Could Knots Unravel Mysteries of Turbulent Fluid Flow? Spaghetti-thin shoelaces, sturdy hawsers, silk cravats — all are routinely tied in knots.

So too, physicists believe, are water, air and the liquid iron churning in Earth’s outer core. Knots twist and turn in the particle pathways of turbulent fluids, as stable in some cases as a sailor’s handiwork. Math jobs, statistics jobs, employment, math, statistics, jobs, employment, mathematics, phd, masters, education, university, college, united states, russia, europe, mathematika, mexico, canada, mathematics, math, jobs, employment. The Mathematical Atlas - Dave Rusin's survey of research-level mathematics, with introductory articles for non-mathematicians and hyperlinked bibliographies in each of dozens of research areas.

Knot a Braid of Links - Award/review service for other math web sites and web pages, with a new selection each week. Platonic Realms - Online resource for the mathematics community: links library, bookstore, quotes, and online articles. The Math Forum - Combined archive and directory of mathematical web sites, mailing lists, newsgroups, and teaching materials. Life in the City Is Essentially One Giant Math Problem. Egyptian Maths. Hexaflexagons 2. How to Turn a Sphere Inside Out.

An Interactive Guide To The Fourier Transform. The Fourier Transform is one of deepest insights ever made.

Unfortunately, the meaning is buried within dense equations: Yikes. Rather than deciphering it symbol-by-symbol, let's experience the idea. Here's a plain-English metaphor: What does the Fourier Transform do? Graham's Number - Video. Sets, Counting, and Probability. This online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life.

Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas. Free online math lectures The Quicktime and MP3 formats are available for download, or you can play the Flash version directly.

Infinities. The concept of infinity is hard to grasp because it is an abstraction.

There are no tangible objects in our lives that are truly infinite in number so we really have nothing to compare it to. The only way to get an infinite number of anything is by invoking infinity elsewhere, which doesn’t really clarify matters much. For example, the number of elementary particles in our visible universe, although immensely large, is still a finite number. If we assume that the density of particles in the universe is roughly the same everywhere and further postulate that the universe is of infinite size, then we can arrive at an infinite number of particles. 6 Must-See Math Videos That Will Inspire And Frighten.

Math is one of those subjects that students and people in general either love or hate.

Part of this is due to individual personalities and interests, but it is also down to how the discipline is taught. Here are three inspirational math videos to excite your school and students about learning math, as well as three ‘not so’ inspirational videos to demonstrate just why math is so important. GEM1518K - Mathematics in Art & Architecture - Project Submission. “For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.” - M.C.

Escher Contents Page 1 Introduction The Art of Alhambra Our Area of Focus Our Aim Page 2 The Principals behind Tessellations - Translation - Rotation - Reflection - Glide Reflection. Moebius Transformations Revealed. Proofs Without Words Gallery. 6174 (number) 6174 is known as Kaprekar's constant[1][2][3] after the Indian mathematician D.

R. Kaprekar. This number is notable for the following property: DC.pdf (application/pdf Object) The eloquence of... Maths: Free maths help, advice and ramblings. If you are the first to solve this problem I will give you complete set of the Richard Feynman Lectures on Physics (read up upon the Feynman Lectures on Physics).

Question: Take a square of arbitrary side length and construct four new squares with a side length half of the original positioned in the corners a quarter of the way down and across the two sides creating the corner. This would look like: Then in each of the new squares in the furthest corner from the first square create a new square with half the side length a quarter of the way down and across the two sides creating the corner. Repeat this step for each newly constructed square to it infinity. Point nine recurring equals one. (This page is entirely factually accurate.

It is neither a joke nor a satire nor a collection of fallacious proofs. All these proofs are genuine and the results are true. Thanks.) Troll pi explained. Here's the "Troll Pi" or "Pi equals 4" image. Here's the breakdown, as simple as I can make it. All of the following facts are true: Panels one to four describe a sequence of curves. 3 Dimensional Fractals & Mandelbulb. 3 Dimensional Fractals and the Search for the 'true' 3D Mandelbrot Three Dimensional Fractal Mappings Years ago, many fractal enthusiasts viewed these intricate and majestic patterns and thought "Wouldn't this be incredible in 3-D?

". Dozens of methods have been developed to view fractals in an arbitrary number of dimensions. Quaternions are 3D shadows of 4D Julia Sets, which, if sliced in a plane, reveal the corresponding 2 dimensional Julia Set. Other attractive developments include 'Quasi-Fuchian" fractals and the recent popularity of the 'Mandelbulb" 3D Mandelbrot - which was exclusively discovered and implemented collaboratively by the inquisitive genius folks at Fractalforums.com. Go there to see what is literally the cutting edge of fractal discovery on a daily basis. Really! Euler's Solution to the Basel Problem : EvolutionBlog. I’m in the mood for some math today, so here’s an amusing little proof I recently showed to my History of Mathematics class. We shall derive the formula \[ \frac{\pi^2}{6}=1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\dots \] Contact networks have no influence on cooperation among individuals.

Researchers at Carlos III University of Madrid and the University of Zaragoza theoretically predict, in a scientific study, that contact networks have no influence on cooperation among individuals. For the past twenty years, there has been a great controversy regarding whether the structure of interactions among individuals (that is, if the existence of a certain contact network or social network) helps to foment cooperation among them in situations in which not cooperating brings benefits without generating the costs of helping.

Many theoretical studies have analyzed this subject, but the conclusions have been contradictory, since the way in which people make decisions is almost always based on a hypothesis of the models with very little basis to justify it. Benford's Law. If you’ve not heard about Benford’s Law before, you’re in for a real treat with this post. Before we get into the theory, however, indulge with me in a little thought experiment. (Gedanken) Gedanken Experiment Actual results. 5 and Penrose Tiling [video] Pattern master wins million-dollar mathematics prize - physics-math - 21 March 2012. 'Infinity Computer' Calculates Area Of Sierpinski Carpet Exactly. Dirac String Trick. Math Fun Facts! Abstract Algebra - Free Harvard Courses. Explained: Sigma.

Virtual Reality Polyhedra. Most Popular Math Fun Facts. A Visual, Intuitive Guide to Imaginary Numbers. Information for readers of sci.math.research. What is the Reimann Hypothesis? Why is it so important. What is it like to have an understanding of very advanced mathematics. Unsolved Problems.