两跳蚤移行路径长度比较  

On the Lengths of Two Cycloids

作　　者：莫国良[1] 王辉[2] 

机构地区：[1]浙江大学城市学院计算机与计算科学学院,杭州310015 [2]西安邮电学院自动化学院,西安710061

出　　处：《高等数学研究》2010年第6期54-55,共2页Studies in College Mathematics

摘　　要：讨论有关文献在谈到曲线弧长公式时所提出的一个关于两跳蚤移行路径长度的问题.通过理论推导并借助图形分析显示,只是在一些离散的特殊时刻,两跳蚤移行的摆线长度才相等.On page 564 of the book ＂Calculus＂ by Dale Varberg, et al, it appears that ＂Two fleas are arguing about who will get the longest ride when Jenny pedals her tricycle home from the park. A will ride between the treads of the front tire; B will ride between the treads of one of the rear tires. Settle the argument by showing that their paths will have equal lengths＂. A study on the lengths of two cycloids shows that the above conclusion is true only at some special cases.

关 键 词：摆线 弧长公式 跳蚤 

分 类 号：O172[理学—数学]