Related papers: Thinking like Archimedes with a 3D printer
Euclid pioneered the concept of a mathematical theory developed from axioms by a series of justified proof steps. From the outset there were critics and improvers. In this century the use of computers to check proofs for correctness sets a…
3D printing has raised a lot of attention from fields outside the manufacturing one in the last years. In this paper, we will illustrate some recent advances of 3D printing technology, applied to the field of telemedicine and remote patient…
Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens…
The 75th anniversary of Turing's seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing's contributions in diverse fields in the light of new developments that his…
Confocal quadrics capture (encode) and geometrize spectral properties of symmetric operators. Certain metric-projective properties of confocal quadrics (most of them established in the first half of the XIX$^{\mathrm{th}}$ century) {\it…
For the past decade, 3D printing (3DP) has become popular due to availability of low-cost 3D printers such as RepRap and Fab@Home; and better software, which offers a broad range of manufacturing platform that enables users to create…
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide…
High-aspect-ratio polymer materials are widely utilized in applications ranging from everyday materials such as clothing to specialized equipment in industrial and medical fields. Traditional fabrication methods, such as extrusion and…
Nowadays is very common to find headlines in the media where it is stated that 3D printing is a technology called to change our lives in the near future. For many authors, we are living in times of a third industrial revolution. Howerver,…
Physical visualizations (i.e., data representations by means of physical objects) have been used for many centuries in medical and anatomical education. Recently, 3D printing techniques started also to emerge. Still, other medical…
{\bf In the fourth extended version of this article, we provide a comprehensive historical survey of 200 different proofs of famous Euclid's theorem on the infinitude of prime numbers (300 {\small B.C.}--2022)}. The author is trying to…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal,…
Three-dimensional (3D) technologies have been developing rapidly recent years, and have influenced industrial, medical, cultural, and many other fields. In this paper, we introduce an automatic 3D human head scanning-printing system, which…
This article illustrates pedagogy through training in the handling of abstractions. Mental arithmetic is not limited to numerical calculation; one can mentally calculate primitives and simplify analytical expressions. Even if there is…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
Computational creativity has contributed heavily to abstract art in modern era, allowing artists to create high quality, abstract two dimension (2D) arts with a high level of controllability and expressibility. However, even with…
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
In the recent years of industrial revolution, 3D printing has shown to grow as an expanding field of new applications. The low cost solutions and short time to market makes it a favorable candidate to be utilized in the dynamic fields of…