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Author: teorth

constants/23a.md

@@ -4,7 +4,7 @@
 
 $C\_{23a}$ is the largest constant for which one has an inequality
 $$ L \geq C\_{23a} C^{3/4} $$
-for all knots, where $L$ is the ropelength of a knot (or link) with [crossing number](https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)) $C$. The _ropelength_ $L$ is the infimum over all embeddings of the knot (or link) of the ratio of the contour length of the knot to its thickness. The _thickness_ is defined as the radius of the smallest circle that passes through any three points on the knot (where colinear points yield an infinite radius). Colloquially, the ropelength is the least amount of rope required to tie a specific knot in a rope of unit radius. See [CKS2002] for the full definition.
+for all knots, where $L$ is the ropelength of a knot (or link) with [crossing number](https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)) $C$. The _ropelength_ $L$ is the infimum over all embeddings of the knot (or link) of the ratio of the contour length of the knot to its thickness. The _thickness_ is defined as the radius of the smallest circle that passes through any three points on the knot (where collinear points yield an infinite radius). Colloquially, the ropelength is the least amount of rope required to tie a specific knot in a rope of unit radius. See [CKS2002] for the full definition.
 
 ## Known upper bounds
 Upper bounds are typically found by finding a tight instance of a specific knot using gradient descent (usually a torus knot).

constants/23b.md

@@ -5,7 +5,7 @@
 $C\_{23b} = b\_{o}$ is the largest constant for which one has an inequality
 $$ L \geq b_{o} C $$
 for all knots that admit an [alternating](https://en.wikipedia.org/wiki/Alternating_knot) diagram, where $L$ is the ropelength of a knot (or link) with [crossing number](https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)) $C$.
-The _ropelength_ $L$ is the infimum over all embeddings of the knot (or link) of the ratio of the contour length of the knot to its thickness. The _thickness_ is defined as the radius of the smallest circle that passes through any three points on the knot (where colinear points yield an infinite radius). Colloquially, the ropelength is the least amount of rope required to tie a specific knot in a rope of unit radius. See [CKS2002] for the full definition.
+The _ropelength_ $L$ is the infimum over all embeddings of the knot (or link) of the ratio of the contour length of the knot to its thickness. The _thickness_ is defined as the radius of the smallest circle that passes through any three points on the knot (where collinear points yield an infinite radius). Colloquially, the ropelength is the least amount of rope required to tie a specific knot in a rope of unit radius. See [CKS2002] for the full definition.
 
 ## Known upper bounds