A smaller sleeping bag for a baby snake
2001 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, Vol. 26, no 1, 173-181 p.Article in journal (Refereed) Published
By a sleeping bag for a baby snake in d dimensions we mean a subset of Rd which can cover, by rotation and translation, every curve of unit length. We construct sleeping bags which are smaller than any previously known in dimensions 3 and higher. In particular, we construct a three-dimensional sleeping bag of volume approximately 0.075803. For large d we construct d-dimensional sleeping bags with volume less than (cvlog d)d/d3d/2 for some constant c. To obtain the last result, we show that every curve of unit length in Rd lies between two parallel hyperplanes at distance at most C1d-3/2vlog d, for some constant c1.
Place, publisher, year, edition, pages
2001. Vol. 26, no 1, 173-181 p.
IdentifiersURN: urn:nbn:se:liu:diva-37669Local ID: 37250OAI: oai:DiVA.org:liu-37669DiVA: diva2:258518