Related papers: Euler: Genius Blind Astronomer Mathematician
We review Euler's idea on the Gammafunction. We will explain, how Euler obtained them and how Euler's ideas anticipate more modern approaches and theories. Furthermore, some questions asked by Euler are answered.
The classical three-body problem arose in an attempt to understand the effect of the Sun on the Moon's Keplerian orbit around the Earth. It has attracted the attention of some of the best physicists and mathematicians and led to the…
We consider the Euler approach to construction and to investigation of the superintegrable systems related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel…
In its Phase I, the Pierre Auger Observatory has led to several observations, driving the field of ultra-high-energy cosmic ray (UHECR) research over the last 20 years. Major achievements obtained so far include the unprecedented precise…
The idea of atoms is old but X-rays provided the first probe into the physical atom. Photographs of X-ray scattering from crystals -Laue spots- were the first visual proof for the physical existence of atoms arranged in a perfect geometric…
When V. M. Slipher gave the 1933 George Darwin lecture to the Royal Astronomical Society, it was natural that he spoke on spectrographic studies of planets. Less than one-sixth of his published work deals with globular clusters and the…
The history of astrometry, the branch of astronomy dealing with the positions of celestial objects, is a lengthy and complex chronicle, having its origins in the earliest records of astronomical observations more than two thousand years…
The scientific revolution in the first half of the seventeenth century, pioneered by figures such as Harvey, Galileo, Gassendi, Kepler and Descartes, was disseminated to the northernmost countries in Europe with considerable delay. In this…
Galileo Galilei had sufficient skill as an observer and instrument builder to be able to measure the positions and apparent sizes of objects seen through his telescopes to an accuracy of 2" or better. However, Galileo had no knowledge of…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
We examine connections between the mathematics behind methods of drawing geographical maps due, on the one hand to Marinos and Ptolemy (1st-2nd c. CE) and on the other hand to Delisle and Euler (18th century). A recent work by the first two…
This paper discusses three matter-of-principle methods for measuring the general relativity correction to the Newtonian values of the position of collinear Lagrangian points L1 and L2 of the Sun-Earth-satellite system. All approaches are…
Mindful of the anomalous perihelion precession of Mercury discovered by U. Le Verrier in the second half of the nineteenth century and its successful explanation by A. Einstein with his General Theory of Relativity in the early years of the…
Among the geniuses of mankind, Einstein was probably one of those who made more erroneous claims, and often changed his opinion during the years on important scientific subjects. However, it is important to bear in mind that his mistakes…
E26 in the Enestrom index. Translated from the Latin original, "Observationes de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus" (1732). In this paper Euler gives a counterexample to Fermat's claim that all numbers of…
Galileo Galilei believed that stars were distant suns whose sizes, measured via his telescope, were a direct indication of distance -- fainter stars (appearing smaller in the telescope) were farther away than brighter ones. Galileo argued…
Einstein identified singularities in spacetimes, such as at the Schwarzschild radius, where later relativists only find a coordinate system assigning multiple values to a single spacetime event. These differing judgments derive from…
Euler used intrinsic equations expressing the radius of curvature as a function of the angle of inclination to find curves similar to their evolutes. We interpret the evolute of a plane curve optically, as the caustic (envelope) of light…
The Pierre Auger Observatory is the world's largest operating detection system for the observation of ultra high energy cosmic rays (UHECRs). The detector allows detailed measurements of their energy spectrum, mass composition and arrival…
Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, Lehmer's generalized Euler numbers are studied to give certain…