Ancient Monument Phi Ratios
Archaeogeodesy is defined as an area of study encompassing prehistoric and ancient place determination, point positioning, astronomy, geodynamic phenomena, measure and representation of the earth, surveying, and navigation on land or water.

Phi Ratios
Stated simply, the golden mean or golden ratio divides a line such that the whole is proportional to the longer part as the longer part is to the shorter part. The golden ratio, x : 1 = 1 : x + 1, stated numerically is 0.618034... : 1.0 = 1.0 : 1.618034..., where Phi like pi is an infinite irrational number (1.6180339887...). Upper case Phi represents 1.618... and lower case phi is 0.618..., Phi  1 = phi. I tend to ignore the Greek, italicized upper and lower case convention, refer to both in lower case, and reference the ratio moreso than the values. The formula obtains from a triangle with sides 2 : 1 and thus a hypotenuse equaling the square root of five. The values equate to half of two sides, [(one plus the square root of five) divided by two] and to [(one minus the square root of five) divided by two]. The x  1 = y and x + 1 = y formulations have relevance in astronomy orbit ratios.
 

Observatory Mound  Acre Octagon arc 51.827238° cosine = 0.618035 (6m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
In 2022 I examined the spatial relationship of the Acre Octagon with Newark Octagon and noted the cosine of their arc distance equals phi. I also noticed Acre Octagon is twice as far from the North Pole as Newark Octagon. More octagon relationships study results: Download Octagons KLM  jqjacobs.net/kml/octagons.kml 
Observatory Circle  Acre Octagon  North Pole noccnpoleacroc arcs ratio @ npole = 1.0 : 0.499999 (6m)

51.8273° cosine = 0.618034 My GPS readings produced a 51.52° azimuth from the center of Observatory Mound to the gateway at the opposite apex of the Octagon work (noom +/5m to noe +/5m, 863m arc). The arc distance from the Newark Octagon's Observatory Mound to the Acre Octagon (noomacroc) equals 51.827238° (cosine = 0.618035). The angle's cosine equals phi (51.827292° cosine = 0.618034...), which matches both the earthwork's azimuth and the lunar major azimuth. Observatory Mound lunar major for 462 C.E. = 51.8273° (474 C.E. at the Octagon centerpoint). Middleton reported a 51.45° azimuth for the Observatory Circle and a mean of 51.98° for the parallel earth banks between the Octagon and Observatory Circle. According to Thomas (1894), the Octagon's azimuth is 52.15° E. of N. A four to pi right triangle has a 51.854° angle. A four to five right triangle has a 51.34° angle. Temporal Epoch Calculations discusses the Newark Octagon azimuth, the lunar major alignment, and possible interpretations.

Intiwatana UTM  Chavin Plaza Circular arc : ns ratio = 1.0 : 0.618027 (5m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 Chavin de Huantar Archaeogeodesy 
Ceremonial Rock  Huanuco Pampa Ushnu arc : ns ratio = 1.0 : 0.618030 (2m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0  
Waynapicchu  Chavin Plaza  Huanuco Pampa Ushnu mwaynchhpqhuapu arcs ratio @ mwayn = 1.0 : 0.921493 (+1m) epoch inca mn = 0.921493 moons per lunar nodal period  
Web Archive 
Observatory Mound  Poverty Point Earthworks  Etzanoa Circle arcs ratio @ popoe = 1.0 : 0.618047 (+15m) phi ratio 1.0 : 0.618034 = 1.0 : 1.618034 
Eagle Mound  Tumi Chucua Zanja  Ute Circle arcs ratio @ nccm = 1.0 : 2.618053 (16m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 Phi squared ratio 1.0 : 2.618034... 
Ute Circle  La Plata Circle utecilplac ns : ew @ uteci = 1.0 : 0.628418 (+2m) pi * 2.0 = 6.283185… Holmes Group article with lidar image of La Plata Circle. 
Ute Circle, one of several Southwest great circles, is smaller than Tumi Chucua and larger than the Great Circle. The two circles in my graphic illustrating their relative sizes are based on mean radii. The sixteen meter circle in the center is the margin of error for the centeroncenter arc distances ratio from Eagle Mound at the center of Newark's Great Circle. 
Octagon Gateway  Poverty Point A  Pueblo Colorado Circle ew ratio @ pcolc = 1.0 : 0.618036 (+6m) ew ratio @ popma = 1.0 : 0.618028 (10m) ew ratio @ nocga = 1.0 : 2.618050 (6m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Observatory Circle  Tumi Chucua Mound  Pueblo Colorado Circle nocctuchmpcolc arcs ratio @ nocc = 1.0 : 0.365010 (2m) epoch hopewell lr = 0.0365011 lunar orbits per rotation 
Observatory Circle  Caracol  Salkantay GPS ew ratio @ salka = 1.0 : 0.618024 (18m) ew ratio @ nocc = 1.0 : 0.618061 (+29m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Observatory Circle  Castillo  Cerro Sallqantay nocccastisallq ew ratio @ nocc = 1.0 : 0.618032 (2m) nocccastisallq ew ratio @ sallq = 1.0 : 0.618035 (+1m) 
Observatory Circle  Machupicchu Courtyard  Salkantay GPS noccmapicsalka arcs ratio @ mapic = 1.0 : 0.0031422 (+4m) Web Archive 
Observatory Circle  Castillo  Gran Caverna II ew ratio @ nocc = 1.0 : 0.618038 (+5m) ew ratio @ grcav = 1.0 : 0.618032 (3m) ew ratio @ casti = 1.0 : 2.618023 (+3m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Octagon Gateway  Castillo  Intipata Middle Ruin nocgacastiintmr ew ratio @ nocga = 1.0 : 0.618020 (9m) nocgacastiintmr ew ratio @ intmr = 1.0 : 0.618039 (+9m) nocgacastiintmr ew ratio @ nocga = 1.0 : 2.618070 (15m) Web Archive 
Eagle Mound  Chavin Plaza  Puerto de la Luna ew ratio @ chhpq = 1.0 : 0.618041 (+5m) ew ratio @ pluna = 1.0 : 0.618031 (4m) ew ratio @ nccm = 1.0 : 2.618041 (+4m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Eagle Mound  Chavin Lanzon  Puma Punku nccmchhlapupup ew @ pupup 1.0 : 0.618017 (26m)

Octagon  Poverty Point A  Pachacamac ew ratio @ popma = 1.0 : 0.618009 (40m) ew ratio @ nocp = 1.0 : 0.618099 (+40m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Octagon Gateway  Poverty Point Earthworks  Acre Octagon ew ratio @ nocg = 1.0 : 0.600004 (+7m) ew ratio @ acroc = 1.0 : 0.624998 (4m) ew ratio @ acroc = 8.000021 : 5.0 (4m) 
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 semiellipse or Cshape, divided into sections by at least four aisles. The diameter of the outermost ridge measures nearly threequarters 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. 
Great Circle  Poverty Point A  Rio Branco Double Quadrangle ew ratio @ ncec = 1.0 : 0.618044 (+10m) ew ratio @ rbrdq = 1.0 : 0.618030 (10m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Newark Octagon  Poverty Point Earthworks  Rio Branco Double Quadrangle nocppopoerbrdq arcs ratio @ nocp = 1.0 : 0.199999 (4m) 
Octagon Gateway  Monte Alban Sunken Plaza  Rio Branco Double Quadrangle nocgamaspzrbrbq arcs ratio @ maspz = 1.0 : 0.666668 (+8m) 
Machupicchu Serpent Rock  Tumi Chucua Zanja  Liberty Circle ew ratio @ mpqsr = 1.0 : 0.618035 (+1m) ew ratio @ libci = 1.0 : 0.618034 (1m) ew ratio @ tuchz = 1.0 : 2.618031 (+1m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Machupicchu Windows  Tumi Chucua Mound  Liberty Circle machwtuchmlibci ew ratio @ machw = 1.0 : 0.618037 (+3m) 
Great Circle  Liberty Circle  Tumi Chucua Zanja nceclibcituchz ew ratio @ ncec = 1.0 : 0.027382 (+5m) nceclibcituchz ew ratio @ ncec = 36.520555 : 1.0 (+5m) epoch hopewell yd = 0.0027379 years per day Eagle Mound  Liberty Circle  Tumi Chucua Zanja nccmlibcituchz ew ratio @ nccm = 1.0 : 0.027393 (6m) nccmlibcituchz ew ratio @ nccm = 1.0 : 36.50539 (6m) epoch hopewell rl = 27.3964671 rotations per lunar orbit Web Archive 
Waynapicchu  Sillustani Stone Tower I  Puma Punku ew ratio @ mwayn = 1.0 : 0.618027 (3m) ew ratio @ sils1 = 1.0 : 0.618052 (+5m) ew ratio @ pupup = 1.0 : 2.617987 (+3m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Ceremonial Rock  Sillustani  Puma Punku ceremsillupupup ew ratio @ cerem = 1.0 : 0.618037 (+1m) Web Archive Web Archive 
Intimachay  Loma X  Huascarán GPS ew ratio @ lomax = 1.0 : 0.618040 (+9m) ew ratio @ intim = 1.0 : 0.618018 (14m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Machupicchu Portal  Loma X  Puma Punku mappolomaxpupup ns ratio @ mappo = 1.0 : 0.618017 (6m) 
Huascarán GPS  Loma X huasclomax arc 14.323676° = 0.2499953 r (30m) 
Huascarán GPS  Rio Branco Double Quadrangle  Loma X huascrbrdqlomax ew ratio @ rbrdq = 1.0 : 0.365236 (7m) epoch inca dy = 365.242257 days per year Huascarán GPS  Rio Branco Double Quadrangle  Loma X Zanja huascrbrdqlomxz ew ratio @ rbrdq = 1.0 : 0.365257 (+1m) epoch inca do = 365.256392 days per orbit web.archive.org 
Tikal I  Aztec Hubbard TriWall Kiva  Primer Edificio Sunken Plaza ew ratio @ ahtwk = 1.0 : 0.618035 (+5m) ew ratio @ tikp1 = 1.0 : 0.618030 (8m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 Aztec Ruins National Monument 
Rio Branco Double Quadrangle  Rio Branco Circle  Acrelandia Double Square ew ratio @ rbrci = 1.0 : 0.617897 (9m) ew ratio @ rbrdq = 1.0 : 2.618393 (6m) ew ratio @ acrds = 1.0 : 0.618086 (+6m) arcs ratio @ acrds = 1.0 : 0.618299 (+28m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0  
Rio Branco Double Quadrangle  Rio Branco Square  Acrelandia Double Square rbrdqrbrsqacrds ew ratio @ acrds = 1.0 : 0.618182 (+16m) rbrdqrbrsqacrds arcs ratio @ acrds = 1.0 : 0.618467 (+45m)  
Rio Branco Double Quadrangle  Acre Double Parallelogram  Acrelandia Double Square rbrdqacrdsacrdp arcs ratio @ rbrdq = 1.0 : 0.499943 (6m) rbrdqacrdsacrts arcs ratio @ rbrdq = 1.0 : 0.500145 (+15m)

Tumi Chucua Zanja  La Loma  Amazonas Double Square ew ratio @ lloma = 1.0 : 0.618074 (+12m) ew ratio @ tuchz = 1.0 : 0.617930 (19m) ew ratio @ amazd = 1.0 : 2.618307 (12m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0

Great Circle Gateway  Tula Pyramid A  Pachacamac Huaca Sol ns ratio @ pachs = 1.0 : 0.618036 (+13m) ns ratio @ tulaa = 1.0 : 0.618028 (21m) ns ratio @ ncgc = 1.0 : 2.618050 (13m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Great Circle  Tula Pyramid A  Pachacamac Huaca Sol ncectulaapachs ns ratio @ pachs = 1.0 : 0.618043 (+52m) Web Archive 
Observatory Circle  Piramide del Sol  Pumasillo ns ratio @ pumas = 1.0 : 0.618033 (7m) ns ratio @ pdsol = 1.0 : 0.618037 (+11m) ns ratio @ nocc = 1.0 : 2.618026 (+7m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0  
Chavin Plaza  Pumasillo  Puma Punku chhpqpumaspupup great circle 180.01815° @ pumas
Web Archive 
Newark Octagon  Dzibilchaltun  Chavin Huaca A ns ratio @ chhha = 1.0 : 1.618038 (9m) ns ratio @ dzibl = 1.0 : 1.618032 (+9m) ns ratio @ dzibl = 1.0 : 1.618032 (+9m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Newark Octagon  Dzibilchaltun  Chavin Plaza nocpdziblchhpq ns ratio @ chhpq = 1.0 : 1.618033 (+3m) Web Archive 
Chavin Plaza Circular  Pachacamac III  Puma Punku ns ratio @ pupup = 1.0 : 0.618037 (+2m) ns ratio @ parp3 = 1.0 : 0.618026 (4m) ns ratio @ chhpc = 1.0 : 2.618054 (+2m) Web Archive 
Machupicchu Carved Rock  Huaca de la Luna latitude ratio = 1.0 : 0.618036 (+3m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Waynapicchu  Huaca del Sol centerline mwaynhdscl latitude ratio = 1.0 : 0.618041 (+11m) Waynapicchu  Huaca del Sol mwaynhdsol latitude ratio @ hdsol = 1.0: 0.618015 (28m) Web Archive Web Archive 
Waynapicchu  Huaca del Sol centerline  Huayna Potosi ns ratio @ mwayn = 1.0 : 0.618042 (+3m) ns ratio @ hdscl = 1.0 : 1.618042 (4m) ns ratio @ hpoto = 1.0 : 2.618013 (+3m) 
Waynapicchu  Huaca del Sol centerline mwaynhdscl latitude ratio = 1.0 : 0.618041 (+11m) Waynapicchu  Huaca del Sol mwaynhdsol latitude ratio @ hdsol = 1.0: 0.618015 (28m) 
Huaca del Sol centerline  Huayna Potosi hdsclhpoto latitude ratio @ equator = 1.0: 0.500006 (+12m) Web Archive Web Archive 
Llactapata Sun Temple  Waynapicchu  Montaña Machupicchu ns ratio @ mwayn = 1.0 : 0.617829 (+1m) ns ratio @ mmapi = 1.0 : 0.618570 (1m) ns ratio @ llact = 1.0 : 2.616633 (+1m) Web Archive Web Archive 
Ceremonial Rock  Acre Triple Square  Tumi Chucua ns ratio @ cerem = 1.0 : 0.618026 (3m) ns ratio @ tuchz = 1.0 : 0.618055 (+5m) ns ratio @ acrts = 1.0 : 2.617980 (+3m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Acre Triple Square  Octagon Gateway acrtsnocga arc 51.853756° tan = 1.273230 (24m) pi : 4.0 = 1.0 : 1.273240 
Acre Triple Square  Observatory Mound acrtsnoom north pole arc distance ratio = 1.0 : 0.500000 (+4m) 
Acre Triple Square  Sphinx acrtssphip ew 98.561162° = cir / 3.65255 (+34m) ew 98.561162° = 100.000313 so (+34m) Web Archive 
Machupicchu Portal  Loma X  Puma Punku ns ratio @ mappo = 1.0 : 0.618017 (6m) ns ratio @ lomax = 1.0 : 0.618077 (+10m) ns ratio @ pupup = 1.0 : 2.617921 (+6m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 
Aguada Fenix  Chimborazo GPS  Aconcagua GPS ns ratio @ acong = 1.0 : 0.618033 (6m) ns ratio @ chimb = 1.0 : 0.618037 (+10m) ns ratio @ fenix = 1.0 : 2.618027 (6m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0 Wikimedia Commons 
Caral Pyramid  Aguada Fenix  Garopaba Sambaqui ns ratio @ fenix = 1.0: 0.618035 (+7m) ns ratio @ carap = 1.0: 0.618030 (12m) ns ratio @ fenix = 1.0: 2.618044 (7m) 
Caral Circular Plaza  Aguada Fenix Pyramid  Chimborazo GPS carcpfenipchimb arcs ratio @ carcp = 1.0 : 0.300003 (+11m) Web Archive 
Site Longitudes 
Site Coordinates Newark Octagon GPS readings and derived coordinates viewed in Google Earth. 
Aconcagua it the highest summit in the Americas as well as the Southern hemisphere. 






Web Archive Wikimedia Commons 
"Intimachay is a small cave situated on the eastern terraces of Machu Picchu. It is a rather empty space accidentally left between natural formations of big granite blocs constituting most of the Machu Picchu hill. However, this natural cavity has been intentionally reshaped to serve for some interesting activities ... two tunnel windows evidently serving for astronomical observations." 

"The orientation of Llactapata’s Sun Temple .... A stonelined channel leads from the primary door of the temple and is directed at Machu Picchu’s Sacred Plaza." 
Web Archive Web Archive Web Archive Web Archive Web Archive Web Archive Web Archive 


Wikipedia: Emperor Qin Shi Huang Ancient Monument Latitudes Evidence Accurate Astronomy Ancient Monument Placemarks 