A Circular Approach to the Broken Pick-Up Sticks Problem

Overview

In this study, we propose a general solution to the Broken Pick-up Sticks Problem which is a variation of the well-known Broken Sticks Problem. Since its solution is unknown to the mathematical society, our approach is the first proposal to the solution of this problem. We converted the original linear stick elements into arced curvilinear elements which were placed onto a circle. We developed a novel method by focusing on the outer points where the arcs met to calculate the probability of forming a polygon. A computer simulation was written using the Monte Carlo Simulation Method. We found a formula that solves the Broken Pick-up Sticks Problem in complete generality. We managed to give a theoretical rigorous proof of this problem by applying the circler method. The general formula is consistent with the results obtained from computer simulation. Exploring the Broken Stick Problem will lead to improvements in probabilistic modeling calculations in various fields such as biology and finance. It has the potential to reveal solutions to many exciting questions, from the possibility of the formation of chemical elements to the first simple life forms.

Awards (2)

• Fourth Award of $500 $500
• National Security Agency Research Directorate : Third Place Award “Principles of Security and Privacy”

Competition history

• ISEF 2022 Mathematics · Entry MATH009 · Atlanta, Georgia, United States Affiliated fair in Turkey

Resources

• ISEF abstract page ↗

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