What Fits Where?

By B.L. Freeborn © 2013

circle-octagon only

Circle and Octagon at Newark, Ohio from Squier -Davis drawing.

The most fascinating part of the Newark Earthworks is the Octagon and how very many things are going on inside it. It is mathematically a very busy place. In every respect this structure is a monument to mathematics and geometry.

It begins with a circle meeting an irregular octagon which is almost a distorted square. They join via a path or neck. Opposite this neck on the southwest side of the circle is an area dubbed the observation area due to its height and view it gives through this neck into the octagon. In addition, the circle has a slight ditch surrounding its exterior perimeter.

We have already noted that the square roots of 7.7 and 7.66 are 2.77 and 2.76. The outside distance of the neck is 270 – 274 feet on the north side and 278 to 281 feet on the south side. Assuming some form of creep is present the average of 270 and 281 is about 276 feet. The square of this value is 75900 feet or just shy of 76,000. The distance proposed between the two centers was 1540 or 2 x 770. The square root of 770 is 27.7. It would seem the original intention was to replicate the 770 in the neck as a multiple of its square root.

Hively/Horn, measuring from the middle top of the mounds, determined the neck measures 292 on the north and 296 on the south. The first number we saw as the distance from the Great Circle to Wright Square, 2920′, and twice this value is 584. The number 296 is the gematria value for Earth in Hebrew. The square root of 8.8 is 2.96. This 8.8 or 88 will appear again shortly. One final point, 292 x 296 = 86432 which reminds one of the diameter of the Sun at 864,337 miles and cannot even remotely be a coincidence.

The present distance across the throat at the base of the mounds measures somewhere in the range of 110 to 113.7 feet. Twice 56 is 112. Twice 56.5 is 113. This is a good indication of the original value.

The Observatory Circle at its southwestern extreme has an observation area. According to Hively the area was 170 feet long by 100 feet and 11 feet high in the year 1847. The number 170 is half of 340. Note that 90 degrees minus 34 is 56.

Octagon with 8 moundsThe octagon is composed of 8 long mounds that are separated at the corners. Within the Octagon there are 8 mounds, one at each break in the corners which seem to orbit within the Octagon. Recall that the earth is one of 8 planets orbiting the Sun. Wright Square also had 8 interior mounds. The eight sides plus the 8 inner mounds suggests the number 88. We have seen this number in the distance this Earthwork lies from The Great Serpent, 88.15 miles, and from Miamisburg Mound, 87.7 nautical miles. Each side averages in length from its mid-point 620 feet. Their sum is 4973 feet. This is a midpoint measurement. A measurement of the exterior perimeter is just over 5000 feet. The mounds measure on average 584 feet in length. The 8 interior mounds create an inner octagon. Measurement of the perimeter at the midpoints of the inner mounds measures 4400 feet.

The exterior circumference of 5000 x 88 = 440,000. This number, 440, appeared when the circumference of the earth in miles was divided by 56.5. It repeats in the perimeter of the inner mounds.Squares in the Newark octagon

The diameter of the Observatory Circle, or a fifth mile, is not restricted to the circle. It can be found twice in the Octagon. The diameter of the Great Circle can be found there as well. This is better explained by looking at the image above. Now we see the “circle inscribed in a square” and “the square inscribed in a circle.”  This is the beloved old world exercise explained earlier.

By way of the next image we can see that the two circumscribed squares have rotated with respect to each other. This will become important when we discuss the cosmology implied here.

Squares rotate

Hively and Horn show and Romain also proves that the diameter of a square 1056 feet (their OCD) is used to generate the shape of the octagon. The diameter of a 1056′ square is 1493′. By making an arc of radius 1493′ from each of the four corners as shown the four remaining corners of the octagon can be generated.

This does not create a regular octagon in a stop sign shape. Instead this creates a square with sides that are broken outwards at the midpoints which is also important in the cosmology implied here.

Building the Newark Octagon

The question as to how big this exterior square is remains. We can measure its dimensions as displayed in the earthwork but it needs to be confirmed. The diagonals are 1728 and 1717 feet. The sides measure roughly 1227, 1212, 1210, and 1213. (Hively) Compare this to a calculated diagonal of 1737 and side of 1228 feet. The largest side of the square is the end facing the circle. It is not an optical illusion that end is larger. The average length of each is then 1215 feet. This is 607′ per each of the 8 bars and 8 inner mounds. This might imply the relationship 6 x 88 = 5280 feet to the mile.

Largest Square within Newark OctagonThe two diameters 1728 and 1717 differ from the calculated 1737. The first differs by 9′ and the second by 20′. In other words, the most northern corner is pushed in considerably to create this number. The number 1717 repeats the 17 which appeared in the observation area. The number 1728 is 864 x 2.

Calculating the largest diameter at Newark Octagon All in all, a very pleasing geometric harmony is produced by continuously repeating the same numbers. The next image adds the largest square used and completes the Octagon.All the Squares within Newark Octagon

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References/Footnotes:

  1. Hively, Ray, and Horn, Robert, Geometry and Astronomy in Prehistoric Ohio, “Journal for the History of Astronomy, Archaeoastronomy,” Supplement, Vol. 13, p.S1; also Science History Publications, 1982.      See:   http://articles.adsabs.harvard.edu
  2. Romain, William F., Ph.D., Newark Earthwork Cosmology: This Island Earth, “Hopewell Archeology: The Newsletter of Hopewell Archeology in the Ohio River Valley,” Vol.6 (2), March 2005.   See:  http://www.nps.gov/mwac/hopewell/v6n2/one.htm
  3. Romain, William F., Ph.D., Design and Layout of the Newark Earthwork Complex, “Hopewell Archeology: The Newsletter of Hopewell Archeology in the Ohio River Valley,” Vol.6 (2), March 2005.  See:   http://www.nps.gov/mwac/hopewell/v6n2/two.htm

Isosceles and Other Equals

By B.L. Freeborn © 2013

Because the Great Circle and Octagon are equally placed from Geller Hill an isosceles triangle is formed. (See image from Geller Hill at bottom.) The angle between them is 50 degrees. The line bisecting it is on the azimuth of 52.2  and this is said to be the same azimuth as the line running through the octagon-circle centerline making them parallel.

Isosceles triangles formed at Newark, Ohio Earthworks. Positions as located by satellite image. Drawing by B.L. Freeborn.

Isosceles triangles formed at Newark, Ohio Earthworks. Positions as located by satellite image. Drawing by B.L. Freeborn, 2013.

The line from Geller Hill to the center of the Observatory Circle creates an angle of 56 degrees as shown in the image. The triangle formed from the intersection of these two triangles is another isosceles triangle of degrees 50 80 50. These three numbers remind us of the numbers that compose 58.5 or very nearly the 584 we saw in the East Fork Works. In the same manner the 50 65 65 triangle reminds us of 5.6565.

It can be determined that the azimuth angle from the center of the Great Circle through the center of Wright Square is 43 degrees. Recall that we had 86 on our number list and 2 x 43 equals 86. Using this angle and 1540 foot distance between the centers of the Octagon-Circle and Hively/Horn’s lengths for the translation of the figures across the plane, we can calculate the distance between the center of the Great Circle and Wright Square as 2920 feet. The image below was created by drawing over a satellite image using what appears to be correct centers and the Square’s position shown by Romain in his diagrams. This distance does not appear to be all that important but in fact 2 x 2920 = 5840. The angle that closes the polygon is 93 degrees or virtually the angle 92.8  at which Wright Square is set. The final angle, 79.5, repeats the idea of 79.2.

All of which confirms the numbers on our list. But there is another set of numbers we should see before we move on to looking at the Octagon and its development.

Hively and Horn base their report on the idea that these structures were built on complex ideas of archaeoastronomy which include rise and set points of the sun, moon and other celestial occurrences. But at certain times they are confused by obvious angles that do not meet with their expectations. The angle through the Wright Square at 92.8 degrees is one and the angle which passes through the center of the Great Circle and out through the center of its neck is another. One might say that if these structures were built to verifiable celestial alignments that this is one very important angle that is off. They calculate its measured azimuth at 66.6  an error of .9 degrees or nearly one full degree from what they expect to find. This does not sound like very much but this sort of error adds up quickly in layouts of this magnitude.

Calculated distance between Great Circle and Wright Square. By B.L. Freeborn 2013.

Calculated distance between Great Circle and Wright Square. By B.L. Freeborn 2013.

But we have seen this number, 66, before. We saw it at East Forks. It is repeated no less than eleven times there. It is in the length and width of the square corner of East Fork, the radius of the top circle and it is used 8 times to space the candles. But this is the only time we have seen 66 in this earthwork … or maybe not!

Note that 7 OCD = 7/5ths mile = 1.4 miles = 7392 feet which equals 66 x 56 x 2 feet. This gives us not only 66 but 56.

Additionally, the distance 6 OCD = 6/5ths mile = 1.2 miles = 6336 feet = 56 x 56.5 x 2 feet. This gives both forms of 56. All of which is remarkably equal once again. And if we were in the habit of writing fractions as 5 of 7 or 5 of 6, then 56 appears again. The 57 is another number of importance. It is seen in the conversion from degrees to radians. There are 57.29 degrees to a radian. People who study objects that move in circles, like planets, prefer to calculate with radians.

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References/Footnotes:

  1. Hively, Ray, and Horn, Robert, Geometry and Astronomy in Prehistoric Ohio, “Journal for the History of Astronomy, Archaeoastronomy,” Supplement, Vol. 13, p.S1; also Science History Publications, 1982.      See:   http://articles.adsabs.harvard.edu
  2. Romain, William F., Ph.D., Newark Earthwork Cosmology: This Island Earth, “Hopewell Archeology: The Newsletter of Hopewell Archeology in the Ohio River Valley,” Vol.6 (2), March 2005.   See:  http://www.nps.gov/mwac/hopewell/v6n2/one.htm
  3. Romain, William F., Ph.D., Design and Layout of the Newark Earthwork Complex, “Hopewell Archeology: The Newsletter of Hopewell Archeology in the Ohio River Valley,” Vol.6 (2), March 2005.  See:   http://www.nps.gov/mwac/hopewell/v6n2/two.htm
View from Geller Hill looking north towards Great Circle and Octagon. 2013

View from Geller Hill looking north towards Great Circle and Octagon. 2013

The Remains according to Romain

By B.L. Freeborn © 2013

William Romain asserts in his article Newark Earthwork Cosmology: This Island Earth that Geller Hill is the center of the measurements for the earthworks. The hill is 1150 feet long by 700 feet wide by 35 feet high (later noted as 75 feet high) in the otherwise level terrain of Newark.

Newark Earthworks as laid out from Geller Hill as William Romain suggested. Drawing by B.L. Freeborn.

Newark Earthworks as laid out from Geller Hill as William Romain suggested. The Great Circle and Octagon are equal distance from Geller Hill. The layout forms an isosceles triangle. Drawing by B.L. Freeborn.

Romain determined that the Octagon center is 7392 feet and the Great Circle center is 7498 feet distant from Geller Hill. Using Hively and Horn’s OCD (Observatory Circle Diameter) of 1054 feet, this is 7.01 OCD and 7.11 OCD respectively. Oddly enough, or should we say not so very coincidentally, these distances are 7.000 fifths mile and 7.1 fifth mile. He further suggests that the direction of the midline of the angle formed is at 53.3 degrees which corrects to an azimuth of 52.2 degrees and this further correlates to the azimuth of the Octagon found by Hively and Horn of 52 degrees.

We need only observe that 7 x 52.2 = 365.4 or almost exactly the number of days in a year!

Hively and Horn further discovered that the Observatory Circle is 5.99 OCD’s from the Great Circle (aka Fairground Circle) and the Octagon is 6.02 OCD’s from Wright Square. A bit of math shows this is 6313 and 6345 feet respectively or 5.98 Fifth miles and exactly 6.00 Fifth miles.

The OCD is based on the diameter of the Observatory Circle. Because the circle is slightly distorted there is plenty of room to accommodate the diameter 1054 as well as 1056. The latter number indicates that the circle is the same size as Marshall’s measurement at the High Bank Works. The radius there is 528 feet or one tenth mile.

The distances between the structures at Newark Earthworks creates the number 76. It is repeated further in angles and center distances. Drawing by B.L. Freeborn.

The distances between the structures at Newark Earthworks creates the number 76. It is repeated further in angles and center distances. Drawing by B.L. Freeborn.

Returning to Romain’s findings we note that it is possible to find a spot on Geller Hill that gives an equal value of 7 fifth miles distance to each structure. Hively/Horn demonstrated that the circle-octagon translates across the plane a distance of 6 OCD units to the circle-square. By combining this conclusion with the 7 unit distance we find the number 76 reappears twice. (See diagram.) Indeed, it appears more often than that. Hively/Horn noted that the small circle adjoining the Octagon had a diameter of 1/7th OCD. Expressing the radius as 76 feet seems simpler. Further still, the angle between the lines projected from Geller Hill is 50 degrees which has a sine of .766. Similarly, the angle formed from the lines joining the Hill to the Great Circle and from there to the Observatory Circle is also 50 degrees with sine of .766 as shown. Turning and continuing to the Octagon forms an angle of 77.7 degrees which correlates with the distance between the two centers of 770 feet x 2 or 1540 feet.

There are four things to consider about this 1540′ distance:

  1. Referring back to the Thornborough Henge layout, the path distance between the two southern circles calculated to this same value 2 x 770 = 1540.
  2. Hively and Horn incorrectly state this distance is 2 OCD or 2108 feet.
  3. Romain in his geometric layout states the distance is 1½ OCD or 1581 feet or 2 x 790. A difference of 40 feet.
  4. Because neither the Octagon or Observatory are purely symmetrical there is no true center which allows for differing opinions as to where the center lies contributing to the above differences.

Further and unfortunately, Romain’s geometric reconstruction of the earthworks fails under the scrutiny of protractor and sharp pencil. However, his conclusion that they were precisely laid out is accurate and provable far beyond what he has demonstrated.

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References/Footnotes:

  1. Hively, Ray, and Horn, Robert, Geometry and Astronomy in Prehistoric Ohio, “Journal for the History of Astronomy, Archaeoastronomy,” Supplement, Vol. 13, p.S1; also Science History Publications, 1982.   See:   http://articles.adsabs.harvard.edu
  2. Romain, William F., Ph.D., Newark Earthwork Cosmology: This Island Earth, “Hopewell Archeology: The Newsletter of Hopewell Archeology in the Ohio River Valley,” Vol.6 (2), March 2005.   See:  http://www.nps.gov/mwac/hopewell/v6n2/one.htm
  3. Romain, William F., Ph.D., Design and Layout of the Newark Earthwork Complex, “Hopewell Archeology: The Newsletter of Hopewell Archeology in the Ohio River Valley,” Vol.6 (2), March 2005.  See:   http://www.nps.gov/mwac/hopewell/v6n2/two.htm

A Simple Idea Only a Foot Long

By B.L. Freeborn © 2013, updated Nov. 2018

Hanukkiah Earthworks or East Fork Works of Southern Ohio with Dimensions

Hanukkiah Earthworks or East Fork Works of Southern Ohio with Dimensions

The ancient world took their Ruler very seriously. The King or Ruler as represented by a man would confirm and declare the standards of measure of his land or the ruler. The terms are not meant to be a play on words. It is just that we have forgotten how important standards of measure are. We forget that is until we are at the gas pump and we think we have been shorted! Oh! Then we remember and call the local weights and measures guy and file a complaint with our current Ruler that the law is not being followed. This tradition is alive and well.

The unit of length found by Rene Millon at Teotihuacan near Mexico City was a length of 57 meters or 187 feet.

Hugh Harleston, Jr. in 1972 found that the unit of length at the same site was 41.66″.1

Robert Horn and Ray Hively2 suggested in 1982 the standard length of Newark was 1054 feet. (This is 527 times two.) They called it an OCD (Observatory Circle Diameter). They otherwise measure in meters.

William Romain follows Horn and Hively and uses OCD’s but he otherwise measures in feet.

Marshall notes a radius of 528 feet at the High Bank Works. This 528 is 1/10th of a mile.

The scale on the East Fork Works indicates the candelabra is 528 feet across or 1/10th mile.

The resemblance between the Indus Inch, Sumerian Inch, and English inch is not by chance. In fact, it can be shown with relative ease the basis for Harleston’s length of 41.66″ is the 36″ yard.  Notice that 36/ 41.66 is .864 and this number is found in the diameter of the Sun at 864,000 miles. The same cannot be done for Millon’s length of 187 feet. Notice also how impractical this unit is. A measuring tape of 100 feet can be bought today for a good price and this is almost half the length Millon is proposing. Nobody routinely carries around a 100′ tape. It is unwieldy. People do routinely carry 16 foot tapes, nearly the length of the standard rod of the old surveyor of 16.5 feet. If one makes it into two pieces it is a stick 8.25′ long or if three pieces 5.5 feet in length. In other words, it can double as a walking stick. If 187 feet is absurd then a standard of 1054 feet or an OCD fails for the same reason.

Unless!… they are suggesting the basic unit was a foot and 187 feet then takes on a whole other meaning. The OCD or 1054 feet takes on another meaning as well. If the diameter is 1054 then the radius is 527 or one foot shy of 528. We should consider a factor called error. The ropes were either not taunt enough to get an accurate measure of 528 feet (1/10th mile) or their foot measure was off by .19%. This is a negligible error when talking about a single foot but the error multiples at greater distances and adds up in this case to a foot.

Most of the world will not agree, but the silliest mistake being made in the study of ancient monuments is the use of the meter. They did not use meters. We should not use meters to measure their monuments. The measure closest to what they probably used is still commercially available, very affordable and still in use in the US. There is a big downside to not understanding why the foot /mile measure should be rigidly adhered to at ancient sites. The lengths and numbers had religious importance and the words through gematria reflected the numbers. For example, in the East Fork we just examined, can one see Millon’s value of 187 feet? It appears on the long side as 187 / 2 = 93.5 or 10 times this = 935 feet. We see it quickly because it is a multiple of 10. Compare the converted units. This 93.5 feet becomes 28.5 meters and then one tenth of this is 2.85 meters. The value preferred in the Torah is 186. It repeats the 86 found in Elohim (Lord).  If we are using 2.85, 28.5, or even 57 meters we will never see the repetition in the gematria of the words. We will certainly never arrive at the concept to which they were alluding. The Sumerian cush was discussed in another article and how via gematria one can arrive at its length. The ancient cush is otherwise called a Megalithic Yard.

Here is another example showing how 66 from a partial inch to thousands of miles appears in the foot system and the metric system:

.66″           66″        66′            660′            66 mile       66,000 mile

equates to:

1.68 cm   168 cm   20.11 m    201.17 m   106.2 km    106,216 km

The message gets lost in the units.

The 187 foot length is not their unit of length as Millon deduced. Its repetition at Teotihuacan merely meant the site was built to focus (worship, recall) that length and its meaning. Observe the same phenomena in the East Fork. The repetition of 66 and its repeat in 132 and even 110 feet as 1320 inches does not mean their base unit was 66 feet. It simply means their base unit was the foot and inch, and that they are trying to tell us something important by emphasizing these lengths.

These numbers 66 and 187 still have valid measurable meaning today. Handed down by the “gods” to the Kings to the people and down through generations to us we are still using these units. We do not remember why they have meaning and we do not remember why 66 and 187 and the rest of this growing number list is important but we are slowing getting there. The mystery is unraveling.

One more important concept about East Fork is to be seen before we move on. The left side has an angle. The line is 825 feet high and the line angled at 30 degrees is 440 feet long. (Note that 825 is 528 reversed and recall there are 5280 feet in a mile.) The base length of the candelabra is 560 feet long. The 30 degrees represents the double hour. Every two hours the earth turns 30 degrees, a basic fact in navigation. The circumference of the earth (7920 x pi = 24880 miles) divided by 440 equals 56.55 which is very nearly this value 560 feet and the number we found on the Decalogue in the form het, vav, het, vav or 5656. This number, 56, is going to pop up everywhere. As far as all the other numbers… let us assemble them in another extraordinary way.

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  1. Tompkins, Peter, “Mysteries of the Mexican Pyramids,” New York: Harper & Row, Publishers, 1976.
  2. Hively, Ray, and Horn, Robert, Geometry and Astronomy in Prehistoric Ohio, “Journal for the History of Astronomy, Archaeoastronomy,” Supplement, Vol. 13, p.S1; also Science History Publications, 1982.      See:  http://articles.adsabs.harvard.edu
  3. Freeborn, B.L., “The Inch, The Megalithic Yard, and The Sumerian Inch,” 2013. See: https://noahsage.com/2013/01/13/the-inch-the-megalitic-yard-and-the-sumerian-inch

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