Elementary algebra for Origami: The trisection problem revisited

نویسنده

  • Hiroyuki Shima
چکیده

This article presents an algebraic background in solving the angle trisection problem using origami-folding. Origami has been originally the art of paper folding, and recently aroused strong interest in a wide discipline of science and technology owing to its deep mathematical implication. Origami is also known to be an efficient tool for solving the trisection problem, one of the three famous problems of ancient Greek mathematics. Emphasis in this article is put on the way how the origami-based construction of the trisection corresponds to obtaining a solution for a cubic equation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Angle Trisection with Origami and Related Topics

It is well known that the trisection of an angle with compass and ruler is not possible in general. What is not so well known (even if it is folklore in the community of geometric constructions and mathematical paper folding) is that angle trisection can be done with other tools, especially by an Origami construction. In this paper we briefly discuss this construction and give a geometric and a...

متن کامل

Proving and Constraint Solving in Computational Origami

Origami (paper folding) has a long tradition in Japan’s culture and education. We are developing a computational origami system, based on symbolic computation system Mathematica, for performing and reasoning about origami on the computer. This system is based on the implementation of the six fundamental origami folding steps (origami axioms) formulated by Huzita. In this paper, we show how our ...

متن کامل

Trisections and Totally Real Origami

1. CONSTRUCTIONS IN GEOMETRY. The study of methods that accomplish trisections is vast and extends back in time approximately 2300 years. My own favorite method of trisection from the Ancients is due to Archimedes, who performed a “neusis” between a circle and line. Basically a neusis (or use of a marked ruler) allows the marking of points on constructed objects of unit distance apart using a r...

متن کامل

Elementary algebra revisited: Randomized algorithms

We look at some simple algorithms for elementary problems in algebra that yield dramatic efficiency improvements over standard methods through randomization. The randomized algorithms are, in a sense, “obvious”. Their formal statement was delayed partly by the need for rigorous analysis, but more so by the need to re-think traditional approaches to elementary algorithms. We illustrate this phil...

متن کامل

Computational Construction of a Maximum Equilateral Triangle Inscribed in an Origami

We present an origami construction of a maximum equilateral triangle inscribed in an origami, and an automated proof of the correctness of the construction. The construction and the correctness proof are achieved by a computational origami system called Eos (E-origami system). In the construction we apply the techniques of geometrical constraint solving, and in the automated proof we apply Gröb...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013