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On the south, wider end of the Wright Mound there are two low-relief oval mounds which, though similar, are not identical in shape. Though maybe a foot tall now, these mounds were presumably taller before centuries of weather damage. These mounds, like the rectangle, appear to be “effigy mounds“, similar to many low-relief mounds found in states to the east, which though often in the shape of an animal, are sometimes geometric.
Like the Rectangle Mound just to the east, there is a “trough” or beaten-down area around them that forms a continuous pathway around these two ovals, indicating people may have once walked or danced around these two shapes. Also like the Rectangle, outside of this trough is a slight berm, or area of raised soil. This berm vanishes at the northwest end of the east oval, suggesting that perhaps this was the entry/exit point to the trough.
These ovals form a shape known as a “lemniscate”, similar to the mathematical infinity sign, the numeral 8 or the analemma on a globe, a shape that suggests cyclical movement of some sort. Unlike these more familiar shapes, however, the figure formed by these two ovals is not symmetrical, suggesting that though joined, each oval may have its own symbolic meaning and purpose.
As with the Rectangle, my sons William and Thomas and I used flags to mark as carefully as we could the rather indistinct edge between the raised ovals and the surrounding trough. We then painted circles around the bases of the flags (enhanced in these photos to make clearer) so they would show up in drone photos at the same time we outlined the waterline of the larger mound. We also used a gnomon to determine and mark a 20’ east/west reference line.
As described with the Wright Mound and the Rectangle, drone photos aren’t always properly proportioned due to the location and pitch of the drone. We have taken great pains to compensate the dot patterns outlining these ovals by comparing the distance between selected flags with the proportions in the drone photos, “warping” the photos slightly with Photoshop to correct for any errors in proportion.
William and I then separated the two ovals into two separate images and printed them out as large as was practical. As with the Rectangle, I then connected the centers of the dots and proceeded to experiment in folding the images both lengthwise and width-wise to find where the two edges line up most closely. This gave me a reasonable estimate of the long and short axes of both ovals. I then drew along these folds and scanned the images.
Though not shown above, these images contain the 20′ east-west reference line made with the gnomon. This enabled us to determine that the dimensions of the West Oval are 27.53′ long by 17′ wide. The East Oval is 28.28′ long by 15.71′ wide. When compared to the east-west line created using the gnomon, the orientation of the long or major axis of the East Oval is 104.56 degrees/284.5 degrees; the orientation of the major axis of the West Oval is 85.6 degrees/265.6 degrees.
To help us determine if these two ovals are intentional geometric figures rather than just roughly oval-shaped piles of dirt, William then created two identical images of each oval, one with red dots and one with blue. Next he inverted the blue images and overlaid them on the red images. This allowed us to look for symmetry in the two ovals. The east oval is very symmetrical, both left-to-right and top-to-bottom, suggesting that it was intended to be an ellipse.
The west oval, however, though somewhat symmetrical top-to-bottom (the northeast side of this oval is distorted by what dowsing indicates is a grave), is not symmetrical left-to-right, indicating it is a more complex geometrical figure that is rounder at the west and more elliptical at the east.
As their measurements indicate, though close, the ovals are not identical –
Though not perfect (the exact shape of the ovals has presumably been degraded by the elements over the years), the ovals are symmetrical enough to suggest they are deliberate geometric shapes. That the two ovals are similar yet not the same suggests that they may have separate though related symbolic significance.
East Oval Analysis
In order to better explore its geometry, I had William enclose each oval in a rectangle that just touched the widest points and included the diagonals. I then had him connect the ends of the longer and shorter axes, forming an inner rhombus or diamond shape.
Is It An Ellipse?
Next I had William use Photoshop to draw an ellipse that touched the extreme points.
Note how closely it fits the dot patterns. This leads me to conclude that this mound was intended to be an ellipse. The elliptical shape – and alignment with the horizon – is significant because it could tie these mounds to mound builders north and east of here (more on this later).
The angles of the diagonals and the diamond sides to the axes are 29.05 degrees and 60.95 degrees, very close to 30 degrees and 60 degrees that would have resulted if this ellipse had been based on the geometry of the vessica piscis – as the dimensions of the Rectangle appear to be. That they do differ indicates that the builders did not choose one of the easier ways to design an ellipse, suggesting that the ellipse’s dimensions and angles may have been important in some ways.
As mentioned above, the long axis is 28.28 feet long and the short axis is 15.71 feet long. The diagonals are 32.35′ and the sides of the diamond are half this length, 16.175′. Even though the length and width of the west oval are both slightly different, these diagonal lengths are essentially the same for both figures. Further, the length 32.35′ is almost exactly the length of the inner root 3 rectangle (32.36′) implied by the surrounding depressions at the Rectangle Mound. This strongly suggests there is important geometric symbolism contained in these three figures.
The ratio of the length to width in this figure is 1.8 or 9:5. This is a special ratio geometrically because it relates three of the important irrational ratios of geometry – pi, phi and the square root of 2 – very closely together.
Pi, phi and the square roots of 2, 3 and 5 often come up in the geometry of circles, squares and rectangles, and are all irrational, meaning that their decimal values go on forever (pi has been calculated to 31.4 trillion decimal places, with no end in sight). Since irrationals never end, people around the world have rounded these numbers to a few decimal places (NASA, for example, sent men to the moon using the value of 3.14 for pi).
While pi and phi actually do relate to one another (pi equals 1.2 times phi squared), I do not know of any way in which these other ratios perfectly relate. However, when rounded to three decimal places, pi, phi and the square root of 2 do relate to each other very closely.
Pi, Phi and the Square Root of 2
As mentioned at the top of this page, strange things tend to happen in this area; thanks to what I assume to be a remarkable coincidence, the length of the east oval, when measured in feet, comes very close to ten times the square root of 2 x 2 – 28.28′ (1.41421… x 10 = 14.1421…; 2 x 14.1421… = 28.2842…).
The width of this figure comes very close to ten times pi/2 – 15.71′ (3.14159…/2 = 1.57079…; 1.57079… x 10 = 15.7079…).
(These ratios are there, of course, regardless of what unit of measure is used.)
The long and short axes of this figure intersect at right angles to each other, forming four adjacent right triangles.
Each side of the inner diamond shape formed by connecting the ends of these axes is therefore the hypotenuse of one of these triangles. Dividing the length and width by two (since the sides of each adjacent inner right triangle are only half the length and width of the entire figure) gives 14.14′ x 7.855′ (10 x the square root of 2 and 10 x pi/4).
Using the Pythagorean theorem gives the hypotenuse length as 16.175′ – very near 10 times 1 + phi or 16.18…’ (due to their unique properties, phi (0.618…) and 1 + phi are often used interchangeably). Whoever designed this figure appears to have incorporated scaled values of the square root of 2, pi and phi in a manner that relates them to each other very well.
Pi and the Square Root of 2
Further, since the length of this figure is 9/5 of the width that means that the shorter axes – 15.71′ – is half a larger length and the long axis – 28.28′ – is 9/10s of a larger length. Solving for this larger length gives 31.42′ – very close to ten times pi.
East Oval Conclusions
Based on the closeness of the dot pattern to the shape of a simple ellipse, I believe it was the builders’ intention to create this specific geometric figure.
I believe the special ratio of length to width – 9:5 – indicates the builders related the important geometric ratios of pi, phi (actually phi + 1) and the square root of 2 to one another through a right triangle derived from this ratio. They appear to have used the values 3.142 for pi, 1.618 for phi + 1 and 1.414 for the square root of 2. To the builders, 2 x the square root of 2 was equal to 9/10 of pi. Phi + 1 resulted from forming a right triangle with sides pi/4 and the square root of 2.
West Oval Analysis
To analyze this oval I again had William create an outer rectangle complete with diagonals and create an inner diamond by connecting the ends of the long and short axes. As mentioned above, the dimensions of the West Oval are 27.53′ long by 17′ wide. The diagonals are identical to those of the East Oval – 32.36′. The angles of these diagonals are 31.72 degrees and 58.28 degrees.
This ellipse fits inside a “Golden Rectangle” in which the ratio of width to length is either 0.618… to 1 or 1 to 1.618…. This is the “Golden” or phi ratio, and may be indicated by the shorter east side of the Rectangle. This ratio is created from a square:
A diagonal is drawn from the center of the bottom side of the square and this length is swung down. A rectangle is then formed based on this new distance. The division of the base line of this figure is the phi division, a unique division in which the ratio of the shorter line segment (formed from the diagonal) to the base of the square – 0.618… to 1 – is the same ratio as the length of the base of the square to the full base length of the rectangle.
This is the only way in which a line can be divided so that the ratios of short length to medium length to overall length are the same. The phi ratio is found many places in nature, from the spiral shell of a chambered nautilus to the arrangement of seeds in a sunflower head (it even governs mathematically the reproductive rates of rabbits through something called the Fibonacci Sequence).
Is It An Ellipse?
I next had William attempt to create a simple ellipse running through the ends of these axes. Unlike the East Oval, however, this oval is clearly not a simple ellipse, though it is a pretty good fit in the upper right quadrant –
Though curved on both ends, the curvature is located more pronounced at the ends, leading many visitors to initially identify this oval as a rectangle.
Is It Two Ellipses?
In looking for curves that fit the two ends (recall that this oval is mostly symmetrical when flipped up and down – as shown here – it is not when flipped end-for-end, indicating that a similar curve won’t fit both) a reasonably good fit can be found at both ends if two overlapping ellipses are created.
The best fit, however, comes if 3 figures are combined – the circle for the west or left end, the ellipse based on the east edge of the square for the lower right quadrant and the simple ellipse in the upper right quadrant –
Why such a complex shape? I don’t know. Perhaps various geometric shapes had specific symbolic meaning to the builders. Whatever the reason, this combination of shapes must have been important for the builders to have gone to so much trouble to create it.
The West Oval is essentially a small rectangle (a double square or root 5 rectangle – called this because the diagonal of a double square is the width x the square root of 5)) with two dissimilar curves on the east and west ends:
This may be related in some way to the Rectangle which has a curved depression on the north side:
When time permits I will further explore the geometry underlying this semicircular depression.
Similarity to Pawnee Star Chart
Though probably coincidental, if the inner rectangle is removed from the West Oval, the resulting dot pattern fits remarkably well with the Skidi Pawnee star chart. The Skidi have been called the greatest astronomers north of Mexico and, among other things, believed the universe was elliptical. They thus drew their chart of the heavens on an oval piece of hide. Though the particulars of its shape are presumably the result of cutting this shape freehand, it is interesting to note that while curved on both ends, not only are these curves different, they match the curvature of the ends of the West Oval –
Is it possible that an oval shape with either a rectangle in the middle and curvature at the ends could have held symbolic importance to the people living in this area at some time in the past? And is it significant that the east end is smaller than the west? In the case of the star chart, could it indicate some sort of growth or progression as one moves east to west, as the sun does during the day or the Morning Star did in the Skidi creation myth? Though purely conjectural at this point, these possibilities seem worth considering when exploring the geometric symbolism of the People of the Tall Grass and Thunder.
These two ovals make up a larger lemniscate or infinity sign figure. Overlaying the geometry William created around the two dot patterns results in this figure:
If the southwest/northeast diagonal of the rectangle enclosing the west oval is extended farther to the northeast it intersects the center of the east oval (blue line). The length of this line is 22.88′, the length of a diagonal of a square with sides of 16.18′ or the square root of 2 times the length of half the diagonal of the west rectangle.
The angle of this line is particularly interesting – it figures prominently in another “golden” polygon, the pentagon/pentagram.
As can be seen in the diagram above the line running through the centers of the two ovals could be the side of a pentagon, either with it’s horizontal side to the bottom (left) or to the top (right).
As can also be seen above, if the corners of a pentagon are connected a five pointed star is formed. The line joining the centers of the ovals could also be part of an interior star –
In the diagram on the right the bottom point of the interior star and surrounding pentagon aligns with the lower corner of the rectangle enclosing the east oval. This arrangement makes it possible to precisely calculate the angles of the long axes of both ellipses: the west ellipse’s long axis has an azimuth of 85.716 degrees east and 265.716 degrees west. The east ellipse has an azimuth of [This section is not yet completed – please visit again later.]
Why This Arrangement?
It has been said regarding ancient monuments and earthworks that ‘form reflects function.’ The function of the ovals seems clear – they were, in all likelihood, created to be ceremonially danced around. They are surrounded by a “trough” of packed soil, suggesting that at least they were ceremonially walked around. But why such an asymmetrical layout? Why not arrange two simple ovals – and clearly the builders wanted ovals rather than circles – either one on top of the other
or side by side?
Using a simple ellipse, like the East Oval used in the above diagrams rather than the more complex West Oval, and arranging the ovals in one of these ways would have provided a lemniscate to dance around and have been easier to layout and build.
Clearly, ease of construction wasn’t a primary concern. So here form would seem to reflect more than just function, it must have some deeper, symbolic meaning. The ovals are arranged the way they are because of the geometric concerns that went into their design, concerns for incorporating certain fundamental ratios and relationships, primary among them the ratio of phi, 1:0.618.
Whatever the reason the people who made these ovals danced on them, it must have had very important symbolism, so important that great pains were taken to make this dance occur in a way that accorded with certain fundamental ideas about the cosmos that were expressed by The People of the Tall Grass and Thunder – as by many other people throughout the world – in terms of number and shape, and the proportions by which they fit together.
Overlaying on the Wright Mound
Since their geometry is presumably related, William superimposed the geometry over the dots of a perspective-compensated image of the full Wright Mound. [This section is not yet completed – please visit again later.]
Why This Shape?
Again, form reflects – at least in part – function. The Wright Mound is widest where the ovals are, tapering to a gentle point to the north. The ovals were for the dancers – what was the space to the north for? Dancing suggests musicians, someone to shake rattles and/or beat drums, and probably singers as well – to Native Americans songs were akin to religious or magical invocations, repeated over and over to build intensity. And though songs were not always accompanied by dancing, dancing was usually accompanied by song.
But there isn’t a lot of room north of the ovals – most people would have had to watch from the surrounding terrace hundreds of feet away (its even possible these rituals were held at night when spectators couldn’t have seen what was happening). This suggests that whatever rituals were performed here may have been done by a relatively few people, perhaps priests or doctors who were privy to sacred knowledge, knowledge that may have been known only to initiates, knowledge that may have included the meanings these people attached to the fundamental ratios of sacred geometry.
While there is much we’ll never know about the rituals once held here and the people who held them, we do know that geometry determined the size and position of their ritual – and sacred – spaces. Geometry literally means “earth measure” and clearly that is what it was used for here – to measure and shape the earth. But there is another factor, also – Native Americans lived in two worlds – the sky and the earth. And again like other people throughout the world, they incorporated alignments to the rising and/or setting points of the sun, moon, planets and stars, which to them were the visible manifestations of powerful spiritual beings.
In the alignment section about the Rectangle Mound, I discuss that a number of shallow depressions may be the remains of where poles once stood. If so, then two of these depressions – if they did once have poles rising from them – could have been used to mark both straight east when standing at the center of the rectangle, and where the sun would rise above the elevated horizon on that day. This suggests the mound builders were aware of important astronomical horizon points and that they placed importance on the equinoxes. It seems likely that similar astronomical alignments may be present with each of the Ovals – presumably along their long axes, which align with the area of the horizon where the sun, moon and planets rise and set (these bodies rise and fall in a band extending approximately 30 degrees both north and south of true east). There are also many stars which rise in this area.
In looking at the East Oval first, its long axes is tilted 13.28 degrees south of east. Though the horizon cannot currently be seen because of the trees around the Wright Mound, checking Google Earth shows that there is a slight high point on the east horizon and a small notch on the west horizon directly in line with the long axis of this mound. Presumably, one or more astronomical body rose and/or set (in the case of the sun, moon or planets, which unlike the fixed stars, rise in different locations over the course of time) in alignment with one or both of these slight horizon features. (It should be mentioned that the horizon in this area is largely featureless, so only small features exist in most locations.)
Because of the tilt of the earth on its axis, the Sun appears to move to the south in the winter (in the northern hemisphere) and to the north in the summer, moving back and forth between its extreme summer and winter rising and setting points. As a result of this seasonal north-south movement the Sun rises twice a year, once in February and once in October, and sets twice a year, in April and in September, in line with the long axis of the East Oval.
[This section is not yet complete – please visit again later.]