DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Jin, Gyo-Taek | - |
dc.contributor.advisor | 진교택 | - |
dc.contributor.author | Park, Seo-Jung | - |
dc.contributor.author | 박서정 | - |
dc.date.accessioned | 2011-12-14T04:55:47Z | - |
dc.date.available | 2011-12-14T04:55:47Z | - |
dc.date.issued | 2007 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=264290&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/42152 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수학전공, 2007.2, [ iv, 13 p. ] | - |
dc.description.abstract | A polygonal knot is a simple closed curve in the Euclidean space R3 obtained by joining finitely many points with straight line segments. The polygon index of a knot k ,denoted by p(k), is the minimal number of edges among all polygonal knots equivalent to k. It is know that if k is a nontrivial knot, then p(k) ¸ 6. Furthermore, the trefoil knot is the only knotted hexagonal knot. An n-secant line for a knot k is an oriented line whose intersection with k has at least n components. An n-secant is an ordered n-tuple of points in k which lie in order on an n-secant line. A 4-secant is called a quadrisecant. It is known that every non-trivial tame knot in $R^3$ has a quadrisecant. Let k be a knot which has finitely many quadrisecants. Then they cut k into finitely many subarcs. Straightening each of the subarcs with the end points fixed, we obtain a polygonal knot $\hat{k}$ which may have self-intersections. We call $\hat{k}$ the quadrisecant approximation of k. The main results show that every hexagonal trefoil knot has exactly three quadrisecants and the quadrisecant approximation of a hexagonal trefoil is a trefoil knot. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | quadrisecant | - |
dc.subject | hexagonal trefoil | - |
dc.subject | quadrisecant approximation | - |
dc.subject | 사중할선근사 | - |
dc.subject | 사중할선 | - |
dc.subject | 육각세잎매듭 | - |
dc.title | Quadrisecant approximation of hexagonal trefoil knots | - |
dc.title.alternative | 육각세잎매듭의 사중할선근사 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 264290/325007 | - |
dc.description.department | 한국과학기술원 : 수학전공, | - |
dc.identifier.uid | 020053216 | - |
dc.contributor.localauthor | Jin, Gyo-Taek | - |
dc.contributor.localauthor | 진교택 | - |
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