Notes for 3 1's three dimensional invariants: Difference between revisions
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The rope length of the trefoil is known to be no more than 16.372, by [[A ropelength bibliography|numerical experiments]], while the [[Article:Quadrisecants Give New Lower Bounds for the Ropelength of a Knot|sharpest known lower bound]] (actually applicable to all non-trivial knots) is 15.66. |
The rope length of the [[3_1|trefoil]] is known to be no more than 16.372, by [[A ropelength bibliography|numerical experiments]], while the [[Article:Quadrisecants Give New Lower Bounds for the Ropelength of a Knot|sharpest known lower bound]] (actually applicable to all non-trivial knots) is 15.66. |
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[[Image:The Trefoil is Fibered.png|right|120px]] The trefoil is a fibered knot! A java applet demonstrating it, written by Robert Barrington Leigh at the University of Toronto, is [http://www.math.toronto.edu/~drorbn/People/BarringtonLeigh/FiberedKnot.html here]. |
[[Image:The Trefoil is Fibered.png|right|120px]] The trefoil is a fibered knot! A java applet demonstrating it, written by Robert Barrington Leigh at the University of Toronto, is [http://www.math.toronto.edu/~drorbn/People/BarringtonLeigh/FiberedKnot.html here]. |
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Latest revision as of 13:15, 14 April 2008
The rope length of the trefoil is known to be no more than 16.372, by numerical experiments, while the sharpest known lower bound (actually applicable to all non-trivial knots) is 15.66.
The trefoil is a fibered knot! A java applet demonstrating it, written by Robert Barrington Leigh at the University of Toronto, is here.
