Squaring the circle is a problem proposed by ancient geometers, and has a symbolic meaning. It means constructing a square with the same area as a given circle with square and compass. The exact squaring of the circle is impossible because π = 3,141592653… is a transcendental irrational number, which means that the figure cannot be constructed with a compass and a ruler (pi cannot be expressed in finite whole numbers by which we measure squares). Only approximations can be made.
The ancient Egyptians used whole numbers to approximate the squaring of the circle (like the example above). A circle with a diameter of nine unities has almost the same surface as a square with a side of eight unities.
The squaring of the circle represents an attempt to unite two opposites which can’t be united: spirit and matter, sky and earth, body and soul (in the sense of conscience). Both circle and square represent a closed cycle. The square, symbol of the quaternity, is a representation of the four elements, the materialization of the circle so to speak. Both circle and square express harmony, but on a different level. They’re also a sort of prison, a closed circuit. That’s the real meaning of the cross (which is another representation of the quaternity): man at the center of the material world.
Figure 1
Figure 1 shows the squaring of the circle following an old masonic method. The circle, the triangle and the square have practically the same surface. The same idea can be found in some portals of medieval churches, like Notre-Dame-du-Port, Clermont-Ferrand, France, and Saint-Gilles-du-Gard, France (below).
The floor plan of St Paul’s cathedral in London consists of a squared circle at the center and seven concentric circles:
Congratulations for this research and knowledge .. Thank you Marc
ReplyDeleteThis colorful design appears to identify the significant geometric lines in a squared circle: http://aitnaru.org/psymmetry.html
ReplyDeleteThe design highlights the fact that only 8 points on a circle (even fewer with simple geometry) must be known to square a circle. The red right triangle alludes to the trigonometry that proves this concept.
The Golden pi-formula
ReplyDeleteA ruler of 2.5 Old Danish feet found in 1875 by P.V.Glob in the Bronze age mound Borum-Eshøj from 1350 BC was 78.55 cm. It gives a foot of 31.42 cm. The Danish feet of 31.38535 cm (was in 1907 replaced by the metre) but had only changed 1 per thousand in 3400 years! A foot is 12 inches, so an inch on Eshøj stick is 2.6183 cm.
Note that 31.42 is close to 10 x pi and 2.618 is the golden ratio in the second (phi^2) so as 12 x 2.6183 = 31.42 the formula for pi = 1.2 x phi^2 is stored in the old ruler. The formula gives a pi-value of 3.14164 .. Where the correct pi is 3.14159 ..
In other words, the correspondence between pi, phi and the old Danish units of measurement more or less imply that the constructors knew the metre.
I have shown that a unique geometric construction of this formula generate the shape of the palisade i Jelling (Royal Danish world heritage from the Viking Age 958 AC) and predicts that the mound-distance is 137.5 meters. It is described in my article: "The Arcane Eshøj Ell" in Acta Archaeologica vol 83 (20dec 2012) pp 275-286.
Re: http://aitnaru.org/cameopi.html
ReplyDeleteSymbolic evidence that this green scalene triangle squares the circle?
The Pi symbol appears in the center of this latest design!
The two vertical yellow lines each represent half the square root of Pi*.
Each vertical line forms a right angle with a portion of the horizontal yellow line, giving 2 sets of perpendicular lines with 4 lines representing half the square root of Pi.
* Large golden circle's diameter = 2000000 units.
Vertical yellow lines = half the square root of Pi x 1000000.
Still running in squared circles ...
ReplyDelete“Morbus cyclometricus” may eventually translate to “sanitas cyclometricus” if this new perspective of Pi confirms the value of all human effort to “square the circle”: http://www.aitnaru.org/images/Pi_Corral.pdf (file attached to web page)
This unique scalene triangle, inscribed within a circle, should at least help promote a new generation of ideas for food and festivities for Pi Day ... and new ideas for squaring the circle!
By the next Pi Day celebration, the new slogan might be: “Some Pi are square, some are round, but no Pi is triangular!”
I knew that squaring the circle was impossible, but I didn't know that it would be so difficult.
ReplyDeleteThis unique isosceles trapezoid (two equally unique overlapping scalene triangles) has remained consistent during many more months of research: http://aitnaru.org/threepoints.html
The abstract dark blue Pi symbol? Two overlapping isosceles right triangles (hypotenuses not shown); length of each side equals half of the square root of Pi (diameter of squared circle equals 2).