Challenging Mathematical Problems with Elementary Solutions, 第 1 卷Holden-Day, 1964 - 440 頁 |
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第 1 到 3 筆結果,共 9 筆
第 43 頁
... sphere or plane equidistant from them . Then A , B , C , D , E cannot all be on the same side of Σ . ( By the two sides of a sphere we mean the inside and the outside . ) For if they were , they would lie on a sphere concentric with Σ ...
... sphere or plane equidistant from them . Then A , B , C , D , E cannot all be on the same side of Σ . ( By the two sides of a sphere we mean the inside and the outside . ) For if they were , they would lie on a sphere concentric with Σ ...
第 45 頁
... sphere passing through all five points . Now suppose that s is a straight line ( fig . 23 ) . In this case Σ must be a plane , since three collinear points on the same side of a sphere cannot be equidistant from that sphere . As in the ...
... sphere passing through all five points . Now suppose that s is a straight line ( fig . 23 ) . In this case Σ must be a plane , since three collinear points on the same side of a sphere cannot be equidistant from that sphere . As in the ...
第 105 頁
... sphere increases the number of pieces . The ( k + 1 ) st sphere meets each of the first k spheres in a circle ; the circles of intersection will all be different , no two of them will be tangent , and - viewed as curves on the ( k + 1 ) ...
... sphere increases the number of pieces . The ( k + 1 ) st sphere meets each of the first k spheres in a circle ; the circles of intersection will all be different , no two of them will be tangent , and - viewed as curves on the ( k + 1 ) ...
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A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares C₁ chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula given Hence inclusion and exclusion intersection k-gons knights L₁ length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane points A1 polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices