the binomial constructor
binomial constructor equationbox symbol equation

The binomial constructor encodes the general two-part structure of the complement of the hyperbolic figure eight knot, and its coherent external transform space—the volume of the 24-dimensional unit hypersphere. Where A_external = the external geometric action of each transform, B_external = the external boundaries that action takes place on—expressed in Planck constants, A_internal= the internal geometric action, and box symbol = the hyperbolic inversion boundary—constructed from the normalized Planck length = l_p, the normalized Planck mass = m_p, and the square of the normalized Planck charge = q_p.

Every constant of Nature uses one of the hyperbolic partition equation's simple ( one–dimensional ) transforms—defining a symmetric transform coherently maintained by this bi–part structure. Those transforms include: two polar expressions ( expressed in powers of zhe_theta and zhe_r ), and 6 Cartesian expressions: the 2–part products, the 3–part products, the 2–part sums, the 3–part sums, the 2–part quadrances, and the 3–part quadrances.

2-part products 1 and 2
3-part products 1
2-part sums plus
3-part sums plus
2-part quadrances plus 1
3-part quadrances plus 1
2-part products 3 and 4
3-part products 2
2-part sums minus
3-part sums minus 1
2-part quadrances minus 1
3-part quadrances minus 1
2-part sums plus 3
3-part sums plus 2
2-part quadrances plus 3
3-part quadrances plus 2
2-part sums minus 3
2-part sums minus 2
2-part quadrances minus 3
3-part quadrances minus 2

Explore the Constants of Nature page to see which transform each constant uses.