Angle trisection with Origami and related topics

Fuchs, Clemens

doi:10.4171/em/179

Cited by 2 publications

(1 citation statement)

References 15 publications

(22 reference statements)

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“…The recent work of scholars such as Tachi, Demaine, Lang, and Hull strongly contributed to the rise of mathematical studies on origami. Furthermore, it has been demonstrated that origami can be applied to solve mathematical problems such as quadratic, cubic, [40] quartic and quintic equations with rational coefficients, [39] trisect an angle, [40,41] and double the cube. [16,40,42] Therefore, mathematics has been extensively applied for the design and optimization process of origami structures.…”

Section: Background and Terminologymentioning

confidence: 99%

Engineering Origami: A Comprehensive Review of Recent Applications, Design Methods, and Tools

et al. 2021

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Origami-based designs refer to the application of the ancient art of origami to solve engineering problems of different nature. Despite being implemented at dimensions that range from the nano to the meter scale, origami-based designs are always defined by the laws that govern their geometrical properties at any scale. It is thus not surprising to notice that the study of their applications has become of cross-disciplinary interest. This article aims to review recent origami-based applications in engineering, design methods and tools, with a focus on research outcomes from 2015 to 2020. First, an introduction to origami history, mathematical background and terminology is given. Origami-based applications in engineering are reviewed largely in the following fields: biomedical engineering, architecture, robotics, space structures, biomimetic engineering, fold-cores, and metamaterials. Second, design methods, design tools, and related manufacturing constraints are discussed. Finally, the article concludes with open questions and future challenges.

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Section: Background and Terminologymentioning

confidence: 99%

Engineering Origami: A Comprehensive Review of Recent Applications, Design Methods, and Tools

et al. 2021

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Angle Trisection with Growth Rate of The Golden Ratio

Mousavi,

Mansouri,

Mousavi

2024

Qeios

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In this paper, we explore the triangulation of angles using the golden ratio and geometric compass principles. By dividing angles into three equal parts based on the golden ratio, we demonstrate a method for solving this geometric problem. Furthermore, we extend our exploration into the third dimension, where a geometric compass can effectively divide a two-dimensional angle into three equal parts. Additionally, our investigation delves into the realm of six-dimensional space-time, where we observe the simultaneous movement of two arms of the compasses based on the golden ratio to achieve the division of every angle into three equal parts. We emphasize the significance of the growth rate associated with the golden ratio in resolving complex mathematical and physical problems. This study provides valuable insights into the application of geometric principles and the golden ratio in solving challenging problems within mathematics and physics.

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Angle trisection with Origami and related topics

Abstract: Clemens Fuchs received his doctoral degree and his habilitation in mathematics from the Graz University of Technology. Currently he is working as senior researcher and lecturer at ETH Zurich. His main fields of interest are in number theory and diophantine geometry.

Cited by 2 publications

References 15 publications

Engineering Origami: A Comprehensive Review of Recent Applications, Design Methods, and Tools

Engineering Origami: A Comprehensive Review of Recent Applications, Design Methods, and Tools

Angle Trisection with Growth Rate of The Golden Ratio

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