background preloader

Mathematics

Facebook Twitter

En el Día de Pi, 10 curiosidades sobre el número irracional. El matemático griego Arquímedes fue uno de los primeros en aproximar su valor.

En el Día de Pi, 10 curiosidades sobre el número irracional

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. Por eso nos unimos a esta fiesta matemática para fomentar la difusión científica. Por eso hoy repasamos algunas curiosidades sobre este número tan irracional como trascendente. ¿Qué es el número Pi? El número Pi se define como la relación que existe entre la longitud o el perímetro de una circunferencia y su diámetro. 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.

Discovery of classic pi formula a ‘cunning piece of magic’ : NewsCenter

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. Friedmann did not set out to look for π nor for the Wallis formula. Which can be reduced to the classic Wallis formula. 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.

Einstein notation - Wikipedia

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.[1] Introduction[edit] Statement of convention[edit] is simplified by the convention to: The upper indices are not exponents but are indices of coordinates, coefficients or basis vectors. Pi Day · Celebrate Mathematics on March 14th. Levi-Civita symbol. Ricci calculus. 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.

Mathematical Beauty: A Q&A with Fields Medalist Michael Atiyah

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. Los misteriosos ‘círculos de hadas’ confirman las teorías de Alan Turing. Un grupo de investigadores ha descubierto en el desierto occidental de Australia unos misteriosos claros entre la vegetación.

Los misteriosos ‘círculos de hadas’ confirman las teorías de Alan Turing

Vistos desde arriba, enseguida llaman la atención dos cosas: por un lado, la forma circular de las calvas y, por el otro, el patrón hexagonal que forman los círculos entre sí. El fenómeno no es nuevo, los más famosos se encontraron en Namibia (África). También en la Europa húmeda, las setas forman lo que la cultura popular llama círculos de hadas o corros de brujas. Sin embargo, no tiene nada de mágico. Estas formaciones siguen patrones ya planteados por el matemático Alan Turing. 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.

Math Mystery: Shinichi Mochizuki and the Impenetrable Proof

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. Probably the first person to notice the papers was Akio Tamagawa, a colleague of Mochizuki's at RIMS. Fesenko e-mailed some top experts in Mochizuki's field of arithmetic geometry, and word of the proof quickly spread.

Adding to the enigma is Mochizuki himself. The Golden Ratio: Design's Biggest Myth. In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation.

The Golden Ratio: Design's Biggest Myth

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.