Mathematicians Make a Major Discovery About Prime Numbers. Paul Erdős, left, and Terence Tao discussing math in 1985.
This past August, Tao and four other mathematicians proved an old Erdős conjecture, marking the first major advance in 76 years in understanding how far apart prime numbers can be. Olena Shmahalo / Quanta Magazine; original courtesy of Terence Tao In May 2013, the mathematician Yitang Zhang launched what has proven to be a banner year and a half for the study of prime numbers, those numbers that aren’t divisible by any smaller number except 1. Zhang, of the University of New Hampshire, showed for the first time that even though primes get increasingly rare as you go further out along the number line, you will never stop finding pairs of primes that are a bounded distance apart — within 70 million, he proved.
The world's largest prime number — visualized. Images: The World's Most Beautiful Equations. Jacquard looms: Videos demonstrating early computer programs. Invented in 1801, Jacquard looms are really an add-on to already existent mechanical loom systems, which allowed those looms to create patterns more complex and intricate than anything that had been done before.
The difference: Punch cards. When you weave, the pattern comes from changes in thread position — which threads were exposed on the surface of the cloth and which were not. But prior to the Jacquard loom, there were only so many threads that any weaver could control at one time, so patterns were simple and blocky. Rolling Hypocycloids. The hypocycloid with n cusps is the curve traced out by a point on a circle rolling inside a circle whose radius is n times larger.
The hypocycloid with 2 cusps is sort of strange: It’s just a line segment! It’s called the Tusi couple. Infinity Imagined. Infinity Imagined. Infinity Imagined. Infinity Imagined. This well-known Egyptian symbol is actually an early math problem. Hartverdrahtet – Infinite complexity in 4096 Bytes - winner of the PC 4kB intro comp. 5 Seriously Mind-Boggling Math Facts. By Natalie Wolchover | January 25, 2013 07:19am ET Credit: public domain Mathematics is one of the only areas of knowledge that can objectively be described as "true," because its theorems are derived from pure logic.
Math Cats, B-Cubed, First in Math, IXL Math. Doodling in Math Class: Connecting Dots. The Mathematical Art Of M.C. Escher. The Fibonacci in Lateralus. The Fibonacci Sequence. How do japanese multiply?? How To: 1 x 8 1=9 - Beauty of Mathematics. The Coastline Paradox & The Koch Snowflake. The nature of nothingness. Zilch… Naught… Nada… It’s easy to dismiss the concept of nothing as, well, nothing.
In fact, nothing is everything to science – understanding the intangible voids has lead to breakthroughs we could never have imagined possible. Artists, Physicists, Mathematicians and Philosophers Contemplate Infinity. As I stepped into the Infinity Environment on Wednesday morning (Feb. 1), I heard faint gasps from those around me.
With apprehension, we entered a stark white, brilliantly lit room with no edges. The curved walls and angled lighting minimized shadows, giving the illusion that we were staring into a continuum. With no visual reference points anywhere in the room, my eyes flickered about, desperate for something to focus on; it was impossible to tell how far space extended, if at all. In seeming infinite, space ceased to exist beyond my eyelashes and nose. What are Amicable Numbers? Los socorridos números de Fibonacci. La secuencia de Fibonacci es una sucesión infinita de números naturales. Se denominan así los números que permiten contar los elementos de un conjunto. Son el primer grupo de números que fueron usados por los seres humanos para contar cosas.
El uno, el dos, el cinco, por nombrar algunos, son números naturales. En la secuencia de Fibonacci cada número viene dado por la suma de los dos anteriores. Fue Leonardo de Pisa, un matemático italiano del siglo XIII, conocido como Fibonacci quien dio nombre a esta sucesión en Liber Abaci, un libro publicado en el año 1202 . Bifurcation diagram. In mathematics, particularly in dynamical systems, a bifurcation diagram shows the possible long-term values (equilibria/fixed points or periodic orbits) of a system as a function of a bifurcation parameter in the system.
It is usual to represent stable solutions with a solid line and unstable solutions with a dotted line. Bifurcations in 1D discrete dynamical systems[edit] Logistic map[edit] Animation showing the formation of bifurcation diagram. Four color theorem. Example of a four-colored map A four-coloring of a map of the states of the United States (ignoring lakes).
In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions.[1] For example, in the map of the United States of America, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not. Despite the motivation from coloring political maps of countries, the theorem is not of particular interest to mapmakers. The four color theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken.
Precise formulation of the theorem[edit] History[edit] The Amazing Mathematics of Nov. 11, 2011. Today's date, 11/11/11, is a once-in-a-century occurrence, adding to a November has been a very fun month for recreational mathematicians.
Last week, a rare eight-digit palindrome date — 11/02/2011, which reads the same frontward and backward — was found to have other mathematical qualities that made it a once-in-10,000-years date. Canal de Vihart. The simplest proof mathematicians needed two tries at.
The most interesting mathematical mistake in the solar system. Scientists still puzzled by a fractal discovered 500 years ago. Mathematics as the raw material for art. Kat Austen, Culture Lab editor (Image: Hiroshi Sugimoto) In a new Paris exhibition, prizewinning mathematicians team up with artists to inspire works that bring intangible concepts to life Mathematics - A Beautiful Elsewhere, Fondation Cartier, Paris, until 18 March.
Known Amicable Pairs. This is an attempt to collect all known amicable pairs.
I would appreciate receiving any kind of updates and corrections. Comments are welcome too. Please visit my pages with various AP lists and statistics; and tables of other kinds of aliquot cycles. The table below contains the number of amicable pairs arranged according to the number of digits in the smallest member. Math in a Minute: Welcome to Hotel Infinity paradox. A mathematical bug shows us why the 3D universe carries the possibility of despair. Really. For N bug-steps, there are two things to consider: how many total possible paths of N steps the bug has available to it, and how many of those N-step paths lead home. For example, let's look at 1D.
After just 2 steps (N=2), where the bug could only go left or right each step, the bug has had 4 possible paths available to it: LR - Home RL - Home. A mathematical bug shows us why the 3D universe leads to Murphy's Law. Let's also not forget that unlike, a path, the movement of any string no matter how thin is at least partially governed by the slight recoiling that occurs at the bends and curves. I think analogies are wonderful for explaining complex systems to simple folk like myself, but I hate it when "scientists" try to prove a mathematical system with an insufficient metaphor.
Uncovering Da Vinci's Rule of the Trees. As trees shed their foliage this fall, they reveal a mysterious, nearly universal growth pattern first observed by Leonardo da Vinci 500 years ago: a simple yet startling relationship that always holds between the size of a tree's trunk and sizes of its branches. The odd genius who showed that one infinity was greater than another. Ralph Abraham. Ralph H. Abraham (b.