10/30/2025.
Lately I've spent a bit of time looking more closely at the Great Circle.
In "The Circular, Square, and Octagonal Earthworks of Ohio", Cyrus Thomas, reporting on a re-survey by James D. Middleton in 1888, notes that
"The [Great Circle] is somewhat elliptical , though not so much so as represented in [the] Ancient Monuments [of Squier and Davis]. The curve is not exactly regular." (Thomas 1889: 13)
This is not quite as extreme as Charles Whittlesey said in his 1837 survey,
"This work is not, as has generally been represented, a true circle; its form is that of an ellipse, its diameters being 1,250 and 1,150 feet respectively."
This is the result of that look at the "imperfection" of the Great Circle.
Let me start by taking a LiDAR look at the Great Circle, produced using the (older) 2015 Ohio LiDAR (OSIP I) data.
I tend to prefer using this set of data since it is easier for me to process the way I want to. What I have done here is highlight every two feet of elevation by dramatically changing the color each two feet. The color otherwise means nothing. Each pixel is 2.5 feet wide.
That makes it pretty easy to see the location of the peak of the mound all around the circle.
I then went and marked (using black, one pixel wide), that peak. The Inset expands the view of that to make it easier to see what I am doing. What looks like an odd feature opening to the northeast is the stairs put in by the CCC in the 1930s.
This next picture shows just that black line, that is, the contour of the peak of the Great Circle.
In their original paper on the Newark Earthworks, Hively and Horn, using the Thomas 1889 booklet, note that the Fairground Circle (what they call the Great Circle) it is not a perfect circle, with the "maximum and minimum diameters differing by about 10m." (Hively/Horn 1982: S10) The Thomas report gives those two diameters as 1,189 feet 1,163 feet.
Back in the 1930s, the CCC helped do a restoration project on the Great Circle. They used the Thomas Report to restore the Great Circle, using the results of the Middleton survey
The re-survey measured points along the top of the Great Circle at 100 foot intervals, so by traversing the angles and directions, it is easy to create a plot of those points.
This picture overlays that survey onto my earlier LiDAR diagram.
We can see that they match up (which is good, right?). So I'll be using the LiDAR diagram to do my examination.
On the bare picture, the maximum and minimim diameters are 477 and 468 pixels, which convert to 1192.5 and 1172.5 feet (if you include both end pixels). This is good enough for what I am trying to do.
The first thing I tried to do was fit an ellipse onto the bare picture, fitting its major and minor axes to the picture, and rotating as necessary.
Here is what I got with an ellipse attempt:
As you can see, this fit is only so-so.
However, James Marshall, who took an extensive look at Hopewell earthworks in 1987, notes that the Indigenous Peoples of the Hopewell Culture did not construct true ellipses, so I guess it's not too surprising that the fit here is not great. (Marshall 1987: 37)
However, what they did do was use half-circles with extensions between them, kind of like race tracks. That's what you see here in another attempt to fit the Great Circle:
That fit isn't too great, either. However, Marshall does note another technique that they did use, called a "draftsman ellipse". We will come back to that later in a different context.
What I ended up using instead was a different technique to try to understand the shape of the Great Circle: I rotated it by 180° and fit the two images over each other. You can see the result of that here:
The black image is the original; the red image is the rotated version.
I think it is pretty clear that something else is going on. The Great Circle is not enlongated like an ellipse or an oval—it's more like a squashed circle, with the squashing happening on its northwest side.
So instead, I went to find the circle that, absent the squashing, fit the circle. That is this picture:
That circle has a diameter of 1,192.5 feet. And then there is that missing part, which has an area of about 1,500 square feet and a maximum width of a bit over 21 feet.
Looking at it as a squashed circle instead of an elongated one puts a different perspective on things. It also lets us see its orientation.
Let me make a diversion here to talk about areas.
One of the features of the Newark Earthworks is that it appears that there was careful engineering to make the large earthworks have corresponding areas. The area of Wright Square is very close to the area of Observatory Circle, and the area of the embedded Square inside the Octagon is very close to the area of the Great Circle.
If the areas of a square and a circle are exactly equal, then the diameter of the circle needs to be 2/√π times a side of the square. 2√π is approximately 1.12838. Because π is a trancendental number, you can never get it in a diagram through using squares and triangles. But you can come close.
For instance, √5/2, the hypotenuse of a right triangle with sides of length 1 and ½, is approximately 1.11803 (99.1% of 2/√π). Over a 1,000 foot distance, that's about 10 feet short.
That means that I can draw the following picture relating the Observatory Circle and the Great Circle, which was first pointed out by William Romain. (Romain 2015)
Instead of using the single pixel width view to illustrate this, I've pulled from the LiDAR data and relief maps something close to the actual width of the circles.
The horizontal red line is the radius of the Observatory Circle, and the vertical one is half that, so that builds our right triangle with sides measuring 1 and ½ radii. (Recall that the diameter of the Observatory Circle is the same as the Square embedded inside the Octagon, so that ratio, above, applies, and the construction works).
Let me label some things. Let us call the common ratio that the Indigenous Peoples used to get from the leg of a square to the diameter of an "equivalent" circle, α, so that D = α·L. Applying that to the earthworks, DGrtCir = α·LOctSq. Similarly, DObsCir = α·LWriSq. We also have DObsCir = LOctSq, which implies DGrtCir = α2·LWriSq. We'll come back to that later.
At the moment, we have two candidates for α: 2/√π and √5/2, one for exact areas, and the other for approximate areas.
There's another place where the Observatory Circle Diameter comes into play—that's the square that defines the Octagon.
We can use the same red right triangle using the legs of that embedded square. Again, it all works and we can see how the size of the Great Circle is related to the size of the Octagon.
The lines of the square are thin and pink. I've been able to place all those red right triangles on top to see how they fit.
So, we've seen how a square can lead to a circle with a (nearly-)equal area. Take one side of a square and half an adjacent (right-angle) side, and grab the hypotenuse.
Well, Wright Square and the Observatory Circle have equivalent areas, so let's apply that to Wright Square.
That is what we have here:
The green line is the hypotenuse and clearly matches the diameter of the Observatory Circle.
That also means that we can tile the Octagon again (or at least its embedded square). The green line from the previous picture is the diameter of the Observatory Circle, which is the length of each leg of the square embedded in the Octagon. Here is that tiling:
Again, it fits the way it is supposed to.
(Note that because of the way the tiling works, each red square is actually a quarter the size of Wright Square itself.)
By the way, there is some slop here, kind of hidden by the width of the mounds. Using the √5/2 factor on the length of the Observatory Circle gives 1,178 feet, which is a bit short of the 1,192.5 feet circle that I fitted earlier.
This picture is just a version of Wright Square with the sides a single pixel wide, also based on one of the Middleton surveys as reported by Thommas.
It shows the proper orientation of Wright Square (per the survey). I've also fiddled the colors because I'm about to do a bunch of overlaying. The Square itself is colored cyan, and the orange lines are the hypotenuses, which, as before, have a length of (very close to) an Observatory Circle Diameter.
Now, you might be wondering, why this odd diversion towards Wright Square? Do you notice the orientation of the "squash" of the Great Circle? Look familiar?
Here's what you get if you overlay Wright Square (from its survey) over the Great Circle (from its survey):
The fit is quite remarkable, and it's what has prompted me to write post. Not only are the squash and Wright Square oriented the same, but Wright Square fits into the Great Circle quite precisely. (Don't forget, any small gap of a pixel is only 2.5 feet.)
[By the way, I don't think anybody really knows why the corners of Wright Square do not point exactly in the cardinal direction.]
A reminder: black shows the actual Great Circle; red shows the idealized unsquashed circle with the diameter of 1,192.5 feet that the the unsquashed portion of the Great Circle follows.
It's almost as if wright Square was the template for the Great Circle.
Don't forget that the orange lines, which are √5/2 the lengths of the Wright Square leg, are the lengths of the diameter of the Observatory Circle.
Thus, we should be able to pretty much reproduce the Great Circle diameter by adding a hypotenuse between them, using the familiar 1, 1/2, √5/2 right triangle. That's here:
The light green shows that hypotenuse. We can now overlay that over the Great Circle and see what we get.
It's as if that northeast side of the Great Circle was squashed to make the circle match the √5/2 length instead of the larger main circle diameter.
Time for another digression.
There is another triangular construction that approximates 2/√π: (4√2)/5. This entails dividing a square's leg into five equal parts, and running a diagonal through four of them.
This picture compares the two approximations.
This is the approximation was highlighted by John Volker (Volker 2003) and I discussed it near the end of "Earthworks Areas".
Over a 1,000 foot distance, this is about 7 feet longer than the 2/√π formula.
So, what happens if we divide Wright Square into fifths?
One thing is we'll get another, slightly different length for the Observatory Circle diameter (not shown, but you can imagine lines running across four small squares diagonallly and seeing that they are about the same length as the orange lines).
But there is something else.
Do you see it?
We have more intersection points, shown by the magenta diagonals. For this we have a right triangle with one leg being 1 and the other being 4/5. The hypotenuse of that is √41/5. Since this is a double step from a Wright Square leg to a Great Circle (main) diagonal, the square root of this is another α. (Remember from above, DGrtCir = α2·LWriSq.) The α derived from this is approximately 1.1316, just slightly more than the 1.1314 of 4√2/5.
If you take Wright Square and divide it into fifths, the 4/5, 4/5, 4√2/5 right triangle takes you to the Observatory Circle Diameter, and the 4/5, 5/5, √41/5 right triangle takes you to the main, unsquashed portion of the Great Circle diameter.
And if you orient the Great Circle with it, the squashed side lines up with one of the sides of Wright Square.
Let me now return way back to Marshall's work, where he talked about a "draftsman ellipse" being used in some Earthworks. This is one of the figures from his paper, enchanced by my coloring.
You can see how the draftsman ellipse works: you use four circular arcs, with equal arcs opposite each other. The red/purple lines demarc the larger arcs, and the blue/purple lines demarc the smaller arcs.
And then finally, we can ask whether the Great Circle was constructed using a similar technique. (Here we have only two arcs: the main one making up most of the circle, and the small one on the squashed side.) We can also ask where the radii run from.
The answer is yes, it looks like they used that technique. The smaller arc (the "squash") uses dark green. We also see where the center (no longer a "centroid") of the main circle is, and where the center of the smaller arc is, 1/5 of a Wright Square leg away.
I need to add that, when I was looking for that smaller arc, I matched it to the curve without even looking for where the "center" of the smaller arc would be, since I did not want to prejudice my results. I was pretty surprised to see that it ended up one one of the 1/5 square lines.
I started this post (a while bacK) because I figured out that the Great Circle was not an ellipse but instead a squashed circle. Interesting, but not much. And then its orientation struck me as close to the orientation of Wright Square. Separately, it had also occurred to me that I could use the "Romain Triangle" (the 1, 1/2, √5/2 triangle) on Wright Square to get to the diameter of the Observatory Circle). That was it, so I started the post.
And then I overlaid Wright Square over the squashed Great Circle, and everything snowballed.
I have no idea how to think about this. In many ways, it feels like numerology to me or looking for hidden meanings in the Kabbalah. It's just too fantastical.
Certainly, I can vouch for the math. But sizes and locations of the mounds can be squishy regarding whether they were restored correctly, or measured correctly, or had somehow changed over the years. And there is squishiness over whether the orientation of the squashed side and Wright Square are really the same.
Am I just seeing stuff that was not in the intent of the Indigenous Peoples? Did they have the precision for this stuff to have had importance to them? Are there just some very interesting coincidences here? It's not as if they couldn't have done it. Every population has its engineering types who can get interested in and obsessed with patterns, and maybe this is just a part of that phenomenon over the whole Newark/Chillicother corridor nearly 2,000 years ago.
What it kind of, maybe, looks like they decided to do was take Wright Square (if that was first), divide it into fifths, make a 5×6 square using those fifths, and put the Great Circle right in the middle, using the 4/5, 5/5 right triangles to make the Circle, but deliberately leaving the northwest side squashed for some reason clear to them and obscure to us, and that squashing reflected 1, 1/2, √5/2 right triangles.
See how weird that sounds? Would they really be interested in these sorts of arcane geometric manipulations? And if not, how the heck did they appear here? Again, extraordinary coincidences?
One possible answer, or maybe "description" is a better word, is that that started out using the α of the 1, 1/2, √5/2 right triangle, and got more sophisticated and accurate approximations as time went by, and that is what left the Great Circle lopsided. But that is pure speculation.
Sometimes I wonder whether, when looking at this, OCD means Observatory Circle Diameter or Obsessive Compulsive Disorder.
For right now, I think I'll just leave it to others to decide for themselves.
References:
Hively/Horn 1982
Geometry and Astronomy in Prehistoric Ohio, by Ray Hively and Robert Horn. Archaeoastronomy, No. 4 (1982).
Marshall 1987
An Atlas of American Indian Geometry, by James A Marshall. Ohio Archaeologist, 37:2 (1987).
Romain 2015
An Archaeology of the Sacred: Adena-Hopewell Astronomy and Landscape Archaeology, by William F. Romain. The Ancient Earthworks Project, Olmsted Falls, OH (2015).
Thomas 1889
The Circular, Square, and Octagonal Earthworks of Ohio, by Cyrus Thomas. Smithsonian Institution, Bureau of Ethnology, Washington, DC (1889).
Volker 2003
The Geometry of the Newark Earthworks, by John Volker. Unpublished manuscript on file in the Department of Archaeology, Ohio History Connection, Columbus.