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On the evening of December 21st, 2019, after having observed the sunset from the North Place, my associate in this project, Blake Trombley, my younger son Thomas and I watched night fall from the Wright Mound. Over the course of about an hour, twilight gave way to night and as it did so, more and more stars became visible.
Though trees obscure the horizon to the east, south and west, the north horizon is visible. Once darkness fell the constellation we call the Big Dipper appeared just above the burial hills to the north (both the Omaha and Pawnee considered these stars a burial party carrying a body on a litter). This mound tapers to a gentle point to the north, and we believe it points, at least in part, to this constellation.
In the daylight this mound points to a hilltop directly north –
The large mound in the pasture of the Wright Place is irregular in shape and this could mean that the shape is not based on any underlying geometry. Like the south side of the Rectangle Mound, though, this mound extends farther to the south on its southwest corner than on its southeast, suggesting this feature may be intentional and that like the two smaller, Oval Mounds on the top of this mound and a third Rectangular Mound located on the terrace directly to the east, there may be underlying geometry present.
Initial Geometric Analysis
The first step in looking for any geometry was to identify the shape of this mound. This was not easily accomplished since the mound’s shape is irregular in both the horizontal and the vertical planes – it’s curvature in both planes is not constant, rising vertically more steeply, for example, on the south and northwest sides. It is difficult as a result to identify level points around the perimeter of this mound, points that are necessary to determine its horizontal shape.
Waterline
Finding a level baseline was made possible in March of 2019 when a catastrophic flood hit eastern Nebraska. The bottom where this mound is located was flooded by the normally dry O’Neill Valley Creek. A good deal of sediment was deposited during this flood, and the valley floor surrounding the mound is higher as a result. However, the water extended above this sediment, creating a visible waterline around the base of this mound. It took ten day before the sediment was dry enough to walk on but at this point my wife Lori and I placed numerous flags along this waterline. Though there were a few spots where water running off the top of the mound made determining the exact waterline difficult, we visited these areas on multiple occasions and are confident that our flags were placed very close to the highest point the flood waters reached. The corners, though, were difficult to determine exactly and are best estimates of where the direction of the waterline changed.
Determining the waterline on the north side was particularly problematic. During the night of the flood winds gusting up to 50 miles per hour from the north probably pushed the water higher in this area. Because of the debris – mostly cornstalks – it was impossible to determine where the waterline would have been if the wind hadn’t been blowing so hard. It’s possible that the waterline in this area may have been somewhat farther north if the wind hadn’t been blowing so hard.
Once the ground was dry enough we painted this waterline with special spray paint made for marking lines on the ground. We then cut down a total of 22 surrounding trees to make it possible for our son William to get good aerial photographs of this line with a small drone.
Ovals
We also flagged the perimeters of the two low-relief ovals located on the south end of this larger mound. Though we did not attempt to outline the shapes of these ovals with paint (these ovals are similar but not identical in shape and size), we did paint circles around each flag (south is at the top in all diagrams and photos).
Because it’s hard to get a 3-dimensional impression of this mound from a 2-dimensional photo, and because soon after the above photo was taken the grass growing on this mound had to be mowed, William and I used yellow paint to mark every other mower width (approximately 42 inches apart), creating something of a contour image of this mound –
Though in most places the slope is very gentle, the south (top) side is quite steep and visibly changes about half way up, being steeper below and less steep above. This change in slope may suggest that this mound was constructed in layers – Native American mounds were frequently enhanced by adding more dirt – and more burials – as time went by.
The north (bottom) side of the mound has a somewhat peculiar shape with a slight down-sloping ridge extending to the north-northeast which can be discerned from the change of direction of the yellow lawnmower lines. There is a slightly concave area on the northwest (bottom right) with a steeper slope (though not as steep as on the south). The northern edge of this area is also apparent in the change in direction of the yellow lines.
There is no well-defined top surface boundary, but the image above is a close approximation of where the level surface of the mound is. The dots indicate slight ridges where the slope of the sides changes. The slightly raised berm around the ovals is also marked by dots.
In order to align our drone photos with north/south/east/west, a gnomon was used to mark the sun’s shadow over approximately 4 ½ hours. In the morning this gnomon – a tripod-based microphone stand that was adjusted to stand perfectly straight up and down – cast a shadow west and a little north of the base of the stand and this point was marked. A string was tied around the base of the stand and carefully adjusted to just reach the tip of this shadow. An arc was then swung to the east, creating a semicircle to the north of the gnomon. In the afternoon the gnomon’s shadow slowly approached and then touched this arc before moving on past. The points of intersection was carefully marked. The two points where the shadow of the gnomon touched the arc are exactly straight east and west from each other. This line was carefully extended to a length of 20 feet and then painted (following a string) to be visible from the drone.
Directional Alignment
Once the drone photos were imported into a computer, Photoshop was used to adjust the image of the mound so that the east-west line created by the gnomon was exactly parallel to the top and bottom of the screen.
Photo Compensation
In order to make sure that slight variations in the location and angle of the drone did not distort the image, we measured three points on the surface of the mound. We then compared the distance between them with the distances in the drone photo by overlaying a triangle that was created based on the measured distance between points. The proportions were not exact, so Photoshop was again used to slightly distort the photo until the proportions in the photo matched the lengths measured on the mound.
The photo on the left is the uncompensated image and the photo on the right is the compensated image. Though subtle, there is a difference between them and it would be impossible to determine accurate shapes and distances using the uncompensated images.
Mound Shape
Unlike the ovals atop this mound and the rectangular mound just to the east, there is only a little about this mound’s shape that suggests it is geometrical (see below). Its shape is irregular and the changes in its shape – except on the south – are gentle.
What is evident, though – especially when standing on it – is that this mound appears to have a deliberate, complex shape. It’s shape and slope seems much more artistic than accidental. For years I’ve suspected the shape may be that of a heart – presumably, a human heart. Comparisons to drawings and other flat images of the human heart were difficult because all the images I found showed the heart from a slightly different angle. So I eventually ordered a foam model of a heart from a school supply store.
There are similarities between the left side of the heart model and the west side of the surface of the mound, similarities that are made more evident on the mound by the obvious changes in direction and shape of both its surface and the slope leading up to it –
Though not an exact match, both the heart model and the mound’s surface have a slight bulge at the top, run straight downward from there, and then angle to the left. And both have something of a point at the bottom. And the mound’s slope on the east (left in this image) is so gradual that it was hard to mark for the image above. However, though there does seem to be some similarity on the surface, the waterline does not resemble the human heart much at all.
When I showed this image to my wife, Lori, she suggested I compare the waterline’s shape to that of a buffalo’s heart. I did so and found that there is a remarkable similarity –
Again, the left side of the two images differ somewhat, but in many ways this is a pretty good match, especially when one considers that the shape of the mound changes with elevation – the base, long ago lost to sedimentation, could possibly have looked even more like the diagram.
(It’s interesting to speculate as to why this mound’s shape changes with elevation – was the builders’ intention to combine both a buffalo heart and a human heart in one mound? I will leave that possibility for the reader to decide…)
The top of the heart is, of course, different, but note how closely the atria, or upper chambers of the heart, correspond to the ovals atop the mound.
I could not find an image showing the location of the heart inside a buffalo, but did find this image of where the heart is inside a cow –
Geometric mounds, such as the ovals and the rectangle, are classified as effigy mounds (most effigy mounds, however, resemble the shapes of animals). I have come to suspect that this mound is in fact an effigy of a buffalo’s heart and wonder if there was at one time a larger image of a buffalo present in the landscape. If so, then the mound we call the “tumulus” could possibly symbolize this hypothetical buffalo’s head.
Why build an earthen mound in the shape of a buffalo’s heart? One possible explanation is suggested by the diagram below explaining the many uses of the buffalo. This chart explains that many tribes placed the buffalo’s heart on the ground after killing it to give new life to the herd. It also says the buffalo’s heart was seen as a source of strength and power for men –
So it seems possible that an earthen mound in the shape of a buffalo’s heart may have served in some way to help the herd stay strong and grow, and also possibly as a place where people could connect with the buffalo’s strength and power. This is all supposition, of course, but it is the best explanation of the mound I have yet found.
Geometry?
Despite the fact that there is no obvious geometry here, since the local mound builders were clearly accomplished geometers William and I have devoted a good deal of time looking for possible underlying geometry.
Symmetry Comparisons
Many geometric figures, including circles, ovals, squares, rectangles and many triangles, possess an internal symmetry. When exploring the geometry of mounds I like to reverse and then overlay their outlines to look for any signs of symmetry. As can be seen in the two images below, there is limited symmetry here. However, on the top-bottom comparison in the center there is a small area of overlap which William overlaid with a blue line –
William then reversed the upside down image and discovered a more extended overlap – since this was more significant, he emphasized the areas on both the top and the bottom of the waterline –
William then included both bottom lines on the waterline image –
Though the overlap on the left is small, if these lines are correctly drawn, then they form two Golden Triangles touching at their points. Golden Triangles, like Golden Rectangles, include the “Golden” or phi ratio, which may be present in the rectangular mound and is definitely present in the ovals atop this mound, indicating the builders placed special importance on “golden” geometric shapes. Golden Triangles are most commonly found in the points of pentagrams – five pointed stars, so some form of pentagonal geometry may be among the factors underlying this mound’s unusual shape.
The other angle formed by the intersection of these lines forms two sides of a decagon, a 10-sided polygon (or two pentagons overlapped) –
Note that a decagon this size not only matches with the lower right portion of the waterline, two of its corners lie on the center east/west line. A smaller decagon can be constructed within it that corresponds with the shorter, lower left portion of the waterline (below left) –
It’s interesting that a north/south line drawn along the left (east) side of this smaller decagon intersects the point where the upper east/west and the upper angled line meet. The image above on the right shows that a third decagon that aligns with the upper angled line can be placed atop the first one.
Not only is decagonal geometry implied by some of the sides of this mound, but the intersection of the two upper lines forms two adjacent sides of a 20-sided polygon –
Though I doubt the designers laid out a 20-sided figure to create the south (top) side of this mounds shape, this image does demonstrate how important 5 and its multiples were to them.
The image below shows two ways that a pentagon fits with the mound’s geometry –
Though this mound is clearly not meant to be a regular polygon, these images suggest that there could be some underlying geometry present.
Enclosing Shapes
After exploring haw 5-, 10- and even a 20-sided figure are suggested by the shape of this mound, our next step was to create a rectangular frame around the compensated waterline that just touched it at its extreme points –
The diagram on the left is the enclosing rectangle. Comparing the height to the width indicates that it is two golden rectangles, one atop the other (center). The image on the right adds the north/south center line.
The fact that this mound can be framed by two golden rectangles further suggests that there may be underlying geometry based on the Golden Ratio present. However, since the corners of the mound are not precise this may not be the exact north/south size of the mound.
To further check for underlying geometry William tried to create an enclosing circle that touched all three extreme points – north (bottom), southeast and southwest –
Though the corners may not be exact, I believe they are close enough that the fact that all three extreme points of the Wright mound lie on a circle whose center is on the vertical center axis is another indication that rather than being just an artistic rendering of a buffalo’s heart, there is some underlying geometry present. (The horizontal center line of this circle lies above that of the center of the enclosing rectangle because the circle extends above the highest point on the mound while the top of the rectangle just touches this same point.)
Below are images of two smaller circles drawn from the same center point as the large circle. The circle on the left has a diameter equal to the width of the waterline and overlaps a portion of the angled south edge. The image on the right shows a smaller circle that overlaps a portion of each lower side.
Comparing the size of these three circles reveals that they are geometrically related, but in a very obscure way. If a square is drawn so that it’s corners just touch the outside circle and an octagon is then created inside this square, the next smaller circle just touches the outside points of this octagon. While the builders probably didn’t create these figures on the ground when laying out this mound, they may have been aware of this 1.306 to 1 ratio and for some reason incorporated it into their design.
If a second octagon is placed inside the first octagon so that it’s points touch the center of the larger octagon’s sides, the circumference of the small circle just touches the centers of the smaller octagon’s sides. That all three circle relate in this fashion seems unlikely to be the result of chance, suggesting that the unusual shape of this mound incorporates multiple interrelated geometric shapes, shapes based on both multiples of 5 and multiples of 8.
Why such complexity? If it is in fact present, then it indicates that a) the builders were very sophisticated geometers who knew of these ratios, and b) they attached important symbolic significance to these interrelated shapes.
It’s worth noting that octagons are not unknown in Native American mound design – there is an immense and complexly astronomically aligned octagonal earthwork near Newark, Ohio.
So why not just build a big octagonal mound? Clearly, there is still much we don’t know about how the final shape of this mound was determined, but if this inner geometry is intentional, it must have been important to the builders to incorporate more than just octagons in their remarkable creation.
Whether based on certain geometric principles or just an artistic rendering of a buffalo’s heart (or both), this mound must have been VERY important to the people who built it for them to have gone to so much trouble in creating it.
More details about the inner geometry of this mound and how it relates to the ovals can be found on the Oval Mounds page.