For example, the unknown area of a circle can be calculated by placing it inside a square of known area. The percentage of simulated points inside the square that also lie inside the circle provides a "good" approximation to the ratio of the circle's area to the square's area.
The first satisfactory definition of a random sequence was proposed in 1966 by the Swedish mathematician Per Martin-Löf (born 1942): a sequence is random if it has no "exceptional, algorithmically testable" property—that is, no such property that can be checked by an algorithm. This means, among other things, that such sequences cannot be generated by a computer program. Similarly, it can be shown that sequences generated by humans contain regularities. A "truly" random sequence can be generated using natural phenomena. On the other hand, we may wish to use a computer program; in that case, we obtain a pseudorandom sequence. The algorithm is "hidden", and to a first approximation the numbers have the properties of a random sequence.
