What is the Monte Carlo method?

The Monte Carlo method is in fact a wide class of research and analysis methods, with a unifying feature to rely on random numbers to examine the problem. The basic assumption is that although certain things can be completely accidental and are not useful for small samples, large samples become predictable and can be used to solve various problems. Take the circle and cut it into a neighborhood. Then we take one of these neighborhoods and place it on the square. If we were to accidentally throw the darts at this square and discount all that fell out of the square, some would land in a circle and some would land outside. The proportion of the darts that landed in the circle, the arrows that landed outside

Of course, if we only throw two or three darts, randomness would make the ratio we arrived quite randomly. This is one of the key points of the Monte Carlo method: the size of the sample must be large enough to reflect the real chances, and it does not have the remote values ​​of drasticky to influence. In the case of accidental throwing arrows, we found that somewhere in low thousands, the Monte Carlo method is starting to bring something very close to Pi. As we get to a high thousand, the value is becoming increasingly accurate.

Of course, throwing thousands of darts on the square would be somewhat difficult. And to make sure it is completely accidentally done would be more or less impossible, which would be more experiment with the idea. But with a computer we can make a really random "throw" and we can quickly make thousands or tens of thousands or even millions of throws. The Monte Carlo method becomes truly viable with the calculation.

One of the oldest thought experiments, such as this, is known as the problem of Buffon's needle, which was first introduced at the end of the 18th century. This represents two parallel strips of wood with the same width and puts on the floor. Then she assumes that we put the needle on the floor and asks what the probability of the needle will land at such an angle to exceed the boundary betweentwo strips. This can be used to calculate PI to an impressive extent. Indeed, the Italian mathematician, Mario Lazzarini, really did this experiment, threw a needle 3408 times and arrived at 3.1415929 (355/113), which is remarkably close to the actual value of PI.

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Monte Carlo method, of course, uses far for a simple PI calculation. This is useful in many situations where accurate results cannot be calculated as a kind of shortcut response. During the early nuclear projects at the age of 40. Century, it was most great in Los Alamos, and these were these sciences who created the term Monte Carlo Method to describe its randomness, because it was similar to many coincidences in Monte Carlo. Different forms of Monte Carlo method can be found in the design of computer, physical chemistry, nuclear and particles, holographic sciences, economics and many other disciplines. Any area where the strength is needed to calculate accurate results such as the movement of millions of atoms can be potentially help with the Monte Carl methodo.