### Abstract

We find the unique smallest convex region in the plane that contains a congruent copy of every triangle of perimeter two. It is the triangle ABC with AB = 2/3, 〈 B = 60°, and BC ≈ 1.00285.

Original language | English |
---|---|

Pages (from-to) | 285-293 |

Number of pages | 9 |

Journal | Geometriae Dedicata |

Volume | 81 |

Issue number | 1-3 |

Publication status | Published - 2000 |

### Fingerprint

### Keywords

- Convex covers
- Isoperimetric triangles.
- Worm problems

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Geometriae Dedicata*,

*81*(1-3), 285-293.

**The Smallest Convex Cover for Triangles of Perimeter Two.** / Füredi, Z.; Wetzel, John E.

Research output: Contribution to journal › Article

*Geometriae Dedicata*, vol. 81, no. 1-3, pp. 285-293.

}

TY - JOUR

T1 - The Smallest Convex Cover for Triangles of Perimeter Two

AU - Füredi, Z.

AU - Wetzel, John E.

PY - 2000

Y1 - 2000

N2 - We find the unique smallest convex region in the plane that contains a congruent copy of every triangle of perimeter two. It is the triangle ABC with AB = 2/3, 〈 B = 60°, and BC ≈ 1.00285.

AB - We find the unique smallest convex region in the plane that contains a congruent copy of every triangle of perimeter two. It is the triangle ABC with AB = 2/3, 〈 B = 60°, and BC ≈ 1.00285.

KW - Convex covers

KW - Isoperimetric triangles.

KW - Worm problems

UR - http://www.scopus.com/inward/record.url?scp=0042226847&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042226847&partnerID=8YFLogxK

M3 - Article

VL - 81

SP - 285

EP - 293

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1-3

ER -