Hello GHMB,
I thought today being PI Day 3/14 would be appropriate to present a novel method of calculating specific Egyptian Royal cubits derived from the ratio differential between a volumetric sphere and cube of equal diameter and the Meter of 39.375 inches. This scale works with particular ranges of Pi ratio to produce the following results. The formula for the volume of the sphere being 4/3 PI R cubed, is well known. Although this process works for any equal diameter Sphere/Cubic ratio, I will utilize the cube of 12 for the following demonstration of how specific PI ratios produce specific ERC units.
PI- 22/7 x radius 6 cubed = 678.8571429 x 4/3 = 905.1428571 / 12 cubed-1728 = .523809523 x Meter-39.375in.= 20.625in. ERC
PI- 864/275 x 6 cubed = 678.327273 x 4/3 = 904.843636 / 1728 = .52363636 x 39.375 = 20.61818 in. ERC
PI- 25/8 x 6 cubed = 675 x 4/3 = 900 / 1728 = .5208333 x 39.375 = 20.5078125 in. ERC
There is a shortcut formula for determining which Pi ratio results in it's relevant ERC unit as follows.
Pi-22/7 x 7 cancels out to 22 x 15/16 ratio = 20.625 ERC etc. This scale only works for the Meter of 39.375in. unit.
To my knowledge and awareness, this geometric correspondence between the volume of cubes and spheres to this specific Metric ratio scale has never been identified previously. Let me know if I am wrong on this issue.
Best regards,
Stephen Dail
I thought today being PI Day 3/14 would be appropriate to present a novel method of calculating specific Egyptian Royal cubits derived from the ratio differential between a volumetric sphere and cube of equal diameter and the Meter of 39.375 inches. This scale works with particular ranges of Pi ratio to produce the following results. The formula for the volume of the sphere being 4/3 PI R cubed, is well known. Although this process works for any equal diameter Sphere/Cubic ratio, I will utilize the cube of 12 for the following demonstration of how specific PI ratios produce specific ERC units.
PI- 22/7 x radius 6 cubed = 678.8571429 x 4/3 = 905.1428571 / 12 cubed-1728 = .523809523 x Meter-39.375in.= 20.625in. ERC
PI- 864/275 x 6 cubed = 678.327273 x 4/3 = 904.843636 / 1728 = .52363636 x 39.375 = 20.61818 in. ERC
PI- 25/8 x 6 cubed = 675 x 4/3 = 900 / 1728 = .5208333 x 39.375 = 20.5078125 in. ERC
There is a shortcut formula for determining which Pi ratio results in it's relevant ERC unit as follows.
Pi-22/7 x 7 cancels out to 22 x 15/16 ratio = 20.625 ERC etc. This scale only works for the Meter of 39.375in. unit.
To my knowledge and awareness, this geometric correspondence between the volume of cubes and spheres to this specific Metric ratio scale has never been identified previously. Let me know if I am wrong on this issue.
Best regards,
Stephen Dail