To “square the circle” implies an ancient problem in the construction of geometric diagrams. In ancient times, basic geometric principles were explored through, for example, the physical manipulation of lengths of strings. The diameter of a circle can be measured by wrapping a cord around a post; the right angle of a square constructs a 3:4:5 triangle, which can be evaluated with a string of 12 equally-spaced knots. Constructing squares and circles of equal perimeter or area using only a compass and rule, however, represents and enduring problem.
Many approximate solutions have been found for various such problems: ancient architects knew that an arch could be made to withstand gravity by measuring the curve of a cord held between two points and then inverting it, but to communicate these measurements to masons who weren’t initiated into the secrets of higher mathematics, simple approximations like 22:7 were used for values like pi.
The ratio 3:11 represents the relative size of Moon and Earth to about 99.9% accuracy. Were the Moon drawn down to the Earth and a giant circle made to encompass the two bodies, this length would equal the perimeter of a square made around the Earth.
The above dimensions were known to the Ancients: the Forum at the Roman city Pompeii, for example, was fashioned in the ratio 3:11.
Using the ancient approximations, the Earth-Moon relationship is embedded in the inner geometry of the mile as follows:
Radius of the Moon = 1,080 miles = 3 x 360
Diameter of the Moon = 2,160 miles = 6 x 360 = 18 x 1 x 2 x 3 x 4 x 5
Radius of the Earth = 3,960 miles = 11 x 360 = 33 x 1 x 2 x 3 x 4 x 5
Radius of the Earth + Radius of the Moon = 5,040 miles = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10
Diameter of the Earth = 7,920 miles = 8 x 9 x 10 x 11
5,280 feet in a mile = ( 10 x 11 x 12 x 13 ) – ( 9 x 10 x 11 x 12 )
In the diagram above, the dotted lines represent identical lengths of string.
To “square the circle” implies an ancient problem in the construction of geometric diagrams. In ancient times, basic geometric principles were explored through, for example, the physical manipulation of lengths of strings. The diameter of a circle can be measured by wrapping a cord around a post; the right angle of a square constructs a 3:4:5 triangle, which can be evaluated with a string of 12 equally-spaced knots. Constructing squares and circles of equal perimeter or area using only a compass and rule, however, represents and enduring problem.
Many approximate solutions have been found for various such problems: ancient architects knew that an arch could be made to withstand gravity by measuring the curve of a cord held between two points and then inverting it, but to communicate these measurements to masons who weren’t initiated into the secrets of higher mathematics, simple approximations like 22:7 were used for values like pi.
The ratio 3:11 represents the relative size of Moon and Earth to about 99.9% accuracy. Were the Moon drawn down to the Earth and a giant circle made to encompass the two bodies, this length would equal the perimeter of a square made around the Earth.
The above dimensions were known to the Ancients: the Forum at the Roman city Pompeii, for example, was fashioned in the ratio 3:11.
Using the ancient approximations, the Earth-Moon relationship is embedded in the inner geometry of the mile as follows:
Radius of the Moon = 1,080 miles = 3 x 360
Diameter of the Moon = 2,160 miles = 6 x 360 = 18 x 1 x 2 x 3 x 4 x 5
Radius of the Earth = 3,960 miles = 11 x 360 = 33 x 1 x 2 x 3 x 4 x 5
Radius of the Earth + Radius of the Moon = 5,040 miles = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10
Diameter of the Earth = 7,920 miles = 8 x 9 x 10 x 11
5,280 feet in a mile = ( 10 x 11 x 12 x 13 ) – ( 9 x 10 x 11 x 12 )