Squaring the circle is the age old problem of constructing a square with the same area(or perimeter) as the circle. Greek mathematicians attempted to solve this ancient riddle using a ruler and compass only. Due to the transcendental nature of π we can only approximate this geometry. Earth, Moon, the Great Pyramid, and Stonehenge all encode this great philosophical quandary.

Stonehenge encodes the squared circle through its bluestones, named so because when it rains they turn blue. If we draw a square around this circle of stones it will have the same perimeter as the sarsen ring of stones on the very outside. The ancients preserved esoteric gnosis in their sacred buildings as a way to ensure that the information would never be lost or occulted by the greed of mortal men.

*“ A tradition which has been credited by many learned men over the centuries is that the Ancients encoded their knowledge of the world in the dimensions of their sacred monuments.”*

*– John Michell*

The Great Pyramid’s height is in relationship to its base sides as a circle’s radius is to its circumference, and thus it ‘squares the circle’. Put another way, the perimeter of the base equals the circumference of a circle whose radius is equal to the height of the pyramid. This is only achieved due to the slope angle being 51 degrees and 51 minutes. (or 51.84 degrees since there are 60 arc minutes in 1 degree) I noticed that in the six days it supposedly took to create heaven and earth, there are exactly 518,400 seconds, which resonates with the decad (the decimal system), and the slope angle. And just recently my friend Dayne Herndon pointed out the fact that 5184 also resonates with the canonical value for the Precession of the Equinoxes of 25,920 years. As 25,920 x 2 = 51,840

What else could the Great Pyramid possibly encode? How about the Prime Meridian as suggested by Carl Munck? This is a future post but for now check out The Code.

How about Pi and Tau?

*“Squaring the circle” is the alchemical process of transferring an airy concept from the mental plane to the physical dimension so that objective conception and birth become a demonstrative reality. – Dr. John Munford*

The Earth-Moon relationship and the Great Pyramid of Giza both encode the secret to the mystery. Both of these correlations are well over 99.9% accurate. This is what Leonardo Da Vinci’s “Vitruvian Man” is all about.

Based on measurements of Leonardo da Vinci’s Vitruvian Man we can see that the sizes of the square and circle aren’t quite the correct size to actually square the area of the circle. (in red) But we can also square the circle with equal perimeters (in blue). Vitruvius’ square (in yellow) is almost exactly halfway between ‘squaring the circle’ with equal area, and ‘squaring the circle’ with equal perimeters. It’s slightly closer to the latter.

The square that Da Vinci used is a consolidation of two distinct solutions to ‘squaring the circle’, or obtaining the unobtainable. Did Leonardo encode the solution of this ancient philosophical mystery by suggesting that man is the mean between two transcendental impossibilities?

*“The workings of the human body are an analogy of the workings of our universe” – Leonardo da Vinci*

**Squaring the Circle Methods**

**Equal Areas:**

Square with area of 4 has width of 2

Circle with area of 4 has width of 2.256758..

9/8 = 1.125

2.256 / 2 = 1.128379

1.125 / 1.128379 = .9970

A 9:8 ratio squares the area of the circle to 99.70% accuracy

In music theory, a 9 to 8 ratio is the whole step, otherwise known as the whole tone, or major second.

**Equal Perimeters:**

Square with perimeter of 4 has width of 1

Circle with circumference of 4 has width of 1.2732396..

Interestingly, our Moon takes 27.32166 days to make 1 revolution about Earth.

(A 99.998% accurate correlation according to NASA)

14/11 = 1.27272727…

1.2732396 / 1 = 1.2732396

1.272727 / 1.2732396 = .9996

A 14:11 ratio squares the circle with equal perimeters to 99.96% accuracy

Earth and Moon solve the first riddle to a very high degree of accuracy. Depending on which measures you use, equatorial, polar and mean diameters, it is at least 99.9% accurate.

*Square the Circle/ Earth-Moon Correlations:*

*(NASA 2014 measurements in miles)*

*Earth-Moon radii / Earth’s radius = Square the Circle with equal perimeters*

*Equatorial radii:*

*5043.175 / 3963.17 = 1.27251039*

*1.27251039 / 1.2732396 = 99.943% accuracy*

*Polar radii:*

*5028.63 / 3949.93 = 1.27309*

*1.27309 / 1.2732396 is 99.988% accuracy*

*Mean radii:*

*5038.7 / 3958.75 = 1.27280 *

*99.965% accuracy*

As you can see you don’t have to cherry pick measurements to achieve a very high degree of accuracy. Earth is a living and breathing organism. Its measurements change over time so this could never be 100% accurate.

“The circle is a symbol of spirit, of heaven, of the unmanifest, the immeasurable and the infinite, while the square is the symbol of the material, the Earth, the measurable and the finite,” …the symbolic essence of the problem was the reconciliation of seemingly opposing principles, and the resolution of dualities – “a sacred, cosmological act.” -Daniel Pinchbeck

The Earth and Moon are the perfect size to solve the riddle. This only works because the Moon is huge. It’s larger than any other of the solar system in proportion to its planet. Some say we have a double planet system.

*“The squaring of the circle is a stage on the way to the unconscious, a point of transition leading to a goal lying as yet unformulated beyond it. It is one of those paths to the centre.” – Carl G. Jung*

Bert Janssen found the squaring of the circle encoded into certain crop circles. His website is definitely worth checking out.

The alchemical marriage between Earth and Moon reveal profound geometrical symbols we use to understand our reality. These relationships are a hint into the mystery of our existence. Perhaps we are more than mere coincidence and product of time and chance. The Divine Universal Architect may have hid these clues in plain sight for all to see and cherish, however it is only the few who possess such esoteric knowledge that have the eyes to see these Secrets in Plain Sight.

*An exercise in contemplative geometry from Robert Lawlor’s Sacred Geometry, 1982.*

*“There are a number of diagrams in the literature of Sacred Geometry all related to the single idea known as ‘Squaring of the Circle’. This is a practice which seeks, with only the usual compass and straight-edge, to construct a square which is virtually equal in perimeter to the circumference of a given circle, or which is virtually equal in area to the area of a given circle. Because the circle is an incommensurable figure based on π, it is impossible to draw a square more than approximately equal to it. Nevertheless the Squaring of the Circle is of great importance to the geometer-cosmologist because for him the circle represents pure, unmanifest spirit-space, while the square represents the manifest and comprehensible world. When a near equality is drawn between the circle and the square, the infinite is able to express its dimensions or qualities through the finite” (p74).*

*The derivation begins with an initial circle (within the square) of radius unity. Along its horizontal diameter are drawn two tangent circles, each with radius one half. Observe that the total circumference of the smaller circles equals the circumference of the initial circle, but the total area of the smaller circles is one half that of the initial circle: “One has become Two” (p73), an image of the primary duality, of yin-yang.*

*Next are drawn two arcs from the ends of the initial circle’s vertical diameter with radius tangent to the far sides of the smaller circles. This radius is φ, the golden ratio, dividing the vertical radius of the initial circle into the golden section of lengths 1/φ and 1/φ2. The two arcs meet to create a vesica that encloses the primary duality — the mouth of Ra, the Word, the vibrating string.*

*Around the initial circle is drawn a tangent square, with side 2, perimeter 8; and, finally, a large circle is drawn with diameter equal to the width of the vesica, 2√φ, giving a circumference of 2π√φ = 7.993, approximately equal to 8. The circle is squared.*

Squaring the circle with Earth and Moon

Unknown Squared Circle: More than meets the Eye

Panagiotis Stefanides says

Interesting:

Ref:

http://www.stefanides.gr/pdf/D=5,083FOUR_1.pdf

http://www.stefanides.gr/Html/theo_circle.htm

http://www.stefanides.gr/Html/QuadCirc.htm

http://www.stefanides.gr/Html/piquad.htm

[email protected] says

Thx Panagiotis, This looks very interesting indeed. 🙂

Robert Aguirre says

Epogdoon!!!

Liddz says

Squaring the circle with the Great pyramid and Earth and moon.

From: Liddz.

The measurements of the Great pyramid can be used to create a circle with a circumference that is equal in measure to the perimeter of a square.

Some researchers claim that the width of the Great pyramid’s square base measures 756 feet while the height of the Great Pyramid measures 481.090909090909091. Other researchers claim that the width of the Great pyramid’s square base measures 759 feet while the height of the Great Pyramid measures 483 feet. Other researchers have claimed that the width of the square base for the Great Egyptian Pyramid has a measure of 755.92 feet while the height of the Great Egyptian Pyramid of Giza has a measure of 481.04 feet.

In cubits the width of the Egyptian Great pyramid’s square base measures 440 cubits meanwhile the height of the great Egyptian pyramid measures 280 cubits.

“Golden ratio claimed to be found with in the measurements of the largest of the 3 Pyramids of Egypt’s Giza Plateau”.

1st version of measurements for the Great Pyramid of Giza”:

One Egyptian cubit is 1.718181818181818 feet, when the width of a Pyramid’s square base is measured to be 756 feet that is 440 cubits and the height of the pyramid is measured to be 481.09090909090909 feet that is 280 cubits. 1.718181818181818 is close to the golden ratio of 1.618181818181818 because if 0.1 is added to 1.618181818181818 the result is 1.718181818181818. 1.718 is also close to 2.718. 2.718 is another mathematical constant known as the E number. Half the width of the Great Egyptian Giza Pyramid’s square base is 220 cubits and 378 feet. The slant height of the largest of the 3 Egyptian Pyramids at Giza is 611.67272727272727 feet that is 356 cubits. 356 cubits divided by 220 cubits results in the Golden ratio approximation of 1.618181818181818818181818181818.

“Alternative measurements for the Great Pyramid of Giza”:

2nd version of measurements for the Great Pyramid of Giza:

One Egyptian Pyramid cubit is 1.725 feet, when the width of a Pyramid’s square base is measured to be 759 feet that is 440 cubits and the height of the pyramid is measured to be 483 feet that is 280 cubits.

1.725 is close to the second approximation of the Golden ratio in the Fibonacci series of numbers when 13 is divided by 8. If the Golden ratio is approximated to 1.625 then that approximation for the Golden ratio is close to 1.725. If 0.1 is added to 1.625 the result is 1.725. Half the width of the Great Egyptian Giza Pyramid’s square base is 220 cubits and 379.5 feet. The slant height of the largest of the 3 Egyptian Pyramids at Giza is 614.1 feet that is 356 cubits. 356 cubits divided by 220 cubits results in the Golden ratio approximation of 1.618181818181818818181818181818.

3rd version of measurements for the Great Pyramid of Giza:

One Egyptian Pyramid cubit is 1.718 feet, when the width of a Pyramid’s square base is measured to be 755.92 feet that is 440 cubits and the height of the pyramid is measured to be 481.04 feet that is 280 cubits. 1.718 is close to the golden ratio of 1.618 because if 0.1 is added to 1.618 the result is 1.718. Remember again that 1.718 is also close to 2.718. 2.718 is another mathematical constant known as the E number. Half the width of the Great Egyptian Giza Pyramid’s square base is 220 cubits and 377.96 feet. The slant height of the largest of the 3 Egyptian Pyramids at Giza is 611.608 feet that is 356 cubits. 356 cubits divided by 220 cubits results in the Golden ratio approximation of 1.618181818181818818181818181818.

If Pi is approximated to 3.1416 and has 2.618 subtracted from it then the result is 0.5236 and 52.36 centimeters is an approximation of the cubit that is used to build the Great Pyramid of Giza. 52.35 centimeters is probably a better approximation for the cubit used to build the Great Pyramid of Giza.

A meter is 100 centimeters and also equal to 39.37 inches. A millimeter is one thousandth of a meter.

1 inch is 2.54 centimeters .12 inches is 1 foot. 5280 feet is 1 mile. 6 miles is 31680 feet.

If Pi is approximated to 3.1415 and has 2.618 subtracted from it then the result is 0.5235 and 0.5235 is an approximation for the Pyramid cubit in meters.

Pi approximated to 3.1415 divided by 6 = 0.5235.

If a circle is created with a radius equal to the full height of the Egyptian Great pyramid then the circumference of that circle will be 1760 cubits and this measure is equal to the perimeter of the Great Egyptian Pyramid’s square base because the width of the Great Egyptian Pyramid’s square base measures 440 cubits according to 1 of the 13 ancient versions of Pi and that ancient version of Pi is the ancient Egyptian version of Pi 22 divided by 7 = 3.142857142857143. The Great Pyramid also contains an isosceles triangle that is made from 2 Kepler scalene triangles. The longest length of a Kepler triangle divided by the shortest length of a Kepler triangle is the Golden ratio of 1.618. If the apothem of the Great Pyramid is divided by half the width of the Great Pyramid’s square base then again the result is the Golden ratio of 1.618. The second shortest length of a Kepler triangle divided by the shortest length of a Kepler triangle is the square root of the Golden ratio and reads 1.27. If the full height of the Great pyramid is divided by half the width of the Great Pyramid’s square base then the result is the square root of the Golden ratio and again that reads 1.27. If the width of the Great pyramid is divided by the height of the Great pyramid the result is half of Pi = 1.57. If half of the perimeter of the Great Pyramid’s square base is divided by the height of the Great pyramid then the result will be 1 of the 13 ancient approximations of Pi = 3.14. The ratio of the width of the great pyramid’s square base divided by the height of the Great Pyramid is 11 divided by 7. The width of the great pyramid’s square base contains 11 equal units of measure while the height of the great Pyramid measures 7 equal units of measure. If half of the Great Pyramid’s square base is subtracted from the full height of the Great pyramid the remaining measure will represent the size of our Earth’s moon when compared to the size of our Earth.

The total surface area of a Pyramid with 11 equal units of measure for the width of the square base and 7 equal units of measure for the height of the Pyramid is 316.8 equal square units of measure. The surface area of a Pyramid with a square base is derived by multiplying half the perimeter of the Pyramid’s square base by the slant height of the Pyramid and then adding the result to the area of square units from the square base of the Pyramid.

(22 is half of this Pyramid’s perimeter of square base)

(8.9 is the measure for the slant height of this Pyramid)

(121 is the number of square equal units in the area of this Pyramid’s square base). “22 x 8.9 = 195.8 + 121 = 316.8.

The surface area of this Pyramid is 316.8 equal square units of measure and the area of this Pyramid’s square base is 121 equal square units of measure. If the surface area of this Pyramid 316.8 equal square units of measure is divided by the area of the square base that’s 121 equal square units of measure the result will is the Golden ratio squared: 2.618181818181818. Also if the surface area of this Pyramid 316.8 equal units of measure is divided into the Golden ratio the larger segment of the division is 195.8 the result of half of this Pyramid’s square perimeter multiplied by the slant height of this Pyramid 8.9, while the smaller segment of the division is the area of this Pyramid’s square base 121 equal square units of measure. 195.8 divided by 121 = 1.618181818181818. 195.8 + 121 = 316.8. Half of this Pyramid’s square base perimeter multiplied by the central slant of this pyramid divided by the area of the square base of this Pyramid = 1.618181818181818. The volume of this Pyramid is 282.333 equal units of measure. The longest edge lengths for the 4 isosceles triangles that make up this Pyramid is 10.464 equal units of measure. The angle for the central slant that is located in the middle of any of the 4 triangular faces of this pyramid is 51.84 degrees. 51.84 degrees is the slant angle of the pyramid with a square base width of 11 equal units of measure while the height of this Pyramid has 7 equal units of measure. If 51.84 is multiplied by 5 equal times the result is 259.2. 259.2 with no decimal points is 25920 the number of years for the Sun to travel around the Zodiac. 25920 divided by 12 is 2160 the numbers of years in an age and also the sum of all the angles of a Cube. 41.98 degrees is the edge angle for a Pyramid with a height of 7 equal units of measure while the Pyramid’s square base has a width of 11 equal units of measure.

Remember again that the ratio of the width of the Great Egyptian Pyramid’s square base divided by the height of the great Egyptian Pyramid is 11 divided by 7. 11 divided by 7 = half of Pi = 1.57.

11 x 40 = 440. The width of the Great Egyptian Pyramid’s base in cubits is 440.

7 x 40 = 280. The height of the Great Egyptian Pyramid in cubits is 280.

The width of the square base of the Great Egyptian Pyramid is 440 equal Egyptian cubits. Half of the perimeter for the great Egyptian Pyramid’s square base is equal 880 cubits. The slant height of the Great Egyptian Pyramid of Giza is 356 cubits.

The width of the square base of the Great Egyptian Pyramid is 440 equal Egyptian cubits. Half of the perimeter for the great Egyptian Pyramid’s square base is equal 880 cubits. The slant height of the Great Egyptian Pyramid of Giza is 356 cubits.

So the area of the square base of the Great Pyramid of Giza is 193600 square Egyptian cubits of measure.

Half of the perimeter of the square base for the Great Egyptian Pyramid multiplied by 356 cubits the apothem of the Great Egyptian Pyramid is 313280 equal cubits of measure.

So the total surface area of the Great Egyptian pyramid is 506880 square cubits of equal measure.

The surface area of the Great Egyptian Pyramid is 506880 equal square cubit units of measure and the area of the Great Egyptian Pyramid’s square base is 193600 equal square cubit units of measure. If the surface area of the Great Egyptian Pyramid 506880 equal square cubit units of measure is divided by the area of the square base that’s 193600 equal square cubit units of measure the result will is the Golden ratio squared: 2.618181818181818. Also if the surface area of the Great Egyptian Pyramid 506880 equal cubit units of measure is divided into the Golden ratio the larger segment of the division is 313280 cubit units of measure the result of half of this Pyramid’s square perimeter multiplied by the slant height of the Great Egyptian Pyramid 356 equal cubit units of measure, while the smaller segment of the division is the area of the Great Egyptian Pyramid’s square base 193600 equal square cubit units of measure. 313280 divided by 193600 = 1.618181818181818. 313280 + 193600 = 506880. Half of the Great Egyptian Pyramid’s square base perimeter multiplied by the central slant of the Great pyramid of Egypt divided by the area of the square base of the Egyptian Great Pyramid = 1.618181818181818.

The volume of the Great pyramid of Giza is 18068333.333 cubit units of measure. The longest edge lengths of the 4 isosceles triangles that make up the Great Pyramid of Giza is 418 cubit units of measure. The angle for the central slant that is located in the middle of any of the 4 triangular faces of the Great Egyptian pyramid of Giza is 51.84 degrees. 51.84 degrees is the slant angle of the Great Egyptian pyramid. If 51.84 is multiplied by 5 equal times the result is 259.2. 259.2 with no decimal points is 25920 the number of years for the Sun to travel around the Zodiac. 25920 divided by 12 is 2160 the numbers of years in an age and also the sum of all the angles of a Cube .The edge angle of the Great Pyramid of Giza is 41.98 degrees.

The width of the great Egyptian Giza pyramid’s square base is 440 cubits and 440 multiplied by 18 is 7920.

The height of the Great Egyptian Giza pyramid is 280 cubits. 280 multiplied by 18 = 5040. 7920 divided by 5040 is half of Pi = 1.571428571428571. 1.571428571428571 multiplied by 2 = Pi approximated to 22 divided by 7 = 3.142857142857143. 7920 and 5040 gain these are measurements for the equatorial diameter of the Earth and also the radius of our Earth combined with the radius of our Earth’s moon.

316.8 is an important number because 316.8 is the circumference of a circle with a diameter of 100.8 when modern Pi is approximated to 22 dived by 7 = 3.142857142857143. 316.8 is the perimeter of a square with a width of 79.2. 316.8 feet is also the measure for the circumference of the largest of the circles that make the floor plan of the megalithic stone monument called Stone Henge in the United Kingdom. 79.2 feet is the diameter of the second largest circle that is involved in the design of the megalithic stone monument known as Stone Henge in the United Kingdom. So if a square is created with a width equal to the diameter of the second largest circle of the floor plan of Stone Henge then the perimeter of that square is equal to the circumference of the largest circle according to Pi approximated to: 22 divided by 7 = 3.142857142857143.

If the decimal points are removed from 316.8 then we get 31680 the circumference of a circle with a radius that is equal to both the radiuses of our Earth of 3960 statute miles and our Earth’s moon of 1080 statute miles. 3960 + 1080 = 5040. So if a circle is created with a radius of 5040 statute miles the circumference of that circle is 31680 statute miles according to pi = 22 divided by 7 = 3.142857142857143. 31680 is the perimeter of a square with a width that is equal to the equatorial diameter of our Earth The equatorial diameter of our Earth is 7920 statute miles. If Pi is approximated to 22 divided by 7 = 3.142857142857143 and then divided in half = 1.571428571428571 and then multiplied by the radius of a circle with a measure equal to 5040 statute miles the result is the equatorial diameter of our planet Earth in statute miles 7920. 360 is the natural measure for the circumference of a circle and 360 multiplied by 22 is 7920. Remember that the perimeter of the Great Egyptian Giza Pyramid’s square base has a measure of 1760 cubits and 1760 multiplied by 18 equal times is 31680.

3168 divided by 6 is also 528.528 hertz is also another important number in relation to Solfeggio. 528 is also divisible by 11. 528 divided by 11 is 48. 5280 feet is also equal to statute 1 mile. 528 divided by 168 is Pi = 3.142857142857143 approximated to 22 divided by 7. 440 yards is 1 quarter of a statute mile and 440 cubits is the measure for the width of the square base of the Great Egyptian Pyramid of Giza.1760 yards is also equal to 1 statute mile. Remember again 1760 cubits is the measure for the perimeter of the square base of the Great Egyptian pyramid of Giza.

Again the width for the square base of the Great Egyptian Pyramid of Giza is 756 feet and the diameter of our Earth’s Sun in Royal Egyptian miles is 756000 while the equatorial diameter of our Earth’s moon in Royal Egyptian miles is 1890 because our Earth’s Sun is 400 times larger than our Earth’s moon. The equatorial diameter of our Earth in Royal Egyptian miles is 6930.

Again the equatorial diameter of our Earth is 7920 statute miles. The equatorial circumference of our Earth is 24881.41 statute miles according to Pi approximated to 3.141592171717172. The circumference of our Earth in Nautical miles is 21600. The polar diameter of our Earth is 6912 Egyptian Royal miles. The polar circumference of our Earth is 21714.688 Egyptian royal miles according to Pi approximated to 3.141592592592593. The height of the Great Egyptian Pyramid of Giza including the sockle that the Great Egyptian Pyramid is built upon is 147.1445089 meters and if this measure is multiplied by 864000 then we also get the polar diameter of our Earth in kilometers: 127132855.6896. The equatorial diameter of our Earth in kilometers is 12756.319 according to Pi approximated to 3.141592805887027, meanwhile the equatorial circumference of our Earth in kilometers is 40075.16 according to Pi approximated to 3.141592805887027.

1 inch is 2.54 centimeters. 12 inches is 1 foot.

100 centimeters is 1 meter. 1 meter is 39.37 inches.

A millimeter is one thousandth of a meter.

1 statute mile is 5280 feet.

1 mile is also 1760 yards.

6 miles is also equal to 31680 feet.

The Royal Egyptian mile has 7 equal units of measure while the statute mile has 8 equal units of measure.

(So the statute mile is longer than the Royal Egyptian mile. So if the statute mile is divided by 8 equal units of measure and then the division is multiplied by 7 equal units of measure the result can be the measure for the Royal Egyptian mile.)

1 Rod is equal to 16.5 feet and 32 rods is equal to 1 mile.

1 yard is equal to 3 feet.

1 nautical mile is equal to 20.25 yards.

1 nautical mile is also equal to 1852 meters.