id: 06285232
dt: j
an: 2014c.00826
au: Singh, Udayan
ti: Estimation of the value of $π$ using Monte Carlo method and related study
of errors.
so: Math. Sch. (Leicester) 42, No. 5, 21-23 (2013).
py: 2013
pu: Mathematical Association (MA), Leicester
la: EN
cc: K50 N50 K90 F50
ut: $π$; Monte Carlo methods; simulation; circles; squares; linear
congruential random number generators; errors; probability; computer
programming; C++
ci:
li:
ab: From the text: The number it holds a special interest in the history as
well as in the current use of mathematics and science. This constant,
is a number whose value is close to 3.14. It is defined mathematically
as “the ratio of the circumference of a circle to the diameter of a
circle". $π$ has numerous applications in mathematics as well as in
science and technology. However, it is an irrational number, i.e. it
cannot be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are
co-prime integers and $q\ne 0$. Because it is irrational, no exact
value of $n$ can been found. Only estimates of $n$ have been put up.
There are several methods to get an approximate value of $π$. One of
them, discussed in this article, is by making use of the Monte Carlo
method. This article describes a simulation method using the
probability that a point chosen at random inside a square lies inside
the inscribed circle.
rv: