Enter the number of crossings, number of loops, and number of strands into the calculator to determine the braid capacity. This calculator can also evaluate any of the variables given the others are known.
Braid Capacity Formula
The following formula is used to calculate the braid capacity.
BC = (K + L - 1) / S
Variables:
- BC is the braid capacity (number of strands)
- K is the number of crossings in the knot or link
- L is the number of loops in the knot or link
- S is the number of strands in the braid
To calculate the braid capacity, add the number of crossings in the knot or link to the number of loops in the knot or link, and subtract 1. Then, divide the result by the number of strands in the braid. The quotient gives the braid capacity, which represents the minimum number of strands needed to represent the knot or link as a closed braid.
What is a Braid Capacity?
Braid capacity is a concept in mathematics, specifically in the field of knot theory. It refers to the minimum number of strands needed to represent a knot or a link as a closed braid. A braid is a mathematical representation of interlacing strands, and the braid capacity gives an idea of the complexity of the knot or link. It is a useful tool in the study and classification of knots and links.
How to Calculate Braid Capacity?
The following steps outline how to calculate the Braid Capacity.
- First, determine the number of crossings in the knot or link (K).
- Next, determine the number of loops in the knot or link (L).
- Next, determine the number of strands in the braid (S).
- Next, use the formula BC = (K + L – 1) / S to calculate the Braid Capacity.
- After inserting the values of K, L, and S into the formula, calculate the result.
- Finally, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Number of crossings (K) = 5
Number of loops (L) = 3
Number of strands (S) = 4
