Related papers: Gerberto e la Geografia Tolemaica
We have proposed a model to obtain the length of the day and month at any geologic time. The day is found to increase by 0.002 sec/century since the seventeenth century. The lengthening of the day is attributed entirely to the increasing…
A short survey on applications of algebraic geometry in topological data analysis.
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Gerbert of Aurillac was Pope Sylvester II form 999 to 1003. His history is presented in order to understand his outstanding contribution in the establishment of quadrivium sciences (arithmetics, music, geometry and astronomy) in the…
A cosmology calculator that computes times and distances as a function of redshift for user-defined cosmological parameters is available on the World Wide Web. This note gives the formulae used by the cosmology calculator and discusses some…
Statistical analysis of samples of the orbits of celestial bodies is complicated by the fact that the Keplerian orbit is a multidimensional object, the coordinate representation of which nonlinearly depends on the choice of orbital…
In a recent article we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models are treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential etc.). This model has the…
The paper proposes an ancient landscape design as an example of graphic design for an age and place where no written documents existed. It is created by a network of earthworks, which constitute the remains of an extensive ancient…
Circular and radial geodesics are studied in the spacetime described by the $\gamma$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical…
This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey…
A re-investigation of the parapegma of Euktemon (5th century BC, Athens), based on the assumption that some star observations may in fact have been calculated rather than directly observed. The calculation follows Pliny, Natural History…
We study the geodesic complexity of the ordered and unordered configuration spaces of graphs in both the $\ell_1$ and $\ell_2$ metrics. We determine the geodesic complexity of the ordered two-point $\varepsilon$-configuration space of any…
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…
An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas. The algorithm works in weak exponential time. This means that outside a…
In this paper we present an analysis of the geological, meteorological and climatic data recorded in Acquapendente (VT) over 24 years. These data are compared to check local variations,long term trends, and correlation with maen annual…
The topological organization of several world cities are studied according to respective representations by complex networks. As a first step, the city maps are processed by a recently developed methodology that allows the most significant…
Metrically homogeneous graphs are connected graphs which, when endowed with the path metric, are homogeneous as metric spaces. Here we consider a class of countable metrically homogeneous graphs. The algebra of an age is a concept…
A survey written for the upcoming "Handbook of Enumerative Combinatorics".
This is a historian's view of how modern astronomy data can be used to discuss the shifting historical worldview of Late Antiquity. In this article an attemp is made to construct an approximate model of how the cycles of astronomical…