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"Everything should be as simple as it is, but not simpler", Albert Einstein
Browsing All Posts filed under »MATHEMATICS«
Dropping In on Gottfried Leibniz
I’ve been curious about Gottfried Leibniz for years, not least because he seems to have wanted to build something like Mathematica and Wolfram|Alpha, and perhaps A New Kind of Science as well—though three centuries too early. So when I took a trip recently to Germany, I was excited to be able to visit his archive in Hanover. Leafing through his yellowed (but […]
Happy Day Fibonacci
May 8, 2013
The Science of Sticky Spheres
February 19, 2013
On the strange attraction of spheres that like to stick together Brian Hayes Take a dozen marbles, all the same size, and squeeze them into a compact, three-dimensional cluster. Now count the number of points where the marbles touch one another. What is the maximum number of contact points you can possibly achieve with 12 […]
Solving systems of linear equations on a quantum computer
February 7, 2013
Stefanie Barz, Ivan Kassal, Martin Ringbauer, Yannick Ole Lipp, Borivoje Dakic, Alán Aspuru-Guzik, Philip Walther Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers, making for one […]
Math formula gives new glimpse into the magical mind of Ramanujan
December 17, 2012
December 22 marks the 125th anniversary of the birth of Srinivasa Ramanujan, an Indian mathematician renowned for somehow intuiting extraordinary numerical patterns and connections without the use of proofs or modern mathematical tools. A devout Hindu, Ramanujan said that his findings were divine, revealed to him in dreams by the goddess Namagiri. “I wanted to […]
An Optical Demonstration of Fractal Geometry
September 17, 2012
Billy Scannel, Ben Van Dusen, Richard Taylor We have built a Sinai cube to illustrate and investigate the scaling properties that result by iterating chaotic trajectories into a well ordered system. We allow red, green and blue light to reflect off a mirrored sphere, which is contained in an otherwise, closed mirrored cube. The resulting […]
Gravitational Field Equations and Theory of Dark Energy and Dark Matter
September 7, 2012
Mathematicians offer unified theory of dark matter, dark energy, altering Einstein field equations A pair of mathematicians—one from Indiana University and the other from Sichuan University in China—have proposed a unified theory of dark matter and dark energy that alters Einstein’s equations describing the fundamentals of gravity. Shouhong Wang, a professor in the IU College […]
Physicists demonstrate that 15=3×5 about half of the time
August 19, 2012
Computing prime factors may sound like an elementary math problem, but try it with a large number, say one that contains more than 600 digits, and the task becomes enormously challenging and impossibly time-consuming. Now, a group of researchers at UC Santa Barbara has designed and fabricated a quantum processor capable of factoring a composite […]
The Emerging Revolution in Game Theory
August 16, 2012
The discovery of a winning strategy for Prisoner’s Dilemma is forcing game theorists to rethink their discipline. Their conclusion? Winning isn’t everything. The world of game theory is currently on fire. In May, Freeman Dyson at Princeton University and William Press at the University of Texas announced that they had discovered a previously unknown strategy […]
Scientific Searches’ Statistics Explained
July 9, 2012
Searching for the Higgs boson and other particles requires scientists to take into account statistics and probability in their analyses. Fermilab physicist Don Lincoln explains these concepts using simple dice. http://youtu.be/73JeQ2RZnwc
Higher Dimensions from String Theory
April 13, 2012
String Theory predicts the existence of more than the 3 space dimensions and 1 time dimension we are all familiar with. According to string theory, there are additional dimensions that we are unfamiliar with because they are curled up into tiny complicated shapes that can only be seen on tiny scales. If we could shrink […]
The ultimate random number generator.
April 12, 2012
The Fastest-Ever Random Number Generator Conjures Digits from Subatomic Noise in a Vacuum It was once thought that vacuums–like the vacuum of space–contained nothing. No particles, no sound, just empty darkness. But it has since come to light, thanks to discoveries in quantum physics, that virtual sub-atomic particles constantly and spontaneously appear and disappear, even […]
Maths and Olympics: How fast could Usain Bolt run?
March 29, 2012
By Kate Kelland (Reuters) – Usain Bolt, already the world’s fastest man, could lop another 0.18 seconds off his 100 meter sprint world record even without running any faster. It’s just a question of getting a few conditions right – and doing the maths. Luckily for the top Jamaican sprinter, John Barrow, a professor of […]
The Mighty Mathematician You’ve Never Heard Of
March 27, 2012
By NATALIE ANGIER Scientists are a famously anonymous lot, but few can match in the depths of her perverse and unmerited obscurity the 20th-century mathematical genius Amalie Noether. Albert Einstein called her the most “significant” and “creative” female mathematician of all time, and others of her contemporaries were inclined to drop the modification by sex. […]
Endre Szemerédi: Abel Prize 2012
March 22, 2012
Pattern master wins million-dollar mathematics prize Imagine I present you with a line of cards labelled 1 through to n, where n is some incredibly large number. I ask you to remove a certain number of cards – which ones you choose is up to you, inevitably leaving ugly random gaps in my carefully ordered sequence. It might […]
Mathematical Model Computes Snow Flake Shapes for the First Time
February 16, 2012
John W. Barrett, Harald Garcke, Robert Nürnberg Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growth in the presence of anisotropic surface energy and anisotropic attachment kinetics. It is by now well understood that the morphological stability […]
Seven equations that rule your world
February 13, 2012
Video: Equations that rule the world Read more: newscientist.com
A classification scheme of Amino Acids in the Genetic Code by Group Theory
February 5, 2012
Sebastian Sachse, Christian Roeder We derive the amino acid assignment to one codon representation (typical 64-dimensional irreducible representation) of the basic classical Lie superalgebra osp(5|2) from biochemical arguments. We motivate the approach of mathematical symmetries to the classification of the building constituents of the biosphere by analogy of its success in particle physics and chemistry. […]
From nothing to something
January 31, 2012
discrete integrable systems Abstract Chinese ancient sage Laozi said ‘Dao sheng yi, yi sheng er, er sheng san, san sheng wanwu, • • •’ that means something even everything comes from ‘nothing’ via ‘Dao’. In this paper, various discrete integrable models, including the known discrete Schwarzian KdV, KP, BKP, CKP, special Viallet equations and many […]
Can the maths in physics be simpler than it is?
January 7, 2012
Nope. ….. Read more: motls.blogspot.com
Mathematicians Solve Minimum Sudoku Problem
January 6, 2012
Sudoku fanatics have long claimed that the smallest number of starting clues a puzzle can contain is 17. Now a year-long calculation proves there are no 16-clue puzzles Sudoku is a number puzzle consisting of a 9 x 9 grid in which some cells contain clues in the form of digits from 1 to 9. […]
The Puzzling Weighted Average
December 5, 2011
“…..Suppose you are given two measurements of the same physical quantity. Make it something easy to visualize, such as the length of a stick. They tell you that when measured with method 1 the result was x1=10 cm, with a estimated uncertainty s1=0.1 cm, and when measured with method 2 the result was x2=11 cm, […]
On the interaction between two point electric charges
November 13, 2011
Alexei M. Frolov The general formula for the interaction potential between two point electric charges is derived. This analytical formula has the correct asymtotic behaviour at large distances between two interacting charges. The derivation of this formula is based on the closed analytical expression for the Uehling potential obtained earlier (A.M. Frolov and D.M. Wardlaw, […]
A revolution in knot theory
November 10, 2011
In the 19th century, Lord Kelvin made the inspired guess that elements are knots in the “ether”. Hydrogen would be one kind of knot, oxygen a different kind of knot—and so forth throughout the periodic table of elements. This idea led Peter Guthrie Tait to prepare meticulous and quite beautiful tables of knots, in an […]
Anthropic decision theory
November 1, 2011
Stuart Armstrong This paper sets out to solve the Sleeping Beauty problem and various related anthropic problems, not through the calculation of anthropic probabilities, but through finding the correct decision to make. Given certain simple assumptions, it turns out to be possible to do so without knowing the underlying anthropic probabilities. Most common anthropic problems […]
About sine and cosine functions
October 30, 2011
Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics Horia I. Petrache In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms […]
Solving the Dirac Equation
October 28, 2011
Alternative Discrete Energy Solutions to the Free Particle Dirac Equation Thomas Edward Brennan The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total angular momentum…… Read […]
Archimedes Palimpsest…
October 26, 2011
….reveals insights centuries ahead of its time Thirteenth-century manuscript, overwritten with prayer book, deciphered after years of painstaking work Years of painstaking work by scientists to expose a manuscript hidden for nearly a thousand years have shed new light on the genius of Archimedes, antiquity’s greatest mathematician. Known as The Archimedes Palimpsest, the manuscript is […]
Mathematical Physics: Problems and Solutions
October 24, 2011
The present issue of the series <Modern Problems in Mathematical Physics> represents the Proceedings of the Students Training Contest Olympiad in Mathematical and Theoretical Physics and includes the statements and the solutions of the problems offered to the participants. The contest Olympiad was held on May 21st-24th, 2010 by Scientific Research Laboratory of Mathematical Physics […]
Pi enthusiast calculates its ten trillionth digit
October 20, 2011
Shigeru Kondo is a seriously committed guy. Ever since discovering he had an interest in calculating pi (aka π) back in his college days, he’s been following the results achieved by others using massive supercomputers. Now, in his late 50′s, with some help from Northwestern University grad school student Alexander Yee, he’s succeeded in calculating […]
Prize awarded for largest mathematical proof
September 9, 2011
The largest proof in mathematics is colossal in every dimension – from the 100-plus people needed to crack it to its 15,000 pages of calculations. Now the man who helped complete a key missing piece of the proof has won a prize. In early November, Michael Aschbacher, an innovator in the abstract field of group theory at the […]
What Do Fermat’s Last Theorem and Electro-magnetic Duality Have in Common?
August 13, 2011
http://online.kitp.ucsb.edu/online/bblunch/frenkel/
You give me noise, I give you organized bundles
July 21, 2011
Research outlines math framework that could help convert ‘junk’ energy into useful power A University at Buffalo-led research team has developed a mathematical framework that could one day form the basis of technologies that turn road vibrations, airport runway noise and other “junk” energy into useful power. The concept all begins with a granular system […]
Alex Bellos: Tell me all about your favourite number
June 29, 2011
What’s your favourite number and why? A mathematics writer wants to know the answer. Yes, really Why are you interested in favourite numbers? I give popular talks about mathematics and I’m often asked about my favourite number. I don’t have an emotional reaction to numbers and so don’t have a favourite. So at first I […]
‘Tau day’ marked by opponents of maths constant pi
June 28, 2011
The mathematical constant pi is under threat from a group of detractors who will be marking “Tau Day” on Tuesday. Tau Day revellers suggest a constant called tau should take its place: twice as large as pi, or about 6.28 – hence the 28 June celebration. Tau proponents say that for many problems in maths, […]
Physicists Hit on Mathematical Description of Superfluid Dynamics
June 11, 2011
— It has been 100 years since the discovery of superconductivity, a state achieved when mercury was cooled, with the help of liquid helium, to nearly the coldest temperature achievable to form a superfluid that provides no resistance to electrons as they flow through it. During that century, scientists have struggled to find a precise […]
Demetrios Christodoulou, wins “Asia’s Nobel Prize”
June 9, 2011
Demetrios Christodoulou, a Greek mathematician and physicist at ETH Zurich, wins the illustrious “Shaw Prize in Mathematical Sciences”. The award of “Asia’s Nobel Prize” honours Christodoulou’s contributions to differential geometry and to the general theory of relativity. His prize is worth USD 500,000. Demetrios Christodoulou, Professor of Mathematics and Physics at ETH Zurich, has won […]
WormHole Division
May 26, 2011
Give your students practice with division by letting them dive into a wormhole. Difficulty of wormholes varies widely, so you may want to design a wormhole before you give it to your class. Explain this video benvitale-funwithnum3ers.blogspot.com
May 15, 2013
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