A centuries-old mathematical puzzle, Quadrature of the Circle (also known as “Squaring the Circle”), is thought to indicate the origin of the British system of measurements.
Squaring the circle is “the challenge to construct a square with the same area as a given circle by using only a finite number of steps with compass and straightedge.” (“Squaring the circle”, Wikipedia) But that is only the classical problem’s imposed limitation. Think of a plastic hula hoop (a circle) which you somehow twist and bend into a square: the area of that square would be the same as the previous hula-hoop circle.
It is generally conceded, as of 1882, that the puzzle is impossible to solve because pi (3.141592654…) is “transcendental”, i.e., not the root of any polynomial with rational coefficients. (“Squaring the circle”, Wikipedia)
However, for the purposes of his argument related to the problem of Quadrature of the Circle, J. Ralston Skinner, in 1894, begins with the caveat: the question of value of the quadrature, as to whether it is the expression of exactitude of relation, does not arise. This “work thus is relieved of any necessity of examination into the question of the possibility of what is called ‘the quadrature,’ or ‘the squaring of the circle’…” (Key To The Hebrew-Egyptian Mystery in the Source of Measures, by J. Ralston Skinner. 1894. Republished by www.kessinger.net)
In other words, for Mr. Skinner’s purposes, he need only approach an exact value. And Skinner comes quite close to this.
One Peter Metius, circa 1585 A.D., reportedly arrived at a solution giving the quadrature value of the circle. Later, in the 19th century, a John A. Parker of New York City is said to have found his own quadrature value.
The value found by Metius was 113 for diameter and 355 for circumference. Parker’s value was 6561 for diameter and 20612 for circumference. Notice how both the Metius and Parker values yield an approximation of Pi when their respective circumferences are divided by their respective diameters.
Parker’s process is a little difficult to grasp. The equilateral triangle and the circle are seen to be “opposite to one another in all the elements of their construction.” “The equilateral triangle is the primary of all shapes in nature formed of straight lines, and of equal sides and angles, and it has the least radius, the least area, and the greatest circumference of any possible shape of equal sides and angles.” (Skinner, op. cit.)
The triangle “has the least number of sides of any possible shape in nature formed in straight lines; and the circle is the ultimatum of nature in extension of the number of sides.” (ibid.)
A triangle has sides equal to 1. Totaling the three sides gives circumference 3.
3 squared multiplied by 3 squared yields 81. Two triangles joined together make a square. The perimeter of this square is 81 multiplied by 4 = 324. The area for this square would be 81 times 81 equals 6561.
“Mr. Parker makes use of an element of measure of the equilateral triangle, by which, as a least unit of measure, to express the measure of the elements of a circle in terms of the numerical value of a square: so that, as a conclusion, a square of 81 to the side, or 6561 in area, shall contain a circle whose area equals 5153; or, rectifying the circumference, a diameter of 6561 shall have a circumference of 5153 x 4 = 20612” (Skinner, op. cit.)
Suppose a cube whose total edges add up to 20612. There being 12 edges, 20612 divided by 12 yields 1717.666667. The one-thousandth part of this equals 1.71766… This number, 1.71766…, as a proportion of the British foot measurement is the ancient, Biblical cubit value.
The 20612 value also corresponds to the British inch measurement: There being 12 inches to the foot, 20612 divided by 12 yields 1717.666667.
A measurement system is discerned to be hidden in the Old Testament. In Hebrew, Jared is construed to be “the mount of descent.” Jared, in Hebrew, consists reportedly of the letters Yodh-Resh-Da’leth, which “is literally, in British, Y-R-D; hence, in Jared, is to be found, literally, our English word yard.” (Skinner, op. cit.)
Similarly, with Enoch, the son of Jared, Skinner (op. cit.) finds it noteworthy that Enoch lived 365 years. 365 is, of course, a measurement of days in the year. Skinner somehow intuits an ancient understanding of the relation between space and time.
(A version of the above first appeared at my Melchizedek Communique web site on December 6, 2009)