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 کاملGeometric Cryptography Identi cation by Angle Trisection Draft
We propose the eld of geometric cryptography where messages and ciphertexts may be represented by geometric quantities such as angles or intervals and where computation is performed by ruler and compass constructions We describe a elegant little zero knowledge identi cation scheme based on the impossibility of trisecting an angle using ruler and compass operations While geometric cryptography m...
متن کاملThe Euclid Abstract Machine: Trisection of the Angle and the Halting Problem
What is the meaning of hypercomputation, the meaning of computing more than the Turing machine? Concrete non-computable functions always hide the halting problem as far as we know. Even the construction of a function that grows faster than any recursive function — the Busy Beaver — a more natural function, hides the halting function, that can easily be put in relation with the Busy Beaver. Is t...
متن کاملTrisection, Pythagorean Angles, and Gaussian Integers
Pythagorean angles, that is angles with rational sines and cosines, provide an interesting environment for studying the question of characterizing trisectable angles. The main result of this paper shows that a Pythagorean angle is trisectable if and only if it is three times some other Pythagorean angle. Using the Euclidean parametrization of Pythagorean angles, this result allows an effective ...
متن کامل"square Trisection". Dissection of a Square in Three Congruent Partitions
A square trisection is a problem of assembling three identical squares from a larger square, using a minimal number of pieces. This paper presents an historical overview of the square trisection problem starting with its origins in the third century. We detail the reasoning behind some of the main known solutions. Finally, we give a new solution and three ruler-and-compass constructions. We con...
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ژورنال
عنوان ژورنال: JOURNAL OF ADVANCES IN MATHEMATICS
سال: 2019
ISSN: 2347-1921
DOI: 10.24297/jam.v17i0.8412