Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T19:11:54.290Z Has data issue: false hasContentIssue false
  • English
  • Français

CONSTRUCTIONS BY RULER AND COMPASS, TOGETHER WITH A FIXED CONIC

Part of: Field extensions Real and complex geometry

Published online by Cambridge University Press:  08 March 2013

SEUNGJIN BAEK ,
INSONG CHOE ,
YOONHO JUNG ,
DONGWOOK LEE  and
JUNGGYO SEO
SEUNGJIN BAEK
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email [email protected]@[email protected]@naver.com
INSONG CHOE*
Affiliation:
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-Gu, Seoul 143-701, Korea
YOONHO JUNG
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email [email protected]@[email protected]@naver.com
DONGWOOK LEE
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email [email protected]@[email protected]@naver.com
JUNGGYO SEO
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email [email protected]@[email protected]@naver.com
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is well known to be impossible to trisect an arbitrary angle and duplicate an arbitrary cube by a ruler and a compass. On the other hand, it is known from ancient times that these constructions can be performed when the use of several conic curves is allowed. In this paper, we prove that any point constructible from conics can be constructed using a ruler and a compass, together with a single fixed nondegenerate conic different from a circle.

Keywords

conic-constructible pointsruler and compassconicsgeometric construction

MSC classification

Secondary: 51M15: Geometric constructions 12F05: Algebraic extensions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 473 - 478
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Eves, H., College Geometry (Johns and Bartlett, Boston, 1995).Google Scholar
Gibbins, A. and Smolinsky, L., ‘Geometric constructions with ellipses’, Math. Intelligencer 31 (1) (2009), 57–62.CrossRefGoogle Scholar
Hummel, P., ‘Solid constructions using conics’, Pi Mu Epsilon J. 11 (8) (2003), 429–435.Google Scholar
Stillwell, J., Mathematics and its History, 2nd edn. Undergraduate Texts in Mathematics (Springer, New York, 2002).CrossRefGoogle Scholar
Videla, C. R., ‘On points constructible from conics’, Math. Intelligencer 19 (2) (1997), 53–57.CrossRefGoogle Scholar