Three Square Code Structures Stonehenge. Life often offers us the polarity of opposites. Something stands in opposition to something else.
This tiny number square gives rise to the pillar arrangement at Stonehenge. It was used in countless ways by ancient historic and even prehistoric civilizations. Currently we are entering a new age. It will be marked by peace and plenty. This is also known as a Golden Age. The same arrangement that formed the Palestinian cubit and the Egyptian cubit also structured the pillar arrangement at Stonehenge. Some information I quote from my own internal link below:
Abu Mūsā Jābir ibn Hayyān explains how this number square was divided into various corners and gnomons. I show how the dotted points below were the options that were used for the appropriate Egyptian and Palestinian cubits. It was also used for builiding Stonehenge.
Multiply the 4 corner numbers: 5 x 7 x 1 x 6 = 210. The Palestinian cubit is 2.107 feet.
Multiply the remaining five numbers which are called the gnomon: 8 x 3 x 4 x 9 x 2 = 1728. The larger Egyptian cubit is 1.728 feet.
15th-century European portrait of “Geber”, Codici Ashburnhamiani 1166, Biblioteca Medicea Laurenziana, Florence
Three Square Code Uses Lower Right Corner and its Gnomon for Stonehenge
Numbers in a row are called a sequence. Sequence is also used in music and dance. Stonehenge uses 5,6,7, and 8:
5 x 6 = 30. This numbers inner stone circles.
7 x 8 = 56. This numbers the outer holes.
Plan of the central stone structure. The stones were dressed and fashioned with mortise and tenon joints before 30 were erected as a 108-foot (33 m) diameter circle of standing stones, with a ring of 30 lintel stones resting on top.
For fun, add 5 + 6 + 7 + 8 = 26. Now, let’s look at the two products and one sum we created from consecutive numbers 5,6,7 and 8: They are 30, 56 and 26. Any beginning student of chemistry knows these numbers define the most stable isotope of iron: (1) 30 neutrons. (2) atomic number 56 (3) Finally 56 – 30 = 26. That is the atomic number of iron. Why is this important? Iron is the ash of nuclear fusion on stars. When enough iron is at the star’s core, it explodes. This creates all the heavier elements than iron.
Here’s the big question: Does Stonehenge represent the cosmic stellar process of creation? Was this known in the distant past? Or, is this just another numerical co-incidence?
Mexican Pyramid Squares the Circle. First. What is “square the circle?” Squaring the circle is a problem proposed by ancientgeometers. It is the challenge of constructing a square with the same area as a given circle. You may only use a finite number of steps with compass and straightedge. In 1882, the task was proven to be impossible. This was a consequence of the Lindemann–Weierstrass theorem. But wait a minute. Lindemann and Weierstrass did not consider R. Buckminister Fuller’s theories in conjunction with the Mexican Pyramid of the Sun.
Mexican Pyramid Really Spheres the Circle
So who was R. Buckminster Fuller?
R. BUCKMINSTER FULLER, 1895 – 1983
The Estate of R. Buckminster Fuller:
Hailed as “one of the greatest minds of our times,” R. Buckminster Fuller was renowned for his comprehensive perspective on the world’s problems. For more than five decades, he developed pioneering solutions that reflected his commitment to the potential of innovative design to create technology that does “more with less”. Born in Milton, Massachusetts, on July 12, 1895, Richard Buckminster Fuller belonged to a family noted for producing strong individualists. They were inclined toward activism and public service. Fuller developed an early understanding of nature during family excursions to Bear Island, Maine. He also became familiar with the principles of boat maintenance and construction. Below are a couple of internal links for further information.
Comparing the Mexican Pyramid of the Sun and Fuller’s Formula for Packing of Spheres
Packing of spheres in successive layers falls under a formula. It was discovered by R. Buckminster Fuller. It’s the number of the particular layer being considered, squared x 10 + 2. You can pinpoint how many spheres successivelyen circle a central sphere. Here are the 1st five examples.
For the 1st layer, 1² x 10 + 2 = 12 spheres.
The 2nd layer we have 2² x 10 + 2 = 42.
For the 3rd layer, 3² x 10 + 2 = 92.
The 4th layer is 4² x 10 + 2 = 162.
The 5th layer is 5² x 10 + 2 = 252.
Ancients looked at what things had in common by common numbers. This was regardless of unit of measure used. We can thus equate the packing of the 5th layer of spheres with the measure of the Mexican Sun Pyramid. Also, Plato’s Ideal City, in his Republic, had 2520 rings. Is this line of thought just fun? Perhaps. But also, perhaps there is no such thing as mere co-incidence?
Mayan Egyptian Connection Spans Atlantic Ocean. Who were the Mayans? The Maya developed their first civilization in the Preclassic period. Scholars continue to discuss when this era of Maya civilization began. Discoveries of Maya occupation at Cuello, Belize have been carbon dated to around 2600 BC. The civilization still had great endurance. Look back some 3,000 years. Mayan Tikal was around from 250 to 700 AD. At its height during the Late Classic, the Tikal city polity had expanded to have a population of well over 100,000.
Egyptian Mayan Connection
We have no written evidence of connection between the two cultures and their countries. But, we do have similarity by measurement. Many are too fixated on proof by written record. They forget that numbers and letters once shared the same symbol. This practice of using the same symbol for both is called gematria- a Greek word. Only our modern languages (except Hebrew) have separate symbols for both. In effect, when you made a measurement, you also could imply a (1) A word. (2) A phrase. (3) An entire sentence. (4) Even a larger unit of writing translated into numbers.
Great Court at Tikal
A surviving Mayan great court is at Tikal. It outlines a rectangle. East to West is 400 feet in length. North to South is 250 feet in width. The courtyard is flanked by platforms, large temples and pyramids. The ratio of the length to the width of the Tikal courtyard is 8:5. Note 400/250 = 8/5 = 1.6. Compare this to the Great Pyramid of Egypt. One side of the square base is smaller Egyptian 440 cubits of 1.71818…feet. Its truncated height is 275 of the same sized cubits. 440÷275 = 8/5 = 1.6.
Based on a mark in an interior chamber naming the work gang. and a reference to the fourth dynasty Egyptian Pharaoh Khufu, Egyptologists believe that the pyramid was built around 2560 BC. As stated above, Mayan carbon dating goes back to 2600 B.C. The dimensions of the Mayan courtyard and of the Great Pyramid had the same ratio of 8 to 5. These numbers are part of the Fibonacci series:
Leonardo Bonacci who was born 600 years before Beethoven. The Fibonacci series, named after him. is colored in red. Beethoven used the Fibonacci numbers in composing his fifth symphony. In the internal link underneath, I relate Fibonacci numbers to ancient number squares. I don’t know that Fibonacci ever made the connection?
BEETHOVEN’S DELIBERATE USE OF THE FIBONACCI NUMBERS
Behind Leonardo Bonacci’s back, the highest red number is 55. Each new number is the sum of the preceding two. Number 34 precedes 55. So, let’s continue the series: 34 + 55 = 89. Next, 55 + 89 = 144. Next 89 + 144 = 233 (the length of Beethoven’s opening section). Next 144 + 233 = 377 (which the length of Beethoven’s development section). Beethoven, being the brilliant genius that he was, knew exactly what he was doing. Note in red numbers. Number five is the 1st separated number. It is not consecutive. Almost every composer uses phrases in 4 bars. The genius of Beethoven made the opening phrase 5 bars long on purpose. He knew what he was doing!
The Best Architecture and Music are at Least Based on Tradition
The Egyptian Mayan connection of the 8 to five ratio is found with Beethoven. Of course, in this symphony Beethoven uses many phrases also use 8 bar phrases. When we listen to his 5th symphony it sounds natural. Can you imagine how he must have struggled to make the bar length come out right? Leonard Bernstein says of Beethoven and the 1st movement in The Joy of Music: “he will give away his life just to make sure that one note follows another inevitably.” In conclusion, I think that in addition to an even greater appreciation of Beethoven, we have graphic proof the relationship between music, numbers and architecture in this post: The Mayan Egyptian Connection and even more. This is why music lessons, theory and composition increase aptitude for mathematics.
Glendalough Cathedral 30 Miles South of Dublin. St. Peter and St Pauls’ Cathedral Achonry, is a former cathedral in the Republic of Ireland: It is within the same enclosure as Our Lady’s Church and the Round Tower.
My source for this measure- 110 feet in height – is the book, Riddles in the British Landscape. It has 148 illustrations and 4 maps. The book is written byRichard Muir, p. 183. Publisher is Thames and Hudson, London, 1981.
Glendalough Cathedral has a Tower Built by a Hidden Number Square Code
Masonic symbol is traceable to the basic number square of antiquity. 110 is found here. Feet are assigned to this figure. Why is this number square Masonic? A pattern outlines a Masonic symbol. We have nine numbers. Take the numbers three at the time as follows:
At a slant, 1, 2, 3 gives you the top triangle of the compass.
7, 8, 9 offers the reciprocal bottom triangulated half of the “T” square.
Finally, 4, 5, 6, offers the slanted diagonal. Again these numbers are tilted in the number square. In the Masonic symbol above it occupied by “G”.
So where is the 110 used at the Glendalough Round Tower? It seems like the square only goes up to nine. But, consider the numbers in the following manner: Two at the time by opposite polarities. We now have:
49 + 61 = 110
94 + 16 = 110
95 + 15 = 110
45 + 65 = 110 etc.
Finding the Hidden 110 at the Glendalough Cathedral
For those who care to go thru the trouble and time, 110 can be found in sixteen different ways on this simple number square. The total of all 16 becomes 1,760. Those who know measurement can recognize 1,760 is another number of measurement: There are exactly 1,760 English yards in one mile. Three feet are in the yard. There are 5,280 feet in the mile. Thus, 5,280 ÷ 3 = 1,760.
Why go through all this trouble? This number square once marked a lost Golden Age of Peace and Plenty. This code needs to be reactivated. Why shouldn’t we all have the same today? The tower at Glendalough Cathedral would then become the symbol of good things to come.
Harappan Civilization & Square of Saturn Aspects. Harappa was part of an Indus Valley Civilization . The square of three of Saturn, pictured above, was preserved in ancient cultures worldwide. Ancients connected this square with the planet, Saturn. Both measurement and engineered are derived from this number square. Why? I believe it goes back to a destroyed civilization that predates recorded history. Perhaps it was Atlantis? Plato wrote of thereality of this legend. Generations of survivors made an attempt to preserve their knowledge of Atlantis through this number square. It was once the ideal behind a Golden Age.
Harappan Civilization and its Scope
Harappan civilization coincides with what is Pakistan and northwest India today. It flourished over the fertile flood plain of the Indus River and its vicinity. Religious practices of the Indus valley culture date back to approx. 5500 BCE. The ruins of Mohenjo-daro were designated a UNESCO World Heritage site in 1980.
Harappa and Mohenjo-daro were built on uniform grid-plan blocks. They had town planning and standard streets. Even houses were set out by a code. By 2350 B.C. the two cities were well established. They traded by land and sea with the Summerians.
Harappa’s citadel parallelogram is 645 from east to west. It measures 1380 feet from north to south. On length and width totals 2025 feet. This figure squares forty-five as: 45² = 2025. Look at the 3 x 3 number square. The nine numbers total 45. This is one way the civilization drew on the 3 x 3 number square.
Here’s a second: Just North of the citadel was the state granary. It measured 150 feet from east to west. The North to south width was 75 feet. One length and width totals 225 feet. Look at the 3 x 3 number square. Any row of three numbers totals 15 feet. Thus, 15² = 225.
There are many other parallels which will be the subject of future blogs. The internal link below offers one example of the depth of the 3 x 3 number square.
Two Seven Two – What are these Three Numbers About? They provide a numerical key to lost prehistoric antiquity. Clues of the past have many forms and fashions. Numbers are one of them. A primarily defined number is megalithic yard. It was 2.72 feet. Professor Alexander Thom of Oxford University established this accepted measure. For background on the subject, study writings of the John Michell. His books have been my companions for over fifty years. Now they are mostly out of print and difficult to acquire.
How Megalithic Measure Comes From the Traditional Arrangement of the 3 x 3 Number Square
A megalithic inch is 0.816 inches. That is a straight read across the bottom- left to right, on the 3 x 3 number square pictured to the right. If you reverse these numbers you have 618. These are the square root numbers of the Golden Section. This was called “phi” by the ancient Greeks- 1.618…. The square root is o.618 feet.
A megalithic yard contains forty megalithic inches. Here’s the arithmetic: 40 x 0.816 = 32.64 inches. Next, 32.64″/12″ = 2.72 feet – or 1 MY. Next:
Add the 8 perimeter numbers. You have 8 + 1 + 6 + 7 + 2 + 9 + 4 + 3 = 40. It is no co-incidence that there are 40 megalithic inches in the megalithic yard.
In summary: Three primary ancient numbers come from the perimeter: (1) The megalithic inch as 816 comes from the bottom three perimeter numbers- left to right. (2) Phi’s square root numbers are from the same bottom perimeter but reversed as right to left (618). (3) The number of megalithic inches in the megalithic yard as 40 from the entire perimeter.
This blog is the tip of the iceberg. Keep reading the posts on DSOworks for more information on the subject as well as on music. It will be forthcoming.
The Painted Hall of the Altamira Cave houses houses a prehistoric gallery. It was discovered in 1868. Since then, the floor has been lowered. This was to study the painted animals on the low ceiling at the time of the discovery. The floor measures 60 feet in length to 30 feet in width. My source for the dimensions is The Atlas of Legendary Places by James Harpur and Jennifer Westwood. The 12″ foot is the intended unit of measure. In fact, this now called “English” foot dates back to an indeterminable distant past. At the British Museum you can find several examples of a cubic inch of gold. It was the standard of weight ancient Greece, Babylon, and Egypt. Here’s how a segmented foot appears on the cube:
A cube has 12 edges.
Twelve edges of one inch per side = 12″= 1 foot.
Measurement Message from the 60 x 30 foot foundation of the Painted Hall
Musicians will most likely notice the 2 to 1 ratio of the floor’s proportions. These same proportions were recommended by Pythagoras. 10.500 years later this Greek philosopher stated the same ratio, after the unison, was most harmonious : The perfect interval of not the same tone (unison) and 1st overtone is the octave. It vibrates in a 2:1 ratio. The designers of the cave exhibition most likely knew this.
Its measure is the product of basic consecutive numbers. 5 x 6 = 30 (the width in feet). 3 x 4 x 5 = 60 (the length in feet). Very important: The formula for the megalithic yard uses all fives and sixes: (5 x 6) ÷ ( 5 + 6) = 2.727272… One megalithic yard is 2.72 feet. The builders of the Great Hall of Altamira knew this.
2nd factor uses 3,4,5 as 3 x 4 x 5 = 60. Numbers 3, 4 and 5 are the basis of the Pythagorean Theorem: 3² x 4² = 5². Also, look at the musical intervals above. These 3,4, and 5 factors figure into these basic harmonious intervals: 4:3 = perfect fourth. 5:4 = the major third.
The diagonal of the 30 x 60 rectangle would be 67 feet. The perimeter around this first half triangle is :30 + 60 + 67 = 157 feet. This figure (157) is one half of the pi figure of 314 made by the triangles made from a diagonal in a rectangle.
Conclusion: The wisdom of a lost civilization is preserved in measure at the Cave of Altamira. Perhaps the builders and artists were the survivors of Atlantis? Measurement message and music message are there. Of course, that the advanced artwork is there is a given!
Common Musical Geometrical Ratios. First, what is a ratio?
Musically, in the diagram above: Every time a higher tone vibrates four times, the lower vibrates three. This creates the sound of a perfect fourth. All the perfect intervals and most harmonious tones of nature can be found at a bowling alley. Also, in the link below I explore the ratios of 6 to 5 found at Atlantis. The size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as:
Plato wrote of Atlantis in Timaeus that numbers 5 and 6 were prominently featured: People were gathered every 5th and 6th years alternately: Thus giving equal honor to odd and even numbers. The gathering of the population was for judgement and atonement.
Measurement Overview by the Traditional 3 x 3 Square. This simplest of number squares has an infinity of hidden number codes. I currently have some 535 posts on DSOworks.com. They are divided primarily between music and this simplest of of ancient number squares. Of course, music and measure overlap. With so many blogs, perspective is difficult. Who has the time to even quickly glance at so much material? The purpose of this blog is simply to provide a measurement overview of the source of measures. A few of the hidden codes are in this internal link.
With Troy, here is the computation. Follow the numbers on the square. 43 + 67 = 110. Backwards 34 + 76 = 110. Total is 220. This works with any opposite columns of two numbers. Megalithic yards were assigned to this number. It defines the length rectangular part of the citadel.
Next, take two numbers at the time again as follows. Watch the number square with three pairs of numbers. 49 + 35 + 81 = 165. Take them in reverse: 94 + 53 + 18 = 165. It works the same way if you work the numbers horizontally.
Both actual measurements of ancient sites and units of measurement came from the 3 x 3 number square. It was once the backbone of a civilization that was destroyed by a cataclysm. A Golden age of peace and plenty once marked this time. Perhaps it is time to return to a Golden Age guided by a simple number square?
Golden Age (disambiguation) – Wikipedia https://en.wikipedia.org/wiki/Golden_Age_(disambiguation)
Golden Age refers to a mythological period of primeval human existence. It was perceived as an ideal state. Human beings were pure and free from suffering. Golden Age may also refer to: Golden age (metaphor), the classical term used as period of perceived greatness.
Measurement Overview – a Partial List
Here a few of the measures mathematically derived from this number square. Review many of them on DSOworks.com. Type in the keyword.
With this in mind look at the common characteristic numbers between these two squares. First, I should mention they are both Fibonacci numbers: Five and eight are part of the series that grow by addition of consecutive numbers: 1,1,2, 3, 5, 8,13,21,34… etc. Hence, their number squares also belong to this same series. These number squares defined key ancient buildings. For this post let’s look some of the common numbers:
On the 5 x 5 any straight row of five numbers totals 65. On the 8 x 8 any two opposite numbers = 65.
On the 5 x 5 any two opposite numbers totals 260. On the 8 x 8 any row totals 260.
The central number on the 5 x 5 is 13. The perimeter around the 8 x 8 is the sum of the numbers 1 through 13 =91 and then multiplied by 10. It duplicates becomes the total of the 910 perimeter around the 8 x 8.
The point is: The designers of Stonehenge and the Great Pyramid both knew and drew on this. More in future posts.