Explainer: what is Chaos Theory? > 문의하기

The least common multiple of and , written as , is the smallest natural number that is a multiple of both and . No matter how consistent you are with the first shot (the break), the smallest of differences in the speed and angle with which you strike the white ball will cause the pack of billiards to scatter in wildly different directions every time. The path is exactly the path of a ball shot from the bottom left corner of at 45 degree angles to the sides of . This path will turn out to be the path of an arithmetic billiard ball moving within the rectangle . We start with the top right square and reflect it in the side that is crossed by the diagonal , which it shares with a neighbouring rectangle (the rectangle below in our example). We leave it up to you to show that never passes along the diagonal of a unit square twice, neither in the same direction, nor in the opposite direction. Show your abilities not only to your close friends but also to the individuals who live in your area. On the other hand, this stability is somewhat of an inconvenience to fighter pilots who prefer their aircraft to make rapid changes with minimal effort.

The millions of cells that make up your heart are constantly contracting and relaxing separately as part of an intricate chaotic system with complicated attractors. If the system is jolted somehow, it may find itself on an altogether different attractor called fibrillation, in which the cells constantly contract and relax in the wrong sequence. The main benefit to having a chaotic heart is that tiny variations in the way those millions of cells contract serves to distribute the load more evenly, reducing wear and tear on your heart and allowing it to pump decades longer than would otherwise be possible. The purpose of a defibrillator - the device that applies a large voltage of electricity across the heart - is not to "restart" the heart cells as such, but rather to give the chaotic system enough of a kick to move it off the fibrillating attractor and back to the healthy heartbeat attractor. In phase space, a stable system will move predictably towards a very simple attractor (which will look like a single point in the phase space if the system settles down, or a simple loop if the system cycles between different configurations repeatedly).

The behaviour of the system can be observed by placing a point at the location representing the starting configuration and watching how that point moves through the phase space. Once there it clings to its attractor as it is buffeted to and fro in a literal sea of chaos, what is billiards and quickly moves back to the surface if temporarily thrown above or dumped below the waves. It is a mathematical toolkit that allows us to extract beautifully ordered structures from a sea of chaos - a window into the complex workings of such diverse natural systems as the beating of the human heart and the trajectories of asteroids. The branch of fractal mathematics, pioneered by the French American mathematician Benoît Mandelbröt, allows us to come to grips with the preferred behaviour of this system, even as the incredibly intricate shape of the attractor prevents us from predicting exactly how the system will evolve once it reaches it. "If the boy does what he should, I will be able to say ‘I’ve shared a bath with a Masters winner’ - brilliant.

Patrons file onto the course after the gates are opened near the first fairway before the start of the 80th Masters Golf Tournament at the Augusta National Golf Club. Patrons wait for the gates to open near the first fairway before the start of the 80th Masters Golf Tournament at the Augusta National Golf Club. Lee Westwood of England chips on the second hole during the first round of the 80th Masters Golf Tournament at the Augusta National Golf Club. He said he scored his last hole in one in Dubai with his parents in attendance. In the case of the weather, the prediction horizon is nowadays about one week (thanks to ever-improving measuring instruments and models). Fortunately, this intricate state of synchronisation is an attractor of the system - but it is not the only one. The mathematician Ian Stewart used the following example to illustrate an attractor. Ian Stewart, The Magical Maze. WHAT IS LUBY PUBLISHING?