TL;DR
This paper introduces a straightforward Monte Carlo approach using coin tosses to estimate π, highlighting a novel interpretation of the probability related to Catalan-number series identities.
Contribution
It presents a new interpretation of the probability involving π/4 through a simple coin-toss Monte Carlo method, connecting probability theory with Catalan-number identities.
Findings
The method provides an intuitive way to estimate π.
The interpretation of π/4 via Catalan numbers appears to be novel.
The approach is simple and accessible for educational purposes.
Abstract
We describe a simple Monte Carlo method for estimating by tossing a coin. Although the underlying Catalan-number series identities appear implicitly in the probability theory literature, the interpretation of presented here seems to be new.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Advanced Mathematical Theories and Applications