假使W是一个R2中封闭的凸区域（不规则）,L是一条固定长度的线段,连接W的边界上的两点.当我们沿着W边界移动L的一端时,另外一端也会在W的边界上移动(因为长度固定),然后L的中点会因为这个移动产生一段轨迹.最终当这种移动绕完整个W的边界后,L的中点轨迹会形成一个新的封闭区域G(显然,它被包含在W中).
试基于线段的固定长度L,来表示W和G的面积的相对关系.
P Let W be a convex region in R2 and let L
be a line segment of length I that connects points on the boundary of W. As we
move one end of L around the boundary, the other end will also move about this
boundary, and the midpoint of L will trace out a curve within W that bounds a
(smaller) region G.
Find
an expression that relates the area of G to the area of W in terms of the
length I of the line segment.
试基于线段的固定长度L,来表示W和G的面积的相对关系.
P Let W be a convex region in R2 and let L
be a line segment of length I that connects points on the boundary of W. As we
move one end of L around the boundary, the other end will also move about this
boundary, and the midpoint of L will trace out a curve within W that bounds a
(smaller) region G.
Find
an expression that relates the area of G to the area of W in terms of the
length I of the line segment.
