John A. Parker of New York City is said to have found his own quadrature value for the “squaring of the circle” problem. Parker’s value was 6561 for diameter and 20612 for circumference. (Background: “Squaring The Circle”, Ersjdamoo’s Blog entry of August 10, 2013)
Relations between the circle and the square are “among the fundamental principles necessary to be considered in mathematical science, particularly in respect to astronomy and navigation…”, wrote Parker in his book, Quadrature Of The Circle. (New York: John Wiley & Son, 1874)
Geometrical truth rests on the properties of straight lines and the properties of curved lines. “To find the quadrature of the circle, is simply to determine the relative value of straight lines and curved lines…” (Parker, op. cit.)
Parker claims to have found what he believes is “the true and exact ratio” of circumference to diameter of “one circle.” Furthermore, that this true and exact ratio is employed by nature in every circle. These key numbers are “20612 parts of circumference to 6561 parts of diameter.”
Parker adapts the term “circumference” to include, besides the circle, also the perimeters of squares, triangles, polygons, etc. “Diameter” is similarly applied to shapes besides the circle, and usually means twice the least radius.
Parker admits it is impossible to square the circle by the application of straight lines. “But this does not prove that the circle is incapable of being squared, or that no equality exists between the circle and the square…”
By Parker’s ratio of circumference to diameter, which he says is the true ratio, “the expression of numbers by which circumference and diameter are made equal, is 20612 parts of circumference to 6561 parts of diameter…” Parker seems to be saying that “Pi” is wrong! His ratio of 20612 / 6561 (3.141594269) is the true ratio, not the heretofore traditional Pi of 3.141592654!