Tag: probability
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A very, very simple method to estimate Pi
Date: 2026-03-15 Author: Michael T.M. Emmerich Every year, on March 14, mathematicians celebrate Pi Day. For my Mathematical Playground blog, I wished to post a short essay on a very, very simple Monte Carlo method for estimating . The nice aspect of this method is that it requires only a few lines of code, does…
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The Gumbel Distribution, Extreme Rainfall, and the Euler–Mascheroni Constant
Nature doesn’t just have averages; it has extremes—the hottest day, the strongest wind, the largest daily rainfall, the highest flood. For extremes, a universal statistical law often appears: the Gumbel distribution. In this post, we meet it through a simple and realistic story about annual maximum rainfall, learn how a basic normalization makes its shape…
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The Tent Map – A Simple Path to Chaos
Michael Emmerich, August 20th 2025 Chaotic time series can emerge from very simple deterministic rules. The tent map is a classical example. It shows how fixed points can be unstable, how orbits diverge, and how randomness-like behavior arises from a piecewise linear rule. The Tent Map The tent map is defined on the interval by…
Michael Emmerich 