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 40 筆
第 35 頁
... circle is proportional to the area of that circle . ( Note that the midpoint of a chord uniquely determines the chord , unless it is a diameter . ) Since any point inside the circle can be the midpoint of a chord , and the points which ...
... circle is proportional to the area of that circle . ( Note that the midpoint of a chord uniquely determines the chord , unless it is a diameter . ) Since any point inside the circle can be the midpoint of a chord , and the points which ...
第 41 頁
... circle or straight line equidistant from them . Then A , B , C , D cannot all be on the same side of s . ( By the two sides of a circle we mean , of course , the inside and the outside . ) For they would then lie on a circle concentric ...
... circle or straight line equidistant from them . Then A , B , C , D cannot all be on the same side of s . ( By the two sides of a circle we mean , of course , the inside and the outside . ) For they would then lie on a circle concentric ...
第 104 頁
... circle increases by 2k the number of parts into which the plane is divided . For the ( k + 1 ) st circle intersects each of the first k circles in two points ; these 2k points divide the ( k + 1 ) st circle into 2k arcs . Each of these ...
... circle increases by 2k the number of parts into which the plane is divided . For the ( k + 1 ) st circle intersects each of the first k circles in two points ; these 2k points divide the ( k + 1 ) st circle into 2k arcs . Each of these ...
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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