Related papers: Dialogues about geometry and light
Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparent proofs of it (see our timeline \S 9). We give two new…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…
Two books, the "De Architectura" by Vitruvius and the "Naturalis Historia" by Pliny the Elder, give us a portrait of the Materials Science, that is, the knowledge of materials, in Rome at the beginning of the Empire. Here, I am reporting…
The field of condensed matter physics had its genesis this century and it has had a remarkable evolution. A closer look at its growth reveals a hidden aim in the collective consciousness of the field - a part of the development this century…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze…
Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)--to Klein. We will see that they are not rivalling but are tied (by…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
The recognition that physical space (or space-time) is curved is a product of the general theory of relativity, such as dramatically shown by the 1919 solar eclipse measurements. However, the mathematical possibility of non-Euclidean…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
The view of nature we adopt in the natural attitude is determined by common sense, without which we could not survive. Classical physics is modelled on this common-sense view of nature, and uses mathematics to formalise our natural…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
Quantum field theory has formed the conceptual framework of most of physics for more than sixty years. It incorporates a complete revision of our conception of the nature of matter and existence itself. Yet it is rarely taught, or even…
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively…
Group theory involves the study of symmetry, and its inherent beauty gives it the potential to be one of the most accessible and enjoyable areas of mathematics, for students and non-mathematicians alike. Unfortunately, many students never…
What is physics? What are the limits of what physics can say about the world? In seeking ever-broader theoretical `umbrellas' for physical phenomena, we are seeking unifying principles. Emergent phenomena have turned out to be some of the…
The search for the first illuminated astronomical sources in the universe is at the edge of the cosmic frontier. Promising techniques for discovering the first objects and their effects span the electromagnetic spectrum and include…