HackerPapers

arXiv:1711.10466math.GT

Analytic sphere eversion using ruled surfaces

Adam Bednorz, Witold Bednorz

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

Abstract

Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and topologically simpler, including also Boy surface (real projective plane), using a family of ruled surfaces. We show their usefulness in visualizing the process using commonly available modeling software.

arXiv comments
25 pages, 16 figures, more information at http://www.fuw.edu.pl/~abednorz/eversion/
Journal reference
Differential Geometry and its Applications 64, 59 (2019)
DOI
doi:10.1016/j.difgeo.2019.02.004
Subjects
math.GTGeometric Topology math-phMathematical Physics math.AGAlgebraic Geometry math.ATAlgebraic Topology

On Hacker News

Linked by 1 identifiable commenter in 1 comment across 1 thread, from Jul 2020 to Jul 2020.

Comments linking this paper, per year.

Discussed in comments1 thread

  1. Sphere Eversion 1 comment

    • If you just look at the set of points at each instant in time, the self-intersections would produce discontinuities. So instead of deforming a raw set of points in 3D space, topologists deform a function which takes a point on the sphere and returns a point in 3D space…

      panicView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.