A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding...A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding time is investigated, producing results that are both counterintuitive and interesting.展开更多
The hypothesis is taken that the shape of a duck breast is as to shed water drops in minimum time. If a water drop is further assumed to be a frictionless bead, then analogy arises with the classic brachistochrone pro...The hypothesis is taken that the shape of a duck breast is as to shed water drops in minimum time. If a water drop is further assumed to be a frictionless bead, then analogy arises with the classic brachistochrone problem. Here a frictionless bead is one constrained to fall along a wire threading it so that it travels between two arbitrary points without friction. The brachistochrone problem is to specify the shape of that wire so that the bead completes its fall in minimum time. The shape of that wire is called a cycloid curve and it is the solution to the brachistochrone problem. Waterfowl might desire that water drops shed their breast region in minimum time and those drops resemble beads in the brachistochrone problem. Thus it might be expected that waterfowl breast profiles resemble the brachistochrone curve (cycloid), and strikingly they do. We find further this match is statistically significant compared to the general bird population, in support of the hypothesis.展开更多
文摘A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding time is investigated, producing results that are both counterintuitive and interesting.
文摘The hypothesis is taken that the shape of a duck breast is as to shed water drops in minimum time. If a water drop is further assumed to be a frictionless bead, then analogy arises with the classic brachistochrone problem. Here a frictionless bead is one constrained to fall along a wire threading it so that it travels between two arbitrary points without friction. The brachistochrone problem is to specify the shape of that wire so that the bead completes its fall in minimum time. The shape of that wire is called a cycloid curve and it is the solution to the brachistochrone problem. Waterfowl might desire that water drops shed their breast region in minimum time and those drops resemble beads in the brachistochrone problem. Thus it might be expected that waterfowl breast profiles resemble the brachistochrone curve (cycloid), and strikingly they do. We find further this match is statistically significant compared to the general bird population, in support of the hypothesis.
