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PUMaC 2010 · 几何（B 组） · 第 5 题

PUMaC 2010 — Geometry (Division B) — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. In a rectangular plot of land, a man walks in a very peculiar fashion. Labeling the corners ABCD , he starts at A and walks to C . Then, he walks to the midpoint of side AD , say A . 1 Then, he walks to the midpoint of side CD say C , and then the midpoint of A D which is A . 1 1 2 He continues in this fashion, indefinitely. The total length of his path if AB = 5 and BC = 12 √ abc is of the form a + b c . Find . 4 1
解析
  1. In a rectangular plot of land, a man walks in a very peculiar fashion. Labeling the corners ABCD , he starts at A and walks to C . Then, he walks to the midpoint of side AD , say A . 1 Then, he walks to the midpoint of side CD say C , and then the midpoint of A D which is A . 1 1 2 He continues in this fashion, indefinitely. The total length of his path if AB = 5 and BC = 12 √ abc is of the form a + b c . Find . 4 [Answer] 793 √ √ − 1 − 2 [Solution] AC + A C = 13 + 61. Hence total length is (1 + 2 + 2 + · · · )(13 + 61) = 1 √ 26 + 2 61.