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Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts
American Journal of Applied Mathematics
Volume 3, Issue 4, August 2015, Pages: 169-173
Received: Nov. 30, 2014; Accepted: Feb. 6, 2015; Published: Jun. 14, 2015
Author
Lorna A. Willis, Department of Physics, Faculty of Science and Technology, University of the West Indies, Mona Campus, Jamaica, West Indies
Article Tools
Abstract
Historically, a contrived trisected line was used to trisect any other line, using the principle of projection. This is in essence about relationship and its accomplishment is about working backwards. Loosely speaking, any angle comprises two connecting lines. Attempts at trisecting any angle, which is dividing it into three equal parts, failed. In this paper any angle is defined as a unique pair of arc and chord of sector of a circle irrespective of arc radius. Two theorems viz. Equal arcs have equal central angles and equal chords have equal central angles are combined to establish a unique relationship between a pair of arc-chord and its composite of three identical pairs of arc-chord, thereby revealing a CYCLIC TRAPEZIUM, where the base defines the angle, and each equal edge defines each of the equal trisected parts of this angle. For a range of angles between 0o and 360o, this relationship is expressed as Lorna Graph, which becomes the practical tool for trisection of any angle, using the working backwards approach. This approach is extended to division of any angle into any number of equal parts.
Keywords
Cyclic Trapezium, Working Backwards, Practical Tool
Lorna A. Willis, Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts, American Journal of Applied Mathematics. Vol. 3, No. 4, 2015, pp. 169-173. doi: 10.11648/j.ajam.20150304.11
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