Pi Results KML

Pi Results
Great Circles, Ancient Monuments, and Pi
2024.03.14 - Happy Pi Day - I've added a few new study results presenting the value of pi and tau, the ratios of circumfernce of a circle to diameter and to radius respectively. The placemark formatting has also been updated.
Archaeogeodesy
The sites in this file are placemarked in the archaeogeodesy.kml file:
Archaeogeodesy Placemarks, Ancient Monuments in Google Earth
Spanning the globe, more than 15,000 placemarks of monuments and anthropogenic features visible in satellite imagery, including the 7,000+ entries in the Excel applet.
Download the 8.8 MB Google Earth file: archaeogeodesy.kml
ArchaeoGeodesy XLS Applet
Download the 3.8 MB Excel file: archaeogeodesy.xls
Links
Recent updates linked in the ArchaeoBlog page.
Stonehenge and Pi
©2024 James Q. Jacobs, all rights reserved. Cite with access date as:
Great Circles, Ancient Monuments, and Pi jqjacobs.net/kml/pi.kml

whitp-pdsol-epara
White Pyramid - Piramide del Sol - El Paraíso
pdsol-epara arc = 38.198387°
pdsol-whitp arc 120.003662°
I illustrated this study result to celebrate Pi Day 2015.
The arc distances from the Pyramid of the Sun in Mexico to the White Pyramid in China and to El Paraiso in Peru respectively equal one-third of earth's circumference and one-third of diameter. Hence, from atop the Pyramid of the Sun to the other two ancient monuments, the arc distancess have the ratio of pi to one. The ratio expresses pi precisely using center-on-center coordinates for the monuments considered.
The White Pyramid (Mao Ling Mausoleum) and the Pyramid of the Sun (Piramide del Sol) are near the same size and were built by the largest cities on their respective continents, cities co-existing on practically opposite sides of the world. El Paraiso is dated to over 3,000 years ago, earlier than Teotihuacan and Chinese unification. El Paraiso was a singularly large Preceramic period monument in the Americas.

whitp-pdsol-pmoon
White Pyramid - Piramide del Sol - Piramide de la Luna
Teotihuacan, the Largest Prehistoric City in the Americas

nocc-tuchm
Observatory Circle - Tumi Chucua Mound
Observatory Mound - Tumi Chucua Mound
Observatory Mound - Tumi Chucua Zanja
noom-tuchz n-s : e-w ratio @ tuchz = 10.0 : 3.14175 (+89m)
Download the KML file - Tumichucua, Newark, and Pi - tumichucua.kml
ArchaeoBlog

tuchz-ailli
Tumi Chucua Zanja - Apu Illimani GPS
Machupicchu Courtyard - Tumi Chucua Zanja - Apu Illimani GPS
mapic-tuchz-ailli n-s ratio @ tuchz = 1.0 : 0.366242 (-0.1m)
epoch inca ry = 366.2422185 rotations per year
Field Reports: Aboriginal Earthworks near the Mouth of the Beni, Bolivia
This paper reports on the ditch-like earthworks at a remote site in the tropical forest of extreme NE Bolivia. In contrast to most earthworks reported elsewhere in South America, those described here are identified, based on ethnographic parallels, as canals and moats and lie on the edge of the active floodplain on the Beni River in a tropical forest environment.

Tikal III - Machupicchu Torreon - Luxor Pylon
Tikal Citadel - Montaña Machupicchu - Karnak Hypostyle Hall
tikci-mmapi-karhh arcs ratio @ mmapi = 1.0 : 3.141594 (-2m)
Web Archive

tikrp-noctm-durwa
Tikal Radial Pyramid - Newark Octagon Mean - Durrington Walls
Tikal Radial Pyramid - Newark Octagon Mean
Intimachay - Newark Octagon Mean - Ring of Brodgar
intim-noctm-rbrod e-w ratio @ noctm = 1.0 : 0.125000 (+0.3m)
Tikal II - Newark Octagon - Durrington Walls
tikp2-nocp-durwa arcs ratio @ tikp2 = 1.0 : 0.314160 (+6m)
Tikal Radial Pyramid - Octagon Gateway - Durrington Walls Circle
tikrp-nocga-duwac arcs @ tikrp = 1.0 : 0.314159 (+1m)
Durrington Walls
Web Archive

Tikal Citadel - Monks Mound - Monte Alban South Pyramid
Tikal Radial Pyramid - Monks Mound - Monte Alban Plaza Pyramid
mm34c-tikrp-malpp arcs ratio @ tikrp = 1.0 : 3.141480 (+27m)
Poverty Point Earthworks - Monks Mound - Monte Alban South Platform
Cahokia Mounds Photo Gallery
Monks Mound, the largest prehistoric monument north of Mexico, is also the largest-in-volume prehistoric earthen construction in the Americas. Monks Mound is one of 69 remaining mounds at Cahokia, most inside the 2,200 acre park preserving the central section of the largest prehistoric city north of Mexico and the largest ancient settlment in North America in its time.

Tikal I - Monte Alban South Platform - Pueblo del Arroyo Tri-Walled Kiva
Tikal Great Plaza - Monte Alban Plaza - Pueblo del Arroyo Kiva C
tikgp-malpp-puarc arcs ratio @ malpp = 1.0 : 3.141597 (-1m)
Web Archive

Tikal V - Caracol
Tikal Acropolis - Caracol
Tikal V - Denali GPS - Huascarán GPS
tikp5-denal-huasc arcs ratio @ huasc = 1.0 : 3.141527 (+67m)
Tikal Radial Pyramid - Denali GPS
tikrp-denal latitude ratio = 1.0 : 0.273033 (+1m)
epoch hopewell or = 0.0027303 orbits per rotation

Tikal III - Calakmul Pyramid - Caracol
Tikal III - Calakmul Pyramid
Tikal V - Caracol

chhap-khugp-khafr
Chavin Portal - Khufu Pyramid - Khafre Pyramid
khugp-khafr e-w 0.003448
Machupicchu Archaeogeodesy
Geodetic Scale
While analysis of the geodetic relationships of monuments requires coordinate precision to provide confidence in results, the context of the relationship considered impacts confidence immensely. The globe is about 40 million meters in circumference and the arc distance from Machupicchu to Newark Earthworks is nearly six million meters. Thus when considering the location of a monument at Newark in relation to Machupicchu, a GPS datum with plus or minus five meter accuracy has a margin of error of five parts in near six million, about one part in one million. Monuments spaced at great distances from each other offer very high confidence in study results when the margin of error is only one part per million. Likewise, to monumentalize an astronomical constant with mathematical precision, the monuments need to be spaced across vast distances. ...
For intra-site anaylsis, precise GPS or direct survey is necessary to attain reasonable confidence in the results. Comparing a monument at Machupicchu to the nearby Waynapicchu and Machupicchu peaks, given near precise datums, the margin of error would be nearer five parts in two thousand, or one part in four hundred. ....
... When two sites on a meridian are compared with a third site, the margin of error proportion can be even more significant. Expressing this difference in relation to another longitude difference in an east-west ratio, the ratio's margin of error can result in zero confidence. ....
Another important factor impacts ancient monument coordinate accuracy, the older the construct the greater the monument displacement due to tectonic motion. I included a tectonics folder in the Chavin KML file to model Chavin's motion since the Neolithic, about the time the Giza pyramids were built (east of Chavin 108.31 degrees, cosine = -0.314159). While greater scale of monuument spacing enables greater accuracy in relationship results and higher precision in correlated numerical expressions, with global distances the tectonic motion variable is a factor, and proportionately moreso the more ancient the monuments. Individual site tectonic motion modeling is required to correct coordinates for ancient positions. ....
... With the tectonic motion variable, which individual monuments or mountains and which relationships are considered is also a significant factor. At the Newark Earthworks complex, tectonic motion is near exactly east-west so site latitude is consistent over long time periods. ... This is just one example of the complex considerations inherent due to tectonic motion. Margins of error are variated by each site's tectonic motion, antiquity, and the particular relationship, a complex combination unique to each consideration.

nocga-chhap-khugp
Octagon Gateway - Chavin de Huantar Portal - Khufu Pyramid
Chavin de Huantar Portal - Khufu Pyramid - Khafre Pyramid
Understanding Chavín and the Origins of Andean Civilization

nocp-khugp-khafr
Newark Octagon - Khufu Pyramid - Khafre Pyramid
khugp-khafr n-s 0.003208°
Newark Octagon - Khufu Pyramid

secac-rbrod-khafr
Sechin Alto Cuarto - Ring of Brodgar - Khafre Pyramid
Taukachi Circular Plaza - Ring of Brodgar - Khufu Pyramid
takcp-rbrod-khugp e-w ratio @ khugp = 1.0: 0.314158 (-14m)
Sechin Bajo - Sphinx
ld = 0.036601 lunar orbits per day
Chankillo A - Khufu Pyramid
ro = 366.2566 rotations per orbit

chhpq-waden-pylon
Chavin Plaza - Waden Mound - Amun-Mut Axes

avecm-wimbl-khugp
Avebury Circles - The Rounds - Khufu Pyramid
Ancient Monument Latitudes Evidence Accurate Astronomy
... Given latitude placements are intentional, monument positioning evidences the earliest known precise astronomical and geodetic measurements. Thus, the greatest of ancient monuments evidence a capability of accurately determining latitude spanning the range of their construction and the earliest evidence of astronomical observatories using exact sciences is implied by latitude positioning. Astronomy is essential to place determination relative to the whole earth. ...
Complex geodesy was evidenced in the Neolithic before the great pyramids were built at one-tenth of circumference arc distance from older Newgrange in Ireland. Avebury in England ... is accurately positioned at the latitude equaling one-seventh of earth's circumference (360/7 equals 51.4285714), double Karnak's latitude. The Avebury complex with the largest megalithic standing stone circle and henge, is located one-one hundredth of the planetary circumference from two major archaeological complexes in Ireland, Newgrange and Tara. ....

newac-khugp-khafr
Newgrange A Cairn - Khufu Pyramid - Khafre Pyramid
During the Neolithic, obliquity of the ecliptic equaled 24 degrees, two-thirds of this arc distance.
Newgrange A Cairn - Denali GPS
Newgrange A Cairn - Denali GPS - Khufu Pyramid
newac-denal-khugp arcs ratio @ newac = 1.0 : 0.599999 (-5m)
newac-denal-khugp arcs ratio @ newac = 5.000006 : 3.0 (-5m)
Newgrange A is the largest earthen circle at the Boyne complex. The center of the henge is the stone cairn.
Archaeogeodesy Study Results for Three Major Neolithic Complexes
History of this Study
The Archaeogeodesy Pages introduce the topic to readers unfamiliar with the research. ... I first wrote of findings in personal communications beginning in 1987. In 1991 I distributed to several colleagues Earth Commensurate Units based on fundamental astronomic motions and I noted the geofractional distance 1/100 of circumference for the Tikal to Chichen Itza arc, and likewise for other arcs. That year I also noted the Chaco Meridian in the American Southwest and the Maya Meridian centered on Tikal, Guatemala. I then concluded,
"That there is a site-to-site ordered array of monuments in both North and South America is no longer doubtful! That astronomically commensurate scaling was utilized in both monument size and site-to-site spacing seems evident."
It was not until thereafter, in Nov. 1991, that I turned to Old World monuments to assess the same possibilities. I quickly discovered that the Avebury and Newgrange complexes were CIR/100 apart. To my surprise, I also noted that the Newgrange to Cheops distance was CIR/10 (one-tenth of earth's circumference). ....

knowt-winhi
Knowth GPS - Windmill Hill
Rath Cormac - Longstones Cove
Archaeogeodesy Study Results for Three Major Neolithic Complexes
When obliquity equaled precisely 24 degrees, at Avebury the summer solstice sunset pointed precisely to Newgrange. ...
... The arc from Knowth Mound to Windmill Hill equals 3.60006° or CIR/99.9985, an excess of only 6.1 m. And the distance from Knowth to Newgrange equals 1/1000 of earth's diameter, therefore the distance from Newgrange to Windmill Hill is 314.19 (100 pi) times that from Newgrange to Knowth. ....
... I wanted to know if the Newgrange and Avebury complexes aligned on the highest point in Western Europe. Of course, they do! GPS coordinates for Mont Blanc confirm the obvious line. A line from Knowth and Newgrange passes between Avebury and Silbury Hill over the Sanctuary, where the respective bearings angles sum 179.98 degrees. Also, the Sanctuary arc distance from Mont Blanc is precisely 8.0° ... At Avebury the bearing of 130.82° to Mont Blanc matches the winter solstice angle during the Neolithic occupation period. ....

newgc-knowt-silhi
Newgrange - Knowth GPS - Silbury Hill

avocm-newgc-rolci
Avebury Circle - Newgrange Circle - Rollright Circle
Stonehenge - Rollright Circle
stonc-rolci arc : e-w ratio = 1.0 : 0.314387 (+14m)
Avebury Circles - Stonehenge - Rollright Circle
avecm-stonc-rolci arcs ratio @ rolci = 1.0 : 1.414235 (-1m)

carrk-grmeb-knowc
Carrowkeel K - Gran Menhir Brisé - Knowth
Grand menhir brisé d'Er Grah
Le Grand menhir brisé d'Er Grah, ou Men ar hroëc'h qui signifie « Pierre de la Fée » en breton ... est un menhir de dimensions exceptionnelles, le plus grand d'Europe : 18,5 m de hauteur lorsqu'il était dressé (20,4 m partie en terre comprise), 3 m de largeur, masse estimée à 280 t.
Ce menhir, dont l'érection remonterait au milieu du Ve millénaire av. J.-C. est aujourd’hui à terre et brisé en quatre morceaux. Il se dressait au milieu d'un ensemble monumental associant exceptionnellement, en un même lieu, les trois familles de monuments mégalithiques :
le tumulus d'Er Grah,
le cairn de la Table des Marchand,
le grand menhir brisé.
Wikimedia Commons
Cairn K at Carrowkeel in County Sligo
Cairns G and K are very fine with interesting cruciform chambers and double-lintelled entrances.
Cairn K, the highest point on Carrowkeel Mountain ... 8 meter long passage opens into a beautiful cruciform chamber which is orented to Queen Maeve's cairn on Knocknarea.
It has a diameter of 21 meters and is about 6 meters high, and is surrounded by a layer of bog which has covered any kerbstones which might surround the base of the cairn. The passage is 7 meters long and leads into a cruciform chamber with a beautiful corbelled ceiling 3 meters high. The passage and axis of the chamber is oriented to Queen Maeve's Cairn on the summit of Knocknarea, as are Cairns E, G and B. The summits of both Maeve's Cairn and Cairn K are at the same altitude.

rbrod-knoce-rolci
Ring of Brodgar - Knowlton Central Circle - Rollright Circle

rbrod-avecm-mohet
Ring of Brodgar - Avebury Circles - Mohenjo-daro East

maeho-ssten-unstc
Maes Howe - Stones of Stennes - Unstan Cairn
Maes Howe - Unstan Cairn
The Heart of Neolithic Orkney
... the results do not express margins of error in the method employed to determine coordinates. Those margins of error are greater at each data point than the resulting ratio is inaccurate ... For intra-site considerations with sites as close to each other as the Ring of Brodgar and the Stones of Stennes, the proportion of the margin of error to total arc distance is significant. Precision is essential for intra-site study because the builders could achieve direct measure. My results can be tested with better methods, and the closer the two sites to each other, the better the methods required. ....
The Heart of Neolithic Orkney KML includes intra-site pi relationships.

avocm-cdolm
Avebury Circle - Champ Dolent Menhir
Menhir de Champ-Dolent
Le menhir de Champ-Dolent est situé à Dol-de-Bretagne dans le département français d'Ille-et-Vilaine.
Le menhir ... un monolithe de forme conique en granite roux à petit grain qui a été extrait d'un site situé à plus de 4 km de distance. Il mesure 9,30 m de hauteur, ce qui en fait l'un des plus grands menhirs dressés de Bretagne. 1. Son périmètre est de 7 m au sol et de 8,70 m à 1,50 m du sol. Son poids est estimé à 50 T. Sa surface a fait l'objet d'un bouchardage.

avecm-durwa-knoce
Avebury Circles - Durrington Walls - Knowlton Henge

popoe-nocc-wohec
Poverty Point Earthworks - Observatory Circle - Woodhenge Circles
Poverty Point World Heritage Site
The central construction consists of six rows of concentric ridges, parts of which were as high as five feet. The ridges form a semi-ellipse or C-shape, divided into sections by at least four aisles. The diameter of the outermost ridge measures nearly three-quarters of a mile. It is thought that these ridges served as foundations for dwellings although little evidence of structures has been found. However, features and midden deposits uncovered during excavations support this hypothesis.
Poverty Point is indeed a rare remnant of an exceptional culture. It has been estimated that landscape preparation and earthworks construction may have required moving as many as 53 million cubic feet of soil.
Poverty Point Earthworks KML file

nocp-nccm-avocm
Newark Octagon - Eagle Mound - Avebury Circle
Newark Octagon - Avebury Circle - Thornborough South
nocp-avocm-thosc e-w ratio @ thosc = 1.0 : 0.003660 (-3m)
epoch hopewell ld = 0.0366010 lunar orbits per day
nocp-avocm-thosc e-w ratio @ thosc = 273.2453 : 1.0 (-3m)
epoch neolithic dl = 27.3216749 days per lunar orbit
Wikimedia Commons

chhha-avocm-thosc
Chavin de Huantar A - Avebury Circle - Thornborough South Center
Stonehenge and Pi

intiw-avebc-thorc
Intihuatana GPS - Avebury Cove Megalith - Thornborough

nocp-nccm-thosc
Newark Octagon - Eagle Mound - Thornborough South
Thornborough Henges and the Ure-Swale Monuments
Assessing Evidence of Geospatial Intelligence in the Neolithic
Jan. 17, 2007 - Inquiry into the geospatial relationships of the Thornborough Henges (to each other and to other Neolithic monuments in the greater viewscape and surrounding landscape) evidences a large regional pattern of monument placement and knowledge of the true scale of the earth. ....
Wikimedia Commons

ncec-nocc-knoce
Great Circle - Observatory Circle - Knowlton Henge
Observatory Mound - Knowlton Henge - Knossus Small Palace
noom-knoce-knosp arcs ratio @ knosp = 1.0 : 0.314162 (+22m)
Newark Archaeogeodesy, Assessing Evidence of Geospatial Intelligence in the Americas
... ground plan represents the actual spatial relationship of the Octagon and Great Circle features of the Newark works to scale. Newark Earthworks has been termed the largest geometric earthwork in the world. The Octagon is certainly the largest single North American geometric earthwork form at 2898.5 feet long. While several earthen circles in Ohio are larger in diameter, Newark's Great Circle likely represents the largest circular work in labor investment. The Great Circle (ncec) is actually an ellipse, measuring 1189 by 1163 feet (mean 358.4 m). The Octagon's Observatory Circle (nocc) is nearer a true circle at 1059 by 1050 feet (mean 321.4 m). The Newark circles are centered over a mile apart, at about 1,934 meters. ....

ncec-fenix-ssten
Great Circle - Aguada Fenix - Stones of Stennes

avocm-ssten-tifag
Avebury Circle - Stones of Stennes - Tifariti Goulet
Stones of Stenness Circle and Henge | Historic Environment Scotland
Step back in time over 5000 years at what may be the earliest henge monument in the British Isles. ...
The Stones of Stenness today consist of four upright stones up to 6m in height in a circle that originally held 12 stones. The focus of the interior was a large hearth. The stones were encircled by a large ditch and bank ....

barnt-ergar-winhi
Barnenez Tumulus - Er Grah Tumulus - Windmill Hill
Tumulus d'Er Grah
Chronologie 4500 à 4000 av. J.-C.

smict-tdmar-lpemo
St. Michel Tumulus - Table des Marchand - Le Petit Mont

Barnenez II - Table des Marchand - Le Petit Mont
epoch neolithic do = 365.2566851 days per orbit

avebc-grmeb-kerga
Avebury Cove - Grand Menhir Brisé - Kergadiou Menhir
Avebury Obelisk - Grand Menhir Brisé - Kergadiou Menhir
avebo-grmeb-kerga e-w ratio @ kerga = 1.0 : 0.618061 (+9m)
Kergadiou menhirs
Kergadiou menhir ... 8.8 metres tall ... beautifully and perfectly smoothed and shaped menhir ... to the northeast is its neighbour, another king sized menhir which unfortunately is not standing upright ... 11 metres in length ...
From these two giant menhirs, it is possible to see the Kerloas menhir when the modern trees are not in leaf ...

nesqc-huamo-acong
Newark Square - Huaca Moxeke - Aconcagua GPS
Early Monumental Architecture on the Peruvian Coast
Moxeke-Pampa de las Llamas complex covers about 220 ha with two major platform mounds and intervening terraced plazas on the site's 1.1 km long centerline (Pozorski and Pozorski 1987b:31). The Moxeke mound measures 170 m by 160 m by 30 m., is tiered with rounded corners, has several terraces and a central atrium (Pozorski and Pozorski 1987b:33). The final rebuilding used massive stone blocks, including carefully shaped and polished square ashlars. The front wall has enormous niches with high relief sculpture. ....

octag-chhha-cotop
Octagon Earthwork - Chavin Huaca A - Cotopaxi

nocp-mapic-salka
Newark Octagon - Machu Picchu Courtyard - Salkantay GPS

carcp-hidol-huacp
Caral Circular Plaza - Huaca de los Idolos - Huaca A Circular Plaza

lomxc-salka-huasc
Loma X Zanja 2100 x 1550m - Salkantay GPS - Huascarán GPS

datdt-denal-huasc
Datong Drum Tower - Denali GPS - Huascarán GPS
Expedición Científica al Huascarán 2017

secal-nocp-nccm
Sechin Alto - Newark Octagon - Eagle Mound
Newark Octagon - Sechin Circular Plaza - Huaca A Circular Plaza
Pre-Inca Astronomy in Peru J. McKim Malville
The major mound of Sechin Alto was the largest structures in the western hemisphere at that time and has rarely been surpassed. With a current base of approximately 73000 sq meters, a top of perhaps 39000 sq meters and a height of 35 meters, its volume is approximately 2,000,000 cubic meters. The average orientation of its sides is 65.3°, close to the rising sun at June solstice. ...
The large mound of Sechin Alto has a U-configuration facing June solstice sunrise. The major axis of the entire Sechin Alto site covers a length 1130 meters. The other smaller mounds in its vicinity have similar orientations. The main mound of Taukachi-Konkán has a U-configuration and a well-defined axis with length of 1136 m and an orientation of 64°. Sechin Bajo is the smallest of the three, with an axial length of 330 meters. It contains a U-shaped structure opening to June solstice sunrise. All of the sites of the Sechin Alto polity have circular as well as rectangular plazas, ranging in size from, 170,000 sq meters (Sechin Alto) to 1800 sq meters (Taukachi-Konkán) ...

noom-noe-pdsol
Observatory Mound - Octagon Apex - Piramide del Sol
Observatory Mound - Octagon Apex - Pyramid of the Moon
noom-noe-pmoon arcs ratio @ noom = 1.0 : 1.0003141 (-0.2m)
Newark Octagon - Observatory Mound
Teotihuacan, the Largest Prehistoric City in the Americas

Llactapata Sector V - Castillo - Ingapirca
Montaña Machupicchu - Itza Nunnery Pyramid - Ingapirca
mmapi-itnup-ingap n-s ratio @ mmapi = 1.0 : 0.314165 (-17m)
Urubamba Intihuatana GPS - Caracol - Ingapirca
uinti-carac-ingap n-s ratio @ uinti = 1.0 : 0.314164 (+18m)

nocga-chhha-chupa
Newark Octagon Gateway - Chavin de Huantar A - Chupan
Understanding Chavín and the Origins of Andean Civilization
Chavín was once compared to the Olmecs and depicted as the Mother Civilization of the Andes. The term Chavín has been applied to a developmental stage of Andean history, to an archaeological period, to an art style and to a hypothetical empire. Chavín has been interpreted as a culture, a civilization and a religion. ....

carcp-chanb-tinya
Caral Circular Plaza - Chankillo B - Tinyash

chana-chupa-tinya
Chankillo A - Chupan - Tinyash
Chankillo, Peru, Ancient Solar Observatory?
2007.03.02 - Chankillo Thirteen Towers news is getting global headlines: ....