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HMMT 二月 2005 · 冲刺赛 · 第 12 题

HMMT February 2005 — Guts Round — Problem 12

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. [7] Two vertices of a cube are given in space. The locus of points that could be a thirdvertex of the cube is the union of n circles. Find n .
    HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 19, 2005 — GUTS ROUND
    √ √

英文原题

[7] Two vertices of a cube are given in space. The locus of points that could be a third
vertex of the cube is the union of n circles. Find n .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 19, 2005 — GUTS ROUND

解析

英文解析

  1. Two vertices of a cube are given in space. The locus of points that could be a thirdvertex of the cube is the union of n circles. Find n .
    Solution: 10
    Let the distance between the two given vertices be 1. If the two given vertices areadjacent, then the other vertices lie on four circles, two of radius 1 and two of radius
    √