Play the game with the Higgs boson

In the mid-March at Moriond 2013 ATLAS and CMS presented the last results about the research of the Higgs' boson. While CMS reduced the excess for the $H \rightarrow \gamma \gamma$ decay channell, ATLAS continued to observe it. This result could be a clue that the boson discovered and announced last year is only the first of a series of Higgs' bosons. Indeed, following Albert De Roeck of CSM, the photon decay could be connected with...
new physics and there are a great deal of models that can come with such a number
In order to resolve the question (is the new boson the only Higgs' boson or simply a Higgs' boson?) we have to wait the end of the maintenance work of LHC, but in the meantime we could play with the Quark Matter Card Game, in particular the variant named Higgs Boson - on Your Own!
Object of the game: to win, by detecting a decay of a Higgs boson. If this does not happen in a given game, one can win by statistics, by collecting the largest number of particle cards.
The proposed game is a variation of Memory

Pierre Deligne and the Weil conjectures

posted by @ulaulaman about #PierreDeligne #AndreWeil #AbelPrize2013 #mathematics
Pierre Deligne, a belgian mathematician, wins the Abel Prize 2013
for seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields
One of the most famous contribution by Deligne was the proof of one of the three Weil conjectures. These conjectures was stated by Andre Weil, the mathematician who proofed the Fermat's last theorem, in 1949 (Numbers of solutions of equations in finite fields) in order to solve the following problem:
how to count the number of solutions to systems of polynomial equations over finite fields(1)
In particular
Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis. The rationality was proved by Dwork (1960), the functional equation by Grothendieck (1965), and the analogue of the Riemann hypothesis was proved by Deligne (1974)

A very brief story of the Pi

posted by @ulaulaman about #PiDay #Archimedes #SrinivasaRamanujan and other mathematical curiosities

Warped by Mike Cavna via Bamdad's Math Comics
As you know, the $\pi$ is defined as the ratio of the circumference to its diameter. This number, which is transcendental, was, apparently, known since ancient times. There are, in fact, some Egyptologists who believe that $\pi$, or perhaps $\tau = 2 \pi$, was known to them since the age og the Giza's pyramid, built between 2589 and 2566 BC, because the relationship between the perimeter and the height is 6.2857.
There are no explicit proof of the fact that, at the time, Egyptian mathematics became aware of a number such as $\pi$, however, between 600 and 1000 years later on a Babylonian tablet it is geometrically established the first value of $\pi$: $25/8 = 3.1250$. From documents written more or less in the same period it can be deduced that also the Egyptians calculated the value of $\pi$, obtaining $(16/9)^2 \simeq 3.1605$.
Indian mathematics, however, seems a little late: in 600 BC on Shulba Sutras, it is calculated for the $\pi$ value like $(9785/5568)^2 \simeq 3.088$, which will be updated later in 150 BC as $\sqrt{10} \simeq 3.1622$, which is a value much closer to the value calculated by the Egyptians.
A good approximation of $\pi$ value is in Mishnat ha-Middot, a geometric treatise by Rabbi Nehemiah: $3 + 1/7 \simeq 3.14286$.
The approximation, however, the most amazing not only for accuracy but also for the method is that proposed by Archimedes, the italo-greek mathematician who invented the method of polygons in order to calculate $\pi$, a costant that for a millennium became known simply as the Archimedes' constant.
He simply calculated the perimeter of polygons inscribed and circumscribed in a circle, thus obtaining a lower and an upper estimate of the value of the constant: \[223/71 < \pi < 22/7\] or \[3.1408 < \pi < 3.1429\] It's clear that his method of calculation is very modern and above suggests that Archimedes was well aware of the transcendental nature of the constant, which could be known only through approximations.
Today $\pi$ is known to 5 trillion digits and if you try to type the symbol $\pi$ on modern scientific calculators, the value they give you is, to the first decimal place, 3.14159265...