Approximately n-secting an angle

• Published in: Information processing letters Vol. 103; no. 1; pp. 19 - 23
• Main Authors: Kim, Seok Woo, Paeng, Seong-Hun, Cho, Hee Je
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 30.06.2007; Elsevier Science; Elsevier Sequoia S.A
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Approximation; Approximation algorithms; Artificial intelligence; Computational geometry; Computer science; control theory; systems; Exact sciences and technology; Geometry; Mathematics; Miscellaneous; n-secting; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Pattern recognition. Digital image processing. Computational geometry; Regular n-gon; Sciences and techniques of general use; Studies; Theoretical computing; Computational geometry; Approximation algorithms; Regular n-gon; n-secting; Integer; Approximation; Computer theory; Information processing; Approximation algorithm; Algorithm analysis
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2007.02.007

It is a well-known fact that there exists an angle that cannot be trisected with a straightedge and a compass. In general, it is impossible to divide an arbitrary angle into n-angles equally with only a straightedge and a compass, where n is a positive integer. We give an efficient algorithm to divide an arbitrary angle into n-angles almost equally with only a straightedge and a compass. Using this method, we can construct an almost regular n-gon for arbitrary n.