### Monte Carlo method

(mathematics and simulation using random samples)

A **Monte Carlo method** is a method of carrying out mathematical
calculations and related simulations that uses chance to estimate
the answer. Calculations are carried out using numbers chosen at
random, yielding an estimate of the solution. It is named for
the city of *Monte Carlo*, which is famous for gambling,
something that also depends upon chance.

For example, to find the area of a weird shape for which there is
no obvious direct calculation, if there is an easy way to determine
whether a specific point is within the weird shape, take random
points throughout a rectangle that circumscribes it, then count out
what percentage of these points fall within the weird shape. That
percentage of the area of the rectangle (an area that is easy to calculate)
gives you an estimate of the area of weird shape. Choosing the
random points must be done in such a way that they are randomly
distributed over the rectangle. The more such points, the better
the estimate.

Quite a few challenging math problems are "solvable" by such chance
methods. Markov chain Monte Carlo (MCMC) is a more specific type of method that incorporates
chance. **Quantum Monte Carlo** methods are the use of Monte
Carlo methods to solve quantum system problems, e.g., using
quantum mechanics.

(*mathematics,simulations,method*)
**Further reading:**

http://en.wikipedia.org/wiki/Monte_Carlo_method

http://en.wikipedia.org/wiki/Quantum_Monte_Carlo

**Referenced by pages:**

Hyperion

Markov chain Monte Carlo (MCMC)

N-body problem

quantum Monte Carlo (QMC)

stellar dynamics

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