文 [1]中定理 5 :用间距为h的平行线把直径为d的圆涂成阴影时 ,所画阴影线的总长度为 :l =2∑[dh]i=1ih(d -ih) ,并提出猜想 :当d为常量时 ,定理 5中的l是h的严格递减函数 .本文将证明这一猜想的特殊情况 :若d为常量且 dh =n∈N (n≥2 ) ,记用间距为h的平行线把直径为d的圆涂成 Theorem 5 in [1]: When a circle of diameter d is shaded by a parallel line with spacing h, the total length of the hatched line is: l = 2 ∑ [dh] i = 1 ih (d -ih) , And put forward a conjecture: When d is a constant, l in Theorem 5 is a strictly decreasing function of h. This article will prove the special case of this conjecture: If d is a constant and dh = n∈N (n≥2), Draw a circle of diameter d with a parallel line of distance h