Matches in SemOpenAlex for { <https://semopenalex.org/work/W2563031559> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W2563031559 abstract "The evolute of a smooth curve in an m-dimensional Euclidean space is the locus of centers of its osculating spheres, and the evolute of a spatial polygon is the polygon whose consecutive vertices are the centers of the spheres through the consecutive (m+1)-tuples of vertices of the original polygon. We study the iterations of these evolute transformations. This work continues the recent study of similar problems in dimension two, see arXiv:1510.07742. Here is a sampler of our results. The set of n-gons with fixed directions of the sides, considered up to parallel translation, is an (n-m)-dimensional vector space, and the second evolute transformation is a linear map of this space. If n=m+2, then the second evolute is homothetic to the original polygon, and if n=m+3, then the first and the third evolutes are homothetic. In general, each eigenvalue of the second evolute map has double multiplicity. We also study curves, with cusps, in 3-dimensional Euclidean space and their evolutes. We provide continuous analogs of the results obtained for polygons, and present a class of curves which are homothetic to their second evolutes; these curves are spatial analogs of the classical hypocycloids." @default.
- W2563031559 created "2017-01-06" @default.
- W2563031559 creator A5053891463 @default.
- W2563031559 creator A5080156489 @default.
- W2563031559 date "2016-11-27" @default.
- W2563031559 modified "2023-09-26" @default.
- W2563031559 title "Iterating evolutes of spatial curves and of spatial polygons" @default.
- W2563031559 cites W1961011958 @default.
- W2563031559 cites W2405976091 @default.
- W2563031559 cites W2963770963 @default.
- W2563031559 cites W603751085 @default.
- W2563031559 hasPublicationYear "2016" @default.
- W2563031559 type Work @default.
- W2563031559 sameAs 2563031559 @default.
- W2563031559 citedByCount "0" @default.
- W2563031559 crossrefType "posted-content" @default.
- W2563031559 hasAuthorship W2563031559A5053891463 @default.
- W2563031559 hasAuthorship W2563031559A5080156489 @default.
- W2563031559 hasConcept C111919701 @default.
- W2563031559 hasConcept C114614502 @default.
- W2563031559 hasConcept C126042441 @default.
- W2563031559 hasConcept C186450821 @default.
- W2563031559 hasConcept C190694206 @default.
- W2563031559 hasConcept C2524010 @default.
- W2563031559 hasConcept C2778572836 @default.
- W2563031559 hasConcept C33923547 @default.
- W2563031559 hasConcept C41008148 @default.
- W2563031559 hasConcept C76155785 @default.
- W2563031559 hasConcept C91709909 @default.
- W2563031559 hasConceptScore W2563031559C111919701 @default.
- W2563031559 hasConceptScore W2563031559C114614502 @default.
- W2563031559 hasConceptScore W2563031559C126042441 @default.
- W2563031559 hasConceptScore W2563031559C186450821 @default.
- W2563031559 hasConceptScore W2563031559C190694206 @default.
- W2563031559 hasConceptScore W2563031559C2524010 @default.
- W2563031559 hasConceptScore W2563031559C2778572836 @default.
- W2563031559 hasConceptScore W2563031559C33923547 @default.
- W2563031559 hasConceptScore W2563031559C41008148 @default.
- W2563031559 hasConceptScore W2563031559C76155785 @default.
- W2563031559 hasConceptScore W2563031559C91709909 @default.
- W2563031559 hasLocation W25630315591 @default.
- W2563031559 hasOpenAccess W2563031559 @default.
- W2563031559 hasPrimaryLocation W25630315591 @default.
- W2563031559 hasRelatedWork W1765578997 @default.
- W2563031559 hasRelatedWork W1834428910 @default.
- W2563031559 hasRelatedWork W1919588188 @default.
- W2563031559 hasRelatedWork W2011380711 @default.
- W2563031559 hasRelatedWork W2043159732 @default.
- W2563031559 hasRelatedWork W2065196403 @default.
- W2563031559 hasRelatedWork W2076344277 @default.
- W2563031559 hasRelatedWork W2079577537 @default.
- W2563031559 hasRelatedWork W2093148532 @default.
- W2563031559 hasRelatedWork W2119592103 @default.
- W2563031559 hasRelatedWork W2182952090 @default.
- W2563031559 hasRelatedWork W2512730052 @default.
- W2563031559 hasRelatedWork W2557547724 @default.
- W2563031559 hasRelatedWork W2885264870 @default.
- W2563031559 hasRelatedWork W2963770963 @default.
- W2563031559 hasRelatedWork W2964005529 @default.
- W2563031559 hasRelatedWork W3003528686 @default.
- W2563031559 hasRelatedWork W3021080389 @default.
- W2563031559 hasRelatedWork W3169516454 @default.
- W2563031559 hasRelatedWork W3178732285 @default.
- W2563031559 isParatext "false" @default.
- W2563031559 isRetracted "false" @default.
- W2563031559 magId "2563031559" @default.
- W2563031559 workType "article" @default.