Abstract
The Greeks knew how to bisect an angle using compass and straightedge constructions. The question whether an angle can be trisected, or divided into n equal parts, by compass and straightedge methods then comes naturally.
The question is simple enough and seems to suggest a simple solution. Here too, appearances are deceptive. It turns out that, like the duplication of the cube, the construction with compass and straightedge is impossible. We can find a construction if we allow a marked ruler and verging solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Sefrin-Weis; 2010, p. 146ff and p. 284ff.
- 2.
On Archimedes see Ver Eecke; 1921; Heath; 1953 and for a reassessment Jaeger; 2008; Paipetis and Ceccarelli; 2010.
- 3.
In German Brennpunkt, in Dutch brandpunt, literally burning point.
- 4.
Voza; 2010.
- 5.
We refer the reader to Jaeger; 2008 for a very enlightening interpretation of these stories in the light of Roman literary styles.
- 6.
On the Jesuit mathematics school in Antwerp see Meskens; 1997.
- 7.
Sancto Vincentio; 1647, Heath; 1956, I p. 404, Ostermann and Wanner; 2012, p. 351.
- 8.
Based on van Looy; 1979, p. 67–76.
- 9.
This method can already be found in Ibn-al-Haytham’s Optica (1011–1021). Ibn-al-Haytham (ca. 965 – ca. 1040) is also known as Alhazen. See Hogendijk; 1979.
- 10.
van Looy; 1979, p. 109.
- 11.
Sancto Vincentio; 1647, p. 111–112.
- 12.
Heath; 1981, p. 23–24.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Meskens, A., Tytgat, P. (2017). Trisecting an angle. In: Exploring Classical Greek Construction Problems with Interactive Geometry Software. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-42863-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-42863-5_5
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-42862-8
Online ISBN: 978-3-319-42863-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)