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http://dx.doi.org/10.7858/eamj.2018.016

The reinterpretation and the visualization of Pappus' methods for trisecting the angle  

Kim, Hyang Sook (Department of Applied Mathematics & Institute of Natural Science Inje University)
Kim, Yang (Department of Applied Mathematics Inje University)
Pak, Jin Suk (Kyungpook National University)
Publication Information
East Asian mathematical journal / v.34, no.2, 2018 , pp. 219-238 More about this Journal
Abstract
The purpose of this paper is to reinterpret and visualize Pappus' methods for trisecting the angle by utilizing the Nicomedes' conchoid and Apollonius' symptom of a hyperbola. In particular, we reinterpret the Pappus' three results which are the methods of hyperbola and circle, the trisection of the arc and focus and directrix of the hyperbola by 3 steps(analysis, construction, and proof) in the current middle school curriculum of Mathematics. Moreover, we visualize the construction of an hyperbola which is represented by means of an eccentricity.
Keywords
Trisection of angle; Reinterpretation; Visualization; Construction; Conchoid; Hyperbola;
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