Length of a tight torus knot

To calculate the length of a 'tight' torus knot given the major radius, minor radius, and knot winding ratio, we need to use a specific formula. Unfortunately, the provided search result does not contain the necessary information to answer this query directly[1]. However, I can provide you with the general approach and formula for calculating the length of a torus knot.

The length of a torus knot can be calculated using the following formula:

$$L = 2\pi R \sqrt{p^2 + (q\frac{r}{R})^2}$$

Where:
- L is the length of the torus knot
- R is the major radius of the torus
- r is the minor radius of the torus
- p and q are coprime integers representing the knot winding ratio

In this formula, p represents the number of times the knot winds around the torus in the toroidal direction, and q represents the number of times it winds in the poloidal direction. The ratio p/q is often used to describe the type of torus knot.

For a 'tight' torus knot, the curve is assumed to lie on the surface of the torus without any slack. This means that the formula above would give you the shortest possible length for a knot with the given parameters.

To use this formula:

1. Identify the major radius (R) and minor radius (r) of the torus.
2. Determine the knot winding ratio (p/q) for your specific torus knot.
3. Substitute these values into the formula.
4. Calculate the result to find the length of the torus knot.

It's important to note that this formula assumes an ideal, perfectly tight knot. In practice, real knots may have some additional length due to factors like thickness of the material used to create the knot or slight deviations from the ideal path.

Citations:
[1] https://www.wolframalpha.com/input?input=tight+torus+knot+major+radius+minor+radius