Abstract

This paper is devoted to exposition of a provable classical solution for the ancient Greeks classical geometric problem of angle trisection [3]. (Pierre Laurent Wantzel, 1837),presented an algebraic proof based on ideas from Galois field showing that, the angle trisection solution correspond to an implicit solution of the cubic equation; , which he stated as geometrically irreducible [23]. The primary objective of this novel work is to show the possibility to solve the trisection of an arbitrary angle using the traditional Greeks tools of geometry, and refutethe presented proof of angle trisection impossibility statement. The exposedproof of the solution is theorem , which is based on the classical rules of Euclidean geometry, contrary to the Archimedes proposition of usinga marked straightedge construction [4], [11].

Highlights

  • Compass and straightedge problems have always been the favorite subject o f classical geometry

  • The aim of this paper is to provide a geometrical approach to verify the claim th at, any give n angle in the superset, can geometrically be trisected from the subset, if and only if any angle element within the subset is trisectible

  • The is regarded as the maximum limit of the proposed angle trisection solution, within which, any given angle inclusive of the angle is trisectible

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Summary

Introduction

Compass and straightedge problems have always been the favorite subject o f classical geometry. There are three classical problems of geometry posed by the ancient Greek geometers which include; “Trisection of an arbitrary angle”, “Squaring of a circle”, and “The duplication of a cube”. Mathematicians have expe nded a vast amounts of energy in efforts to find solutions for the three problems, but no geometrical solutions have been discovered by this day. Though the three problems are closely related, the focus of this work is to separately provide an elegant solu tion for the problem of angle trisection. The problem of angle trisection concerns the classical partitioning of a given angle i n to th re e mean proportions using the traditional Greek’s tools of geometry (classical compass and straightedge). In ce n tu ry, 7308 | P a g e August, 2016 https : / / ci rw o rld . co m/

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