Related papers: Thinking like Archimedes with a 3D printer
3D printing technology can help to visualize proofs in mathematics. In this document we aim to illustrate how 3D printing can help to visualize concepts and mathematical proofs. As already known to educators in ancient Greece, models allow…
In this primer, we will describe a number of projects that can be completed with a 3D printer, particularly by mathematics professors and their students. For many of the projects, we will utilize Mathematica to design objects that…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
These are notes and slides from a Pecha-Kucha talk given on March 6, 2013. The presentation tinkered with the question whether calculus on graphs could have emerged by the time of Archimedes, if the concept of a function would have been…
Three-dimensional (3D) visualization has opened up a Universe of possible scientific data representations. 3D printing has the potential to make seemingly abstract and esoteric data sets accessible, particularly through the lens of…
Part 1 : For more than two millennia, ever since Euclid's geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe restriction of our views of space-time,…
We explore the stability of floating objects through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes' Principle. We investigate a variety of floating…
This is a case study of teaching 3D design and 3D printing in a project-based computing course for undergraduate math majors. This article discusses content organization, implementation, project grading, and includes a personal reflection.…
In his famous work, "Measurement of a Circle," Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern…
We know that the algorithm of Theon of Smyrna (70-135 AD) made it possible to highlight fine frames of $\sqrt2$ by rationals. However, this same algorithm also applies to $\sqrt3$ and makes it possible to find the famous Archimedes…
Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an…
An overview concerning 3D printing (a.k.a. additive manufacturing) within the context of Science, Technology, Engineering, and Mathematics (STEM) education at the college/university level is provided. The vast majority of quoted papers…
In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder…
In this paper we are exploring the possibilities of 3D printing in the fabrication of mirrors for astronomy. Taking the advantages of 3D printing to solve the existing problems caused by traditional manufacturing, two proof-of-concept…
Are we smarter now than Socrates was in his time? Society as a whole certainly enjoys a higher degree of education, but humans as a species probably don't get intrinsically smarter with time. Our knowledge base, however, continues to grow…
Is collective intelligence just individual intelligence writ large, or are there fundamental differences? This position paper argues that a cognitive history methodology can shed light into the nature of collective intelligence and its…
Paul Erdos claimed that mathematics is not yet ready to settle the 3x+1 conjecture. I agree, but very soon it will be! With the exponential growth of computer-generated mathematics, we (or rather our silicon brethrern) would have a shot at…
We have made an attempt to reproduce 17 objects of the IMAGINARY Open Mathematics Exhibition (www.imaginary.org) using low-cost, desktop 3D printers. The IMAGINARY open math is an international project by the Mathematisches…
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…
Astronomy, a captivating field that draws upon science, mathematics, and engineering, has traditionally relied on visual representations to convey the wonders of the cosmos. While this approach effectively engages the sighted population,…