Newton's Nose Cone problem
Volume 7, Issue 1
C. Henry Edwards, The University of Georgia
The historical roots of the calculus of variations trace back to Newton's
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.