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The Pierre Auger Observatory, a hybrid detector for the study of ultra-high energy cosmic rays (UHECRs), is now approaching completion. After describing Auger present status and performance, with an emphasis on the advantages provided by…
One of the many number theoretic topics investigated by the ancient Greeks was perfect numbers, which are positive integers equal to the sum of their proper positive integral divisors. Mathematicians from Euclid to Euler investigated these…
The objective of this paper is not simply to present an historical overview of Einstein's cosmological considerations, but to discuss the central role they played in shaping the paradigm of relativistic cosmology. This, we'll show, was a…
Observational cosmology of the first decades of the Twentieth Century was dominated by two giants: Edwin Hubble and Harlow Shapley. Hubble's major contributions were to the study and classification of individual galaxies with large…
Year 2005 was the World Year of Physics, and it was commemorated worldwide as the 100th anniversary of Albert Einstein's legendary works in which the foundations of at least three areas of modern physics were laid: statistical mechanics,…
Exactly 500 years ago, Nicolaus Copernicus drew a lattice of lines on a panel above the doorway to his rooms at Olsztyn Castle, then in the Bishopric of Warmia. Although its design has long been regarded as some kind of reflecting vertical…
The objective reality of the Earth's motion about the Sun was finally proven observationally by Bradley (1727) when he correctly explained the ~20'' annual, elliptical motions of stars as being due to aberration of starlight caused by the…
The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the…
The nonlinear stability domain of Lagrange's celebrated 1772 solution of a three-body problem is obtained numerically as a function of the masses of the bodies and the common eccentricity of their Keplerian orbits. This domain shows that…
The goal of the Pierre Auger Observatory is to determine the still unknown nature and origin of ultra-high energy cosmic rays. The study of these elusive particles probes astrophysical sites of particle acceleration as well as fundamental…
Translated from the Latin original, "Observationes circa bina biquadrata quorum summam in duo alia biquadrata resolvere liceat" (1772). E428 in the Enestroem index. This paper is about finding A,B,C,D such that $A^4+B^4=C^4+D^4$. In sect.…
Isaac Newton is usually associated with the idea of absolute space and time, and with ballistic light-corpuscle arguments. However, Newton was also a proponent of wave/particle duality, and published a "new" variable-density aether model in…
Ultra-high energy cosmic rays (UHECRs) have been studied with the data of the Pierre Auger Observatory for more than fifteen years. An essential feature of the Observatory is its hybrid design: UHECRs are detected through the observation of…
Armed with an astrolabe and Kepler's laws one can arrive at accurate estimates of the orbits of planets.
The Sun has been observed through a telescope for four centuries. However, its study made a prodigious leap at the end of the nineteenth century with the appearance of photography and spectroscopy, then at the beginning of the following…
The one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., both at the Lagrangian points of stable equilibrium and at those…
We provide a brief biography of seven French astronomers and physicists and of a Russian astronomer from the 19th and 20th centuries. Roger Bouigue (1920-) was the director of Toulouse Observatory in the 1960s. Claude-Louis Mathieu…
The problem of drawing geographical maps is the one of mapping a subset of the sphere, representing a country or some other region on the surface of the Earth, into the Euclidean plane, minimising certain distortion properties that are…
The scientific achievements of the Pierre Auger Collaboration cover diverse and complementary fields of research. The search for the origin of ultra-high energy cosmic rays (UHECRs) is based on the measurement of the energy spectrum and…
Great opportunities arise for teaching physics, astronomy, and their histories when new discoveries are made that involve concepts accessible to students at every level. Such an opportunity currently exists thanks to the fact that notes…