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Sullivan, John M. Denne, Elizabeth Jane 2015-09-28T15:19:45Z 2015-09-28T15:19:45Z 10000-01-01 2004 2004 The Main Theorem shows that every nontrivial tame knot in R3 has an alternating quadrisecant. This result refines the previous work about quadrisecants and gives greater geometric insight into knots. The Main Theorem provides new proofs to two previously known theorems about the total curvature and second hull of knotted curves. Moreover, essential alternating quadrisecants may be used to dramatically improve the known lower bounds on the ropelength of thick knots. Made available in DSpace on 2015-09-28T15:19:45Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3130908.pdf: 3154680 bytes, checksum: 6f6136a4c65aa54a8b2f8704ba34ce2d (MD5) Previous issue date: 2004 Embargo set by: Seth Robbins for item 88111 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 119 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004. http://hdl.handle.net/2142/86830 (MiAaPQ)AAI3130908 eng Mathematics Alternating Quadrisecants of Knots text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.