 
 
Acre Octagon 150m 9.895957 67.519215 188 


Golden Mean Longitude 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 formula 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 is 1.618... and lower case Phi is 0.618..., Phi  1 = Phi. The golden ratio 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, [(the square root of five plus one) divided by two] and to [(square root of five minus one) divided by two]. Also, Phi squared equals Phi plus one. The x  1 = y and x + 1 = y formulations have relevance in the astronomy equations.

Observatory Mound  Acre Octagon arc 51.827238° cosine = 0.618035 (6m) phi ratio 1.0 : 0.618034 = 1.618034 : 1.0 
Observatory Circle  Acre Octagon noccacroc arc 51.827748° cosine = 0.618028 (+51m) 
Observatory Circle  Acre Octagon  North Pole noccnpoleacroc arcs ratio @ npole = 1.0 : 0.499999 (6m) 
Observatory Circle  Acre Octagon  North Pole noccacrocnpole arcs ratio @ npole = 1.0 : 0.499999 (6m) 
Observatory Mound  Acre Octagon noomacroc arc 51.827238° cosine = 0.618035 (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. 

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) 
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) 
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. 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. 
Observatory Circle  High Bank Octagon  Acre Octagon ew ratio @ nocc = 1.0 : 0.031409 (12m) pi to 8 decimals = 3.14159265 
Observatory Mound  Huaca del Sol centerline  Acre Octagon ns ratio @ hdscl = 1.0 : 0.036624 (1m) epoch hopewell ry = 366.242358 rotations per year 
Newark Octagon  Huaca del Sol  Acre Octagon nocphdsolacroc ns ratio @ hdsol = 1.0 : 0.036629 (+17m) epoch hopewell ro = 366.2564674 rotations per orbit 

Machupicchu Courtyard  Chavin Plaza  Acre Octagon ew ratio @ mapic = 1.0 : 0.921496 (+2m) epoch inca mn = 0.9214926 moons per lunar nodal period 
Waynapicchu  Chavin Plaza Circular  Acre Octagon ew ratio @ mwayn = 1.0 : 0.921503 (+6m) epoch inca mn = 0.921493 moons per lunar nodal period 
Intiwatana UTM  Chavin Plaza Circular intihchhpc arc : ns ratio = 1.0 : 0.618027 (5m) phi ratio: 1.0 : 0.618034 = 1.0 : 1.618034 