Related papers: Plane Geometry: An Elementary School Textbook (ca.…
This paper wants to show how practical geometry, created to give a concrete help to people involved in trade, in land-surveying and even in astronomy, underwent a transformation that underlined its didactical value and turned it first into…
The article is devoted to the problem of incorporation geographic information systems (GIS) in world school practice. The authors single out the stages of GIS application in school geographical education based on the retrospective analysis…
In this paper, we describe a very simple method to calculate the positions of the planets in the sky. The technique used enables us to calculate planetary positions to an accuracy of $\stackrel{<}{_{\sim}} 1^{\circ}$ for $\pm 50$ years from…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Unquestionably the greatest discovery of the Pythagoreans is the existence of incommensurable magnitudes, most probably the incommensurability of the diameter to the side of a square, but there is no agreement among historians of Greek…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
We present a scoping review of published literature on ethnomathematics and Indigenous mathematics as a step towards a goal to decolonize the prevailing Eurocentric view of the provenance of mathematics. Mathematical practices were…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
This is an entry for Physics Today's recent essay contest, written as a "Search and Discovery" news story, imagining what major breakthroughs might be shaking the physics world one hundred years from now.
Is there any hope for us to draw a plausible picture of the future of exoplanet research? Here we extrapolate from the first 25 years of exoplanet discovery into the year 2050. If the power law for the cumulative exoplanet count continues,…
We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical assumptions that are sufficient to rederive them,…
In this short review, we trace the evolution of inference in astronomy, highlighting key milestones rather than providing an exhaustive survey. We focus on the shift from classical optimization to Bayesian inference, the rise of…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
This essay is a tour around many of the lesser known pregeometric models of physics, as well as the mainstream approaches to quantum gravity, in search of common themes which may provide a glimpse of the final theory which must lie behind…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
There is one, and only one way, consistent with fundamental physics, that the efficiency of general digital computation can continue increasing indefinitely, and that is to apply the principles of reversible computing. We need to begin…
Of the great theories of classical mathematics, projective geometry, with its powerful concepts of symmetry and duality, has been exceptional in continuing to intrigue investigators. The challenge put forth by Errett Bishop (1928-1983),…
Are the sciences not advancing at an ever increasing speed? We contrast this popular perspective with the view that science funding may actually see diminishing returns, at least regarding established fields. In order to stimulate a larger…