Newton's Nose Cone problem

Volume 7, Issue 1
Winter 1997

The historical roots of the calculus of variations trace back to Newton's Principia Mathematica problem concerning the shape of a solid of revolution that experiences minimal resistance to rapid motion through a "rare medium" consisting of elastic particles. Newton's stated solution to this problem barely hinted at the complexity and sophistication of his underlying analysis, and remained enigmatic to most readers of the Principia, at least until the late nineteenth century when rigorous foundations for the variational calculus began to be laid. This article exploits modern computer algebra to explore the meaning and origin of Newton's analysis and solution.