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角平分線,
阿基米德螺線,
化圓為方,
尼科梅德斯蚌線,
倍立方,
切瓦旋輪線,
麥克勞林三等分曲線,
莫雷定理,
Neusis 作圖法,
摺紙,
皮爾龐特素數,
Hippias 的割圓曲線,
戰斧,
三等分曲線
使用 探索
參考文獻
Bogomolny, A. "Angle Trisection." http://www.cut-the-knot.org/pythagoras/archi.shtml.Bogomolny, A. "Angle Trisection by Hippocrates." http://www.cut-the-knot.org/Curriculum/Geometry/Hippocrates.html.Bold, B. "The Problem of Trisecting an Angle." Ch. 5 in Famous Problems of Geometry and How to Solve Them. New York: Dover, pp. 33-37, 1982.Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 190-191, 1996.Courant, R. and Robbins, H. "Trisecting the Angle." §3.3.3 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 137-138, 1996.Coxeter, H. S. M. "Angle Trisection." §2.2 in Introduction to Geometry, 2nd ed. New York: Wiley, p. 28, 1969.Dixon, R. Mathographics. New York: Dover, pp. 50-51, 1991.Dörrie, H. "Trisection of an Angle." §36 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 172-177, 1965.Dudley, U. The Trisectors. Washington, DC: Math. Assoc. Amer., 1994.Geometry Center. "Angle Trisection." http://www.geom.umn.edu:80/docs/forum/angtri/.Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 25-26, 1991.Klein, F. "The Delian Problem and the Trisection of the Angle." Ch. 2 in "Famous Problems of Elementary Geometry: The Duplication of the Cube, the Trisection of the Angle, and the Quadrature of the Circle." In Famous Problems and Other Monographs. New York: Chelsea, pp. 13-15, 1980.Loy, J. "Trisection of an Angle." http://www.jimloy.com/geometry/trisect.htm.Ogilvy, C. S. "Solution to Problem E 1153." Amer. Math. Monthly 62, 584, 1955. Ogilvy, C. S. "Angle Trisection." Excursions in Geometry. New York: Dover, pp. 135-141, 1990.Peterson, G. "Approximation to an Angle Trisection." Two-Year Coll. Math. J. 14, 166-167, 1983.Scudder, H. T. "How to Trisect and Angle with a Carpenter's Square." Amer. Math. Monthly 35, 250-251, 1928.Sloane, N. J. A. Sequences A158599 and A158600 in "The On-Line Encyclopedia of Integer Sequences."Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, 1999.Wantzel, M. L. "Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas." J. Math. pures appliq. 1, 366-372, 1836.Wazewski, T. Ann. Soc. Polonaise Math. 18, 164, 1945.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 25, 1991.Yates, R. C. The Trisection Problem. Reston, VA: National Council of Teachers of Mathematics, 1971.
請引用本文為
Weisstein, Eric W. "角的三等分。" 來源 Web 資源。 https://mathworld.tw/AngleTrisection.html
學科分類
和 
弧度（分別為 
和 
），可以進行三等分。此外，一些角在幾何上是可三等分的，但最初無法構造出來，例如 
（Honsberger 1991）。此外，使用有刻度的直尺（Neusis 作圖法）可以完成任意角的三等分，如上圖所示（Courant 和 Robbins 1996）。
，度量為 
的近似值，首先平分 
，然後三等分弦 
（上圖左側）。所需的近似值是角度為 
，度量為 
（上圖右側）。為了將 
與 
聯絡起來，在三角形 
和 
上使用正弦定理，得到
。由於我們也有 
，這可以寫成![sint=2[sin(1/2alpha)cost-sintcos(1/2alpha)].](/images/equations/AngleTrisection/NumberedEquation2.svg)
，得到
的角度 
，此近似值與 
的誤差也在 
以內，如上圖所示，並在下表（Petersen 1983）中進行了總結，其中角度以度為單位。
(
)
(
)
(
)
(
)
具有麥克勞林級數
的非常好的近似值。