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- Title
Janos Bolyai's Angle Trisection Revisited.
- Authors
DIRNBÖCK, HANS; WEISS, GUNTER
- Abstract
J. Bolyai proposed an elegant recipe for the angle trisection via the intersection of the arcs of the unit circle with that of an equilateral hyperbola c. It seems worthwhile to investigate the geometric background of this recipe and use it as the basic idea for finding the nth part of a given angle. In this paper, we shall apply this idea for the trivial case n = 4, and for 5. Following Bolyai in the case 5, one has to intersect the unit circle with cubic curve c. There, and in the cases n > 5, we find only numerical solutions, which shows the limitation of Bolyai's method. Therefore, we propose another construction based on epicycloids inscribed to the unit circle. By this method is even possible to construct the (m)th part of a given angle.
- Subjects
BOLYAI, Janos, 1802-1860; HYPERBOLA; GEOMETRY; CUBIC curves; TRISECTION of angle
- Publication
KoG, 2022, Vol 26, Issue 26, p52
- ISSN
1331-1611
- Publication type
Article
- DOI
10.31896/k.26.5