Five More Universal Constants

   Welcome to the Five More Universal Constants section of our Measuring Pi Squaring Phi web site.

   Besides proving the true value of Pi (both geometrically and physical measurement), after squaring the circumference of a circle to the perimeter of a square, we have discovered at least five more universal math constants that show a universal constant relationship between Pi and Phi.  If we describe our newly discovered true Pi as Pi1 = 4 / sqrt Phi = 3.144605511…, we could name these additional constants Pi2, Pi3, Pi4, Pi5, and Pi6 (π2, π3, π4, π5, and π6).  Their respective values are:

  1. Pi1 = 4 / sqrt Phi          = 3.144605511…   (circumf of circle / diam of circle)
  2. Pi2 = sqrt Phi                = 1.272019650…   (diam of squared circle / side of squared square)
  3. Pi3 = sqrt Phi / sqrt 2  = 0.899453721…   (diam of squared circle / diagonal of squared square)
  4. Pi4 = sqrt Phi                 = 1.272019650…   (area of squared circle / area of squared square)
  5. Pi5 = 2/3 sqrt Phi          = 0.8480131…       (surface area of squared circle / surface area of squared square)
  6. Pi6 = 2/3 Phi                  = 1.078689326…   (volume of squared circle / volume of squared square)

The following Excel video spreadsheet shows the details of the above relationships between the attributes (radius, diameter, circumference, area, etc.) of each of the circles and their respective squares (side, diagonal, perimeter, area, etc.) that were “squared” (circumference to perimeter).