai docenti di rispondere online al nostro brevissimo questionario di valutazione. Gli applets sono stati sviluppati dal “Freudenthal Institut Researchgroup in Mathematics education” di Utrecht, in Olanda nel corso di parecchi anni di ricerca e di sperimentazione. Ora alcuni di questi Applets sono messi a disposizione delle Scuole svizzere grazie alla disponibilità dell’Istituto olandese e al progetto comune sviluppato dal Centro didattico del cantone Ticino, dal Fritic del canton Friborgo e da ICT Basler Schulen del canton Basilea. Ogni programmino è accompagnato da una breve descrizione e da una scheda didattica dettagliata. I programmini possono essere utilizzati liberamente.