Full Description
This book in a single contribution for the first time examines the historical development of the concepts of vortex, vorticity, knot, chirality, and helicity between 1517 and 1969. It considers their origins in early pictorial and conceptual studies, their subsequent formalization in mathematical analysis, and their eventual consolidation as interconnected elements within fluid mechanics, mathematical physics, geophysics, and astrophysics.
Attention is given to the progression from qualitative representations to formal definitions, including the emergence of vorticity, curl, and the gradient operator, as well as to the introduction of knot, chirality, and helicity as new means of describing physical and geometrical structure. The discussion emphasizes the extent to which these notions evolved in parallel, with recurring intersections between geometry, physics, and analysis.
The volume is intended for undergraduate and postgraduate students and researchers in applied mathematics, fluid mechanics, dynamo theory, topology, knot theory, geophysics, astrophysics, and the history of mathematical physics.
Contents
Preface.- Introduction.- The early studies of vortex latin from year to year.- The early mathematical studies of the zero vorticity condition of fluid motion and vorticity from year to year.- The mathematical studies of the rays and the propagation of light from year to year.- The mathematical studies of fluid motion the magnetic and galvanic forces and vortex motions in the year and year.- The mathematical studies of molecular vortices vortex atoms spherical vortex and the notion vorticity from year to year.- The development of the mathematical symbol nabla from year to year.- The conceptual physical and mathematical studies of worble and knot from year to year.- The conceptual physical and mathematical studies of chirality in year and year.- The mathematical studies of helicity and schraubensinn German from year to year.- Concluding remarks.- References.- Index.
