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.
| Published in | American Journal of Applied Mathematics (Volume 3, Issue 4) |
| DOI | 10.11648/j.ajam.20150304.11 |
| Page(s) | 169-173 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Cyclic Trapezium, Working Backwards, Practical Tool
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APA Style
Lorna A. Willis. (2015). Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts. American Journal of Applied Mathematics, 3(4), 169-173. https://doi.org/10.11648/j.ajam.20150304.11
ACS Style
Lorna A. Willis. Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts. Am. J. Appl. Math. 2015, 3(4), 169-173. doi: 10.11648/j.ajam.20150304.11
AMA Style
Lorna A. Willis. Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts. Am J Appl Math. 2015;3(4):169-173. doi: 10.11648/j.ajam.20150304.11
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Download@article{10.11648/j.ajam.20150304.11,
author = {Lorna A. Willis},
title = {Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {4},
pages = {169-173},
doi = {10.11648/j.ajam.20150304.11},
url = {https://doi.org/10.11648/j.ajam.20150304.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150304.11},
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.},
year = {2015}
}
TY - JOUR T1 - Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts AU - Lorna A. Willis Y1 - 2015/06/14 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.20150304.11 DO - 10.11648/j.ajam.20150304.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 169 EP - 173 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20150304.11 AB - 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. VL - 3 IS - 4 ER -
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