Skip to main content
SpringerLink
Log in

Reflecting a triangle in the plane

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

We prove that if the three angles of a triangleT in the plane are different from (60°, 60°, 60°), (30°, 30°, 120°), (45°,45°,90°),(30°,60°,90°), then the set of vertices of those triangles which are obtained fromT by repeating ‘edge-reflection’ is everywhere dense in the plane.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hadwiger, H., Debrunner, H.: Combinatorial geometry in the plane. New York: Holt, Reinhart and Winston 1964

    Google Scholar 

  2. Laczkovich, M.: Tiling of polygons with similar triangles. Combinatorica10, 281–306 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Maehara, H.: Extending a flexible unit-bar framework to a rigid one. Ann. Discrete Math.

  4. Wagon, S.: The Banach-Tarski Paradox Cambridge: Cambridge University Press (1985)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Mathematical Institute of the Hungarian Academy of Sciences, Yale University, New York University, New York

    Imre Bárány

  2. CNRS, Paris, France

    Peter Frankl

  3. Department of Mathematics, Faculty of Education, Ryukyu University, Nishihara-cho, 903-01, Okinawa, Japan

    Hiroshi Maehara

Authors
  1. Imre Bárány
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Frankl
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hiroshi Maehara
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bárány, I., Frankl, P. & Maehara, H. Reflecting a triangle in the plane. Graphs and Combinatorics 9, 97–104 (1993). https://doi.org/10.1007/BF02988297

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02988297

Keywords

Search

Navigation