Shortest closed curve to inspect a sphere

Wenk, James F.

Title:

Shortest closed curve to inspect a sphere

dc.contributor.advisor	Ghomi, Mohammad
dc.contributor.author	Wenk, James F.
dc.contributor.committeeMember	Belegradek, Igor
dc.contributor.committeeMember	Cantarella, Jason
dc.contributor.committeeMember	Kusner, Rob
dc.contributor.committeeMember	Livshyts, Galyna
dc.contributor.committeeMember	Loss, Michael
dc.contributor.department	Mathematics
dc.date.accessioned	2022-08-25T13:38:49Z
dc.date.available	2022-08-25T13:38:49Z
dc.date.created	2022-08
dc.date.issued	2022-07-30
dc.date.submitted	August 2022
dc.date.updated	2022-08-25T13:38:49Z
dc.description.abstract	We show that in Euclidean 3-space any closed curve γ which lies outside the unit sphere and contains the sphere within its convex hull has length ≥ 4π. Equality holds only when γ is composed of 4 semicircles of length π, arranged in the shape of a baseball seam, as conjectured by V. A. Zalgaller in 1996.
dc.description.degree	Ph.D.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1853/67306
dc.language.iso	en_US
dc.publisher	Georgia Institute of Technology
dc.subject	Convex hull
dc.subject	Rectifiable curve
dc.subject	Crofton’s formulas
dc.subject	Inradius
dc.subject	Unfolding
dc.title	Shortest closed curve to inspect a sphere
dc.type	Text
dc.type.genre	Dissertation
dspace.entity.type	Publication
local.contributor.advisor	Ghomi, Mohammad
local.contributor.corporatename	College of Sciences
local.contributor.corporatename	School of Mathematics
relation.isAdvisorOfPublication	2ff77925-db3c-48d6-abc8-b3dfbc983cd1
relation.isOrgUnitOfPublication	85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication	84e5d930-8c17-4e24-96cc-63f5ab63da69
thesis.degree.level	Doctoral