2014/09/16 by Jordi Guàrdia, Guàrdia, Jordi, Eulàlia Tramuns +1
Engineering · Mathematics · #12F05 #51M15 #Advanced Materials and Mechanics #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #Robotic Mechanisms and Dynamics #math.NT #msc:12F05 #msc:51M15
paper · pdf · doi:10.48550/arxiv.1409.4974
10 pages
openalex publication_date 2014/09/16 · arxiv created 2014/09/25 · arxiv updated 2014/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a formalization of geometric instruments that considers separately geometric and arithmetic aspects of them. We introduce the concept of tool, which formalizes a physical instrument as a set of axioms representing its geometric capabilities. We also define a map as a tool together with a set of points and curves as an initial reference. We rewrite known results using this new approach and give new relations between origami and other instruments, some obtained considering them as tools and others considering them as maps.