LaPlace's Equation Model

What is this model?

Random numbers on computers are almost never "true" random numbers. That is, since the computer calculates its random numbers through a series of algorithms, even if it is hard to detect a pattern, the numbers are not genuinely random. This model allows for students to explore what is known as "pseudo random numbers" and the algorithms that run behind such calculations. Through a series of shifts, multipliers, and other calculations, random numbers are generated and used to estimate the area under a curve. The integral calculated in this model is the area of the unit circle, equal to pi. Many trials yield a more accurate result, as the Law of Large Numbers states, so the model takes into account increasing amounts of random numbers to calculate pi.

What can this Model be used to teach?

Understand the idea of pseudo random numbers and the process behind calculating them

Understand the Law of Large Numbers

Related Models

Two Algorithms for Monte Carlo Integrals (Excel)

Problematic Patterns in Random Noise (Excel)

Projectile Motion (Vensim)