There is a tree, circumference of which is 4 ft.
geometry/spider.on.tree New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
There is a tree, circumference of which is 4 ft. On the tree, 5 ft above the ground, there is a dead fly. A spider can climb the tree at 45 degrees with the horizontal. At which point on the ground should the spider start climbing the tree so that the spider can eat the fly? -- Erol Esen <esen@CS.ColoState.EDU>
Show solution
Assuming the spider does not wish to (or cannot) change direction from 45 deg. to the right to 45 deg. to the left, the easiest solution is to imagine she is retracing the path from the fly to the ground. The first 4 feet of vertical distance takes her 4 feet horizontally, but that's exactly once around the circumference; the last 1 foot takes her an additional 1 foot, or 1/4 circumference. So the spider should start from a point 1/4 of the way around the tree from the fly, and set out at 45 degrees in the direction nearest the fly. -- David A. Karr <karr@cs.cornell.edu> (January 1994) [ Editor: for the related path at a constant bearing on a sphere, see geometry/spiral. ]