Related papers: Some mathematical and geometrical interpretations …
Despite being one of the most recognisable buildings from ancient Rome, the Pantheon is poorly understood. While its architecture has been well studied, its function remains uncertain. This paper argues that both the design and the meaning…
This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some…
Magic squares have always been and are still fascinating for many people, be it only because of their mathematical properties. Their origin is still but certain : we find no magic squares in Greece, and only a 3x3 one in China at the…
In recent archaeological investigations of Pompeii Regio V houses, a series of new, rather enigmatic images on the floors of the entrance and of the Tablinium of the so called House of Orion have been unearthed. These images are presented…
The Nabateans built several monuments in Petra and elsewhere displaying a decoration with a preference for astronomical motifs, possibly as a reflection of their religion. However, due to the lack of direct written accounts and the scarcity…
In general, small bodies of the solar system, e.g., asteroids and comets, have a very irregular shape. This feature affects significantly the gravitational potential around these irregular bodies, which hinders dynamical studies. The…
This study is based on Roman wooden force pumps. It appears that they were used in small numbers to raise water from wells, and more commonly as portable pumps to fight fires. The force pump is attributed to Ctesibius of Alexandria (fl.…
The origin of the highly eccentric, inclined, and resonance-locked orbit of Pluto has long been a puzzle. A possible explanation has been proposed recently [Malhotra, R., {\it Nature} 365:819-21 (1993)] which suggests that these…
During the voyages that led him to discover the new continent bearing his name, Amerigo Vespucci made interesting astronomical observations of the southern sky. In the past, his data have been interpreted with criteria that do not follow…
Stellar occultations provide a powerful tool to explore objects of the outer solar system. The Gaia mission now provides milli-arcsec accuracy on the predictions of these events and makes possible observations that were previously…
A series of peculiar, visual alignments between the pyramids of the pharaohs of the 4, 5 and 6 Egyptian dynasties exists. These alignments governed from the very beginning the planning of the funerary monuments of successive kings and, in…
The megalithic enclosures of Gobekli Tepe (Urfa, Turkey) are the most ancient sacred structures of stone known so far, dating back to the 10 millennium BC. The possible presence of astronomical targets for these structures is analysed, and…
Daunia is a region in northern Apulia with many interesting archaeological sites, particularly of the Neolithic and Bronze Age. Beginning from the fifth millennium BC, the farmers living in the wide plain of Daunia dug hypogea and holes in…
Translation from the Latin of "Annotationes in locum quendam Cartesii ad circuli quadraturam spectantem" (1763). The passage Euler is referring to is the "Excerpta" in part 6, p. 6 of Descartes' 1701 "Opuscula posthuma". Before reading this…
Augusta Praetoria Salassorum, modern Aosta, was founded around 25 BC to celebrate the victory of Augustus army on the Salassi. Aosta is a city of the founder under many respects; for instance, one of the two twin temples of the forum was…
For its beautiful rings, active atmosphere and mysterious magnetic field, Saturn is a fascinating planet. It also holds some of the keys to understanding the formation of our Solar System and the evolution of giant planets in general. While…
Alonso de la Veracruz conducted a physical study of image, regarding the activities of Soul in which image is produced, as organic operations. This research was particularly important since, at that time, image was systematically used to…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder…
We initiate the study of torus surgeries on knot traces. Our key technical insight is realizing the annulus twisting construction of Osoinach as a torus surgery on a knot trace. We present several applications of this idea. We find exotic…