Mathematical understanding of nature: essays on amazing physical phenomena and their understanding by mathematicians

Abstract

The eccentricity of the Keplerian orbit of Mars Rescuing the empennage Return along a sinusoid The Dirichlet integral and the Laplace operator Snell's law of refraction Water depth and Cartesian science A drop of water refracting light Maximal deviation angle of a beam The rainbow Mirages Tide, Gibbs phenomenon, and tomography Rotation of a liquid What force drives a bicycle forward? Hooke and Keplerian ellipses and their conformal transformations The stability of the inverted pendulum and Kapitsa's sewing machine Space flight of a photo camera cap The angular velocity of a clock hand and Feynman's oself-propagating pseudoeducationo Planetary rings Symmetry (and Curie's principle) Courant's erroneous theorems Ill-posed problems of mechanics Rational fractions of flows Journey to the center of the earth Mean frequency of explosions (according to Ya. B. Zel'dovich) and de Sitter's world The Bernoulli fountains of the Nikologorsky bridge Shape formation in a three-liter glass jar Lidov's moon landing problem The advance and retreat of glaciers The ergodic theory of geometric progressions The Malthusian partitioning of the world Percolation and the hydrodynamics of the universe Buffon's problem and integral geometry Average projected area The mathematical notion of potential Inversion in cylindrical mirrors in the subway Adiabatic invariants Universality of Hack's exponent for river lengths Resonances in the Shukhov tower, in the Sobolev equation, and in the tanks of spin-stabilized rockets The theory of rigid body rotation and hydrodynamics