Chases and Escapes: Virtue or Vertigo for the Lady in the Lake?
The ideas of pursuit and evasion pervade much of human existence and as a result have always been a huge part of human entertainment – it has been said that half of all fictional writing boils down to a single conflict between the hunter and the hunted. But more than just recreational, the study of chases and escapes is also mathematically interesting and has applications to computer science, surveillance, traffic control, and military strategy. After learning some fundamental concepts from game theory, we will discuss the classic pursuit-evasion problem, “The Lady in the Lake,” in which a woman finds herself in a rowboat in the middle of a circular lake while a pursuer waits for her along the shore. If the pursuer runs at four times the woman’s rowing speed, can the woman reach a spot on the shore before her purser does? We will uncover the woman’s optimal escape strategy in order to answer this question and much further, find the minimum speed relative to her pursuer’s that the woman must row to evade capture.