The Angle Trisection Solution (A Compass-Straightedge (Ruler) Construction)

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Kimuya M Alex


This paper is devoted to exposition of a provable classical solution for the ancient Greek’s 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 Greek’s 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].

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ALEX, Kimuya M. The Angle Trisection Solution (A Compass-Straightedge (Ruler) Construction). JOURNAL OF ADVANCES IN MATHEMATICS, [S.l.], v. 13, n. 4, p. 7308-7332, sep. 2017. ISSN 2347-1921. Available at: <>. Date accessed: 20 oct. 2017. doi:


1. K. M. Alex. 2017 The Possibility of Angle trisection (A Compass Straightedge Construction), Journal of Mathematics and System Science, Vol.7, (January, 25, 2017), P. 25-42. doi: 10.17265/2159-5291/2017.01.003.
2. W.S. Anglin. 1994. Mathematics: A Concise History and Philosophy, Springer-Verlag, New York, (1994), pp. 75-80.
3.C. B. Boyer. 1991.A History of Mathematics, 2nd Ed., John Wiley & Sons, Inc, (1991), p.64.
4.H.Dorrie. 1965. 100 Great Problems of Elementary Mathematics, Dover Publications, New York, (1965), P. 173.
5.J. Castellanos. 1994-2007. What is Non-Euclidean Geometry?, , (1994)-(2007).
6. Burton, M. David. 1999.A History of Mathematics: An Introduction, 4th Ed., McGraw-Hill, p. 116, (1999).
7. R. Descartes. 1664.La Géométrie, C. Angot, Paris, (1664) (first published in 1637).
8.H. Florentino Ĺatortue. 2017. The Solution to the Impossible Problem, Library of Congress Control Number: 2017905297, NY, Printed in the United States of America, (2017).
9.C.A.Hart and D. D. Feldman. 1912, 2013. Plane and Solid Geometry, American Book Company, Chicago, (1912), (2013), p.341-342.
10. Dudley, U. 1983. What to do when the trisection comes. The Mathematical Intelligencer 5, (1), (1983), p.21.
11.Dudley, Underwood. 1994.The Trisectors, The Mathematical Association of America.
12. R. Fitzpatrick. 1883–1885. Euclid’s Elements of Geometry, from Euclidis Elementa, edidit et Latine interpretatus est I.L. Heiberg, in aedibus, B.G. Teubneri.
13. C.A.Hart and Daniel D Feldman. 1912, 2013. Plane and Solid Geometry, American Book Company, Chicago, (1912), (2013), p.96, p.171.
14. Henderson, W David et al. 2005. Experiencing Geometry/Euclidean and Non-Euclidean with History (3rd Ed), Pearson/ Prentice-Hall, ISBN 0-13-143748-8.
15. Thomas, I. 1939, 1941.Selections Illustrating the History of Greek Mathematics, William Heinemann, London, and Harvard University Press, Cambridge, MA.
16. Stillwell, John. 1989. Mathematics and Its History, Springer-Verlag, New York.
17. Faber, Richard L. 1983. Foundations of Euclidean and Non-Euclidean Geometry, New York, Marcel Dekker, lnc. ISBN 0-8247-1748-1.
18.J. Marshall. 2014. What Are Euclidean and Non-Euclidean Geometry?, , October 17, (2014).
19. Burton, D. M. 1999.A History of Mathematics: An Introduction, 4th Ed., McGraw-Hill, (1999), p. 116.
20.S. Mustonen. 2013. Simple Constructions’ of Regular n-sided Polygons at Any Given Accuracy, University of Helsinki, April, 30, (2013).
21.Hartshorne, Robin. 2000.Geometry: Euclid and Beyond, Springer-Verlag, (2000), p. 10.
22.University of Toronto. 1997. The Three Impossible Constructions of Geometry, , 14 Aug, (1997).
23.P.L. Wantzel. 1837. Recherches sur les moyens de reconnaitre si un problème de géométrie peut se résoudre avec la règle et le compass. Journal de Mathematiques pures et appliques, (1837), Vol. 2, pp.366-372.