Timing

A batter swings the bat hoping to be in the right place at the right time to hit the ball. The knot discussed last week forms a path. The paths of adjacent knots cross. The challenge of timing remains.

Consider distance around the outside of the donut and distance around the center of the donut. These are the poloidal and toroidal distances. These "distances" form the sides of a right triangle. An integral hypotenuse produces synchronized timing.

Last week we discussed the knot found in the electron chain segment. The poloidal and toroidal "distances" of 74445 (or 3*5*7*709) and 76172 (or, 4*137*139) produce an hypotenuse equal to 106509.302922327... .

We would like a rational value for the hypotenuse, but must settle for an approximation. A seeming large number of rational candidates exist. Quite surprisingly, the best candidate emerged almost effortlessly.

The numerator of the rational approximation consists of the prime factors: 7^2, 347, and 253,153. The denominator consists of the prime factors: 3, 19, and 709. The importance of this number will be a future thought.