The first mathematician known to have calculated the volume of a sphere in antiquity is Archimedes.
The volume of a sphere encapsulated in the smallest possible cylinder is exactly 2/3 because pi cancels itself out.
In my latest post on Egyptian stadia, I should have mentioned the square of pi cancels itself out precisely, but not exactly, by expressing the radius in relation to the inverse square of pi in the calculation of centripetal acceleration which involves the square of pi.
I know of an ancient Egyptian design which appears to show that the ratio of Archimedes (as displayed on his tombstone) was known as 2/3, potentially an empirical determination, and if there was an approximation of pi such as 22/7 then this cancels itself out.
The same design incorporates the ratio of the volume of a sphere to a cube, and also the volume of a sphere to the volume of a pyramid.
It is a coincidence that a key ratio is Pi/6 and that 6 x length of a cubit is close to Pi, which requires a cubit of precisely, but not exactly, 523.6 mm, as 523.6 mm yields a value of 3.1416, so Newton may have spotted this coincidence for a metric division of the globe even before the invention of the metre.
Mark
Mark
Mark
Edited 1 time(s). Last edit at 09/28/2023 07:08PM by Mark Heaton.