Related papers: From Euclid to Riemann and Beyond
This article serves as an introduction to the special volume on Positive Geometry in the journal Le Matematiche. We attempt to answer the question in the title by describing the origins and objects of positive geometry at this early stage…
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 curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofold formulation of the study of particle interactions and…
The aim of this thesis is to question some of the basic assumptions that go into building the $\Lambda$CDM model of our universe. The assumptions we focus on are the initial conditions of the universe, the fundamental forces in the universe…
In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments…
In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of…
Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to…
While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
The main purpose of this article is to study conditions for a curve on a submanifold $M\subset\mathbb{R}^n$, constructed in a particular way involving the Euclidean distance to $M$, to be a geodesic. We also present the naturally arising…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
There are many problems and configurations in Euclidean geometry that were never extended to the framework of (normed or) finite dimensional real Banach spaces, although their original versions are inspiring for this type of generalization,…
The aim of this work is to use the notions of Riemann's geometry introduced in Part I, to analyze the foundations of Einstein's theory of general relativity.
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…