USA.: Grand Valley State University (GVSU). Mathematics Department. Undergraduate Research. April 30, 2013, Paper 2, P.p.: 1-26, EnglishThe Mathematical Game
In late 2012, Prof. Bernard Beauzamy of the Societe de Calcul Mathematique SA proposed a "mathematical game" inspired by the massive fi res that occurred in Siberia during the summer of 2012.
This article is our entry for the competition. In this contest, Siberia is divided into regions called "trapezes", bounded by latitute and longitude lines (see gures in the appendix), and for each region a percentage is given of urban, cultivated, and virgin zones. Probabilities are de ned that a fire would start in a region over a given period of time, which would lead to damage, with urban areas facing sign cantly larger damages than cultivated or virgin areas.
Also provided are rules for fire-fighting that involve the placement of fire brigades and airplanes in the center of each trapeze, rules for the spread and dousing of fires, and more rules for the speed of fire-fighting equipment and the availability of water.
The objective is to distribute the fire-fighters among 94 di erent trapezes, and to de ne strategies to send out the fire-fighters depending on the location of the fires, in order to minimize total damage and total fire-fighting costs.Contents.
Introduction.
The Mathematical Game.
Outline of this Article & Summary of Strategy.
Structure and Assumptions.
Given by Prof. Beauzamy.
Preliminary Formulas and Calculations.
Summary of Key Results.
Additional Assumptions by Our Team.
3 Location of Brigades and Airplanes.
Key Issues.
Our Placement of Fire-Fighters.
4 Fighting Fires in Siberia.
Urban, Cultivated, and Virgin Areas in Each Trapeze.
One-Alarm Fires Without Extra Water.
One-Alarm Fires With Extra Water.
Two-Alarm Fires Without Extra Water.
Two-Alarm Fires With Extra Water.
More Dicult Fires.
Three Questions.
References.
Acknowledgements.
Appendix: The Trapezes of Siberia.
