2015.02.12 - I've added more results, data, graphics, and a set of Machu Picchu ratios to the Golden Mean Longitudes KML file. As with the previous two golden longitude triads (discussed below), Newark Earthworks is once again one of the monuments involved. Thus, six major Americam monument complexes have three golden mean longitude ratios with Newark Earthworks, adding Machu Picchu and Chichen Itza to Poverty Point, Chavin de Huantar, Pachacamac, and Tiwanaku.
Golden Mean Longitudes
Itza Castillo - Newark Octagon - Machu Picchu
Poverty Point - Newark Octagon - Pachacamac
Great Circle - Chavin de Huantar - Tiwanaku
Castillo - Observatory Circle e-w @ Huayna Picchu = 1.0 : 1.61803
Castillo - Octagon Gateway e-w @ Machu Picchu Peak = 1.0 : 1.61804
Great Circle - Chavin de Huantar e-w @ Puma Punku = 1.0 : 1.61801
Newark Octagon - Pachacamac e-w @ Poverty Point = 1.0 : 1.61810
View the research results in Google Earth: phi_golden_ratios.kml
The Golden Ratio is x : 1 = 1 : x + 1, stated numerically 0.61803... : 1.0 = 1.0 : 1.61803..., where
phi, an irrational number like pi, equals 1.6180339887.... Basically, the golden mean whole is proportional to the longer part as the longer part is to the shorter part. Could this longitudinal arrangement with golden mean ratios of known astronomy sites have function to astronomers?
Three Monuments, Two Astronomy Ratios
2015.01.17 - On a continental scale, three of the greatest monumental sites in the ancient Americas precisely express the ratio of a fundamental astronomical constant, the number of lunar orbits per earth rotation. In this case the ratio expressed is lunar orbit per ten rotations (illustrated below, click image for larger view). With the ten times multiple, the two arcs provide scales nearly 2,400 and over 6,500 kilometers long with a five meter inaccuracy in relation to the precise constant.
The center-on-center arc inaccuracy is about the same as the inaccuracy in the method determining the monument centerpoint coordinates, and is minute in relation to the scale of the monuments. Comparing monuments on a global scale, I employ centerpoint coordinates. Substituting either of the Tikal Great Plaza pyramid coordinates for Tikal Plaza (their midpoint) shifts the 2,400 kilometer arc 10 meters in either direction. Correlating the two arcs to the precise astronomical ratio, at Tikal Pyramid II the Cahokia arc is six meters long compared to 16 meters short at Tikal Pyramid I.
Examine the monument coordinates and site relationships close-up in Google Earth: cahokia_3650.kml
While precision is not intention, the relationship is not a singularity either. With an interesting addition, the lunar orbit per ten rotations ratio repeats in the relationship of three major monuments in the Andes; Pachacamac, Sechin Alto, and Marcahuamachuco. At Marcahuamacucho's Castillo complex the arcs to Sechin Alto and Pachacamac expresses the same lunar orbits per rotation ratio (arcs ratio @ marcc = 1.0 : 0.36500). The interesting addition, at Marcahuamacucho's Monjas complex the arcs to Sechin Alto and Pachacamac express the lunar orbits per day constant (arcs ratio @ marcm = 1.0 : 0.36600).
lunar orbit per rotation (lr) = 0.0365011
lunar orbit per day (ld) = 0.0366010
In 365 lunar orbits there are 10,000 rotations.
In 366 lunar orbits there are 10,000 days.
As noted in the graphic above, the Tikal-Tiwanaku relationship of the same two coordinates (tikgp-pupup) expresses the ratio of eclipse nodal intervals per lunar orbit turn (et), again a precise astronomical ratio. The Newark-Pachacamac relationship expresses this constant redundantly plus the Pachacamac to Newark Circles mean arc (pachs-nocc-ncec) equals four times lunar orbit per rotation, in other words four times 0.036501 circumference. The relationships are illustrated below and previously discussed in Newark Archaeogeodesy. For more on the importance of lunar motion per rotation, the readily-observable fundamental astronomical ratio, see Eclipses, Cosmic Clockwork of the Ancients.
2015.01.17 - An updated v2015 of archaeogeodesy.xls is online, with the site variables set to the finding discussed above. The applet provides ancient astronomy research functions and calculates arc distances and bearings for
three sites, ratios of arcs, latitude, and longitude, and more. The thousands of site coordinates for mounds,
pyramids, and other monuments worldwide include hundreds of newly documented Amazon geoglyphs.
Emperor Qin and the Golden Mean
2015.01.14 - I recently focused on the ancient pyramids in East Asia, including Emperor Qin's mausoleum. The massive Qin Shi Huang pyramid was also a focus of my latitude study. Several new files illustrate the findings. While not as precise as the latitude placements of Chavin (asin 1/6) and Monk's Mound (atan 4/5), or the nodal to anomalistic colatitude ratio of the Octagon and Capitolium, the Qin monument does overlap two significant latitudes, the golden mean between the equator and the pole along with three-fifths of a radian from the equator. Will these baselines inform locating the actual tomb? Examine the details in a new Google Earth file, qin.kml.
At the Qin Shi Huang pyramid, the latitude equals 0.600067 radians and the colatitude to latitude ratio is 1.0 : 0.61816. The two baselines transect the pyramid field north of Xian, passing just north of the Yan Ling Pyramid (yalip, latitude = 0.59996 radians, = 0.61806 colatitude). At the phi baseline, the ratio of distance to the pole and to the equator is one to phi (1.0 : 1.618034 = 0.618034 : 1.0). This equals the ratio at the pole of the distance to the equator and to the baseline, thus the golden mean (φ = 1.6180340). Two arcs are a golden ratio if their proportions equal the ratio of their sum to the larger arc, in this case [lat : colat = colat : (lat + colat)].
The golden mean latitude of Qin's mausoleum, feng shui on a global scale. Download qin.kml.
The golden ratio latitude of Emperor Qin's mausoleum is not my first observation of this ratio for major monuments. In the Americas, I noted two phi longitude ratios for Newark Earthworks. The golden mean is accurately expressed by the longitudes of three major monuments, Pachacamac, Newark Octagon, and Poverty Point (pachs-nocp-popma e-w @ pachs = 1.0 : 0.61801,
e-w @ nocp = 1.0 : 0.61810) and repeats for the longitude differences between Newark Circle, Chavin, and Tiwanaku (ncec-chhha-pupup e-w @ chhha = 1.0 : 0.61811, e-w @ pupup = 1.0 : 0.61801).
Download the Google Earth placemarks file:
The distances from Newark and Chavin to their respective opposite poles only approximates the golden ratio, while their relationship with Pachacamac presents a very accurate astronomy ratio (as previously discussed). Here follows a new graphic illustrating the arc (click to enlarge).
A permalinked page with further discussion and other site-to-site results will follow. For now, I wanted to start the 2015 blog in order to post new and updated files and to report these findings—the tip of an iceberg.
More: Ancient Monument Latitudes Evidence Accurate Astronomy
Newark Archaeogeodesy -
Assessing Evidence of Geospatial Intelligence in the Americas
2015.01.06 - Hundreds of Geoglifos Discovered in the
Amazon article updated with newly discovered geoglyphs. Nearly 400 Amazon geoglyphs are now surveyed. All the visible lines and the largest earthworks are outlined. I continue to monitor Google Earth imagery updates.
Previous Years Linked Below