Great Circles, Ancient Monuments, and Pi

White Pyramid  Piramide del Sol  El Paraíso pdsolepara arc = 38.198387° pdsolwhitp arc 120.003662° arcs ratio @ pdsol = 1.0 : 3.141590 (+4m) pi 3.14159265… : 1.0 : 0.3183099… 
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 onethird of earth's circumference and onethird 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 centeroncenter 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 coexisting 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. 
White Pyramid  Piramide del Sol  Piramide de la Luna mean arc @ whitp 120.00030° = cir / 2.9999924 (+34m) mean arc @ whitp 120.00030° = 0.3333342 cir (+34m) Teotihuacan, the Largest Prehistoric City in the Americas 
Observatory Circle  Tumi Chucua Mound ns : ew ratio @ tuchm = 10.0 : 3.14157 (14m) pi = 3.14159265… : 1.0 : 0.3183099… 
Observatory Mound  Tumi Chucua Mound noomtuchm ns 51.198828° noomtuchm ew 16.289942° ns : ew ratio @ tuchm = 10.0 : 3.14192 (+19m) 
Observatory Mound  Tumi Chucua Zanja noomtuchz ns : ew ratio @ tuchz = 10.0 : 3.14175 (+89m) 
Tumi Chucua Zanja  Apu Illimani GPS arc 5.729995° = 0.1000073 radians (+46m) arc 5.729995° = cir / 62.8272778 (+46m) pi * 2.0 = 6.2831853... : 1.0 : 0.159154943…  
Machupicchu Courtyard  Tumi Chucua Zanja  Apu Illimani GPS mapictuchzailli ns ratio @ tuchz = 1.0 : 0.366242 (0.1m) epoch inca ry = 366.2422185 rotations per year

Tikal III  Machupicchu Torreon  Luxor Pylon arcs ratio @ macht = 1.0 : 0.318309 (14m) arcs ratio @ macht = 1.0 : 3.141600 (14m) pi 3.14159265… : 1.0 : 0.3183099… 
Tikal Citadel  Montaña Machupicchu  Karnak Hypostyle Hall tikcimmapikarhh arcs ratio @ mmapi = 1.0 : 3.141594 (2m) Web Archive 
Tikal Radial Pyramid  Newark Octagon Mean  Durrington Walls arcs ratio @ tikrp = 1.0 : 0.314160 (+8m) pi 3.14159265… : 1.0 : 0.3183099… 
Tikal Radial Pyramid  Newark Octagon Mean tikrpnoctm ew 7.180746° sine = 0.125000 (1m) 
Intimachay  Newark Octagon Mean  Ring of Brodgar intimnoctmrbrod ew ratio @ noctm = 1.0 : 0.125000 (+0.3m) 
Tikal II  Newark Octagon  Durrington Walls tikp2nocpdurwa arcs ratio @ tikp2 = 1.0 : 0.314160 (+6m) 
Tikal Radial Pyramid  Octagon Gateway  Durrington Walls Circle tikrpnocgaduwac arcs @ tikrp = 1.0 : 0.314159 (+1m) 
Durrington Walls durwa lat : lon = 1.0 : 0.628364 pi * 2.0 = 6.2831853... : 1.0 : 0.159154943... Web Archive 
Tikal Citadel  Monks Mound  Monte Alban South Pyramid arcs ratio @ tikci = 1.0 : 0.318312 (+4m) arcs ratio @ tikci = 1.0 : 3.141574 (+4m) pi 3.14159265… : 1.0 : 0.3183099…  
Tikal Radial Pyramid  Monks Mound  Monte Alban Plaza Pyramid mm34ctikrpmalpp arcs ratio @ tikrp = 1.0 : 3.141480 (+27m)  
Poverty Point Earthworks  Monks Mound  Monte Alban South Platform popoemm34cmalsp ew ratio @ mm34c = 1.0 : 0.800000 (0.3m) mm34c latitude 38.6605208° tangent = 0.8000204

Tikal I  Monte Alban South Platform  Pueblo del Arroyo TriWalled Kiva arcs ratio @ malsp = 1.0 : 0.318312 (+5m) arcs ratio @ tikci = 1.0 : 3.141574 (+5m) pi 3.14159265… : 1.0 : 0.3183099… 
Tikal Great Plaza  Monte Alban Plaza  Pueblo del Arroyo Kiva C tikgpmalpppuarc arcs ratio @ malpp = 1.0 : 3.141597 (1m) Web Archive 
Tikal V  Caracol arc 3.600066° = 0.0314165 d (+7m) arc 3.600066° = 0.0100002 cir (+7m) pi 3.14159265… : 1.0 : 0.3183099… 
Tikal Acropolis  Caracol tikaccarac arc 3.600056° = 0.0314164 d (+6m) 
Tikal V  Denali GPS  Huascarán GPS tikp5denalhuasc arcs ratio @ huasc = 1.0 : 3.141527 (+67m) pi 3.14159265… : 1.0 : 0.3183099… 
Tikal Radial Pyramid  Denali GPS tikrpdenal latitude ratio = 1.0 : 0.273033 (+1m) epoch hopewell or = 0.0027303 orbits per rotation Web Archive Web Archive 
Tikal III  Calakmul Pyramid  Caracol arcs ratio @ calap = 1.0 : 0.318316 (2m) arcs ratio @ calap = 1.0 : 3.141537 (2m) pi 3.14159265… : 1.0 : 0.3183099… 
Tikal III  Calakmul Pyramid tikp3calap arc 0.900060° = 0.0025002 cir (+7m) 
Tikal V  Caracol tikp5carac arc 3.600026° = 0.03141615 d (+3m) Web Archive 
Chavin Portal  Khufu Pyramid  Khafre Pyramid chhapkhugp ew 108.312096° chhapkhafr ew 108.308648° khugpkhafr ew 0.003448 ew ratio @ chhap mean 108.31037° sine = 0.314164 (+34m) 108.310067° = asin 0.314159 ew ratio @ khugp = 1.0 : 31,413.02 (+0.04m) ew ratio @ khafr = 1.0 : 31,412.02 (+0.05m) pi 3.14159265… : 1.0 : 0.3183099…
Web Archive 
Octagon Gateway  Chavin de Huantar Portal  Khufu Pyramid khugpchhap ew 108.312096° cosine = 0.314193 khugpnocga ew 113.580922° cosine = 0.400044 cosine ratio = 1.0 : 1.273243 pi : 4.0 = 1.0 : 1.273240 
Chavin de Huantar Portal  Khufu Pyramid  Khafre Pyramid chhapkhugpkhafr mean ew 108.310372° cosine = 0.31416432 (+34m) Understanding Chavín and the Origins of Andean Civilization Web Archive 
Newark Octagon  Khufu Pyramid  Khafre Pyramid khugpkhafr ns 0.003208° nocpkhugp ns 10.075501° nocpkhafr ns 10.078709° ns ratio @ khugp = 1.0 : 3,141.742 (0.02m) ns ratio @ khafr = 1.0 : 3,140.742 (+0.10m) pi 3.14159265… : 1.0 : 0.3183099… 
Newark Octagon  Khufu Pyramid nocpkhugp ew 113.578470° cosine = 0.400005 (+32m) Web Archive 
Sechin Alto Cuarto  Ring of Brodgar  Khafre Pyramid ew ratio @ khafr = 1.0 : 0.314159 (3m) pi 3.14159265… : 1.0 : 0.3183099… 
Taukachi Circular Plaza  Ring of Brodgar  Khufu Pyramid takcprbrodkhugp ew ratio @ khugp = 1.0: 0.314158 (14m) 
Sechin Bajo  Sphinx secbasphip arc 111.469762° cosine = 0.366010 (+2m) ld = 0.036601 lunar orbits per day 
Chankillo A  Khufu Pyramid chanakhugp arc 111.485331° cosine = 0.366263 (+44m) ro = 366.2566 rotations per orbit Web Archive 
Chavin Plaza  Waden Mound  AmunMut Axes ew ratio @ pylon = 1.0 : 0.314159 (+2m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Avebury Circles  The Rounds  Khufu Pyramid arcs ratio @ wimbl = 1.0 : 31.416981 (4m) pi 3.14159265… : 1.0 : 0.3183099…

Newgrange A Cairn  Khufu Pyramid  Khafre Pyramid newackhugp arc 35.999682° = 0.0999991 cir (35m) newackhafr arc 36.000377° = 0.1000010 cir (+42m) mean arc @ newac 36.00003° = 0.314159524 d (+3m) mean arc @ newac 36.00003° = 0.1000001 cir (+3m) pi 3.14159265… : 1.0 : 0.3183099…  
During the Neolithic, obliquity of the ecliptic equaled 24 degrees, twothirds of this arc distance.  
Newgrange A Cairn  Denali GPS newacdenal arc 59.999544° = 0.1666654 cir (51m)  
Newgrange A Cairn  Denali GPS  Khufu Pyramid newacdenalkhugp arcs ratio @ newac = 1.0 : 0.599999 (5m) newacdenalkhugp 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.
Web Archive 
Knowth GPS  Windmill Hill arc 3.600055° = 0.0314164 d (+6m) arc 3.600055° = 0.0100002 cir (+6m) pi 3.14159265… : 1.0 : 0.3183099…  
Rath Cormac  Longstones Cove racorlonco arc 3.600030° = 0.0314162 d (+3m)

Newgrange  Knowth GPS  Silbury Hill arcs ratio @ newgc = 1.0 : 0.003143 (+1m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Avebury Circle  Newgrange Circle  Rollright Circle arcs ratio @ avocm = 1.0 : 6.282486 (+7m) pi * 2.0 = 6.2831853... : 1.0 : 0.159154943… ns ratio @ rolci = 1.0 : 3.143727 (41m) pi 3.14159265… : 1.0 : 0.3183099… 
Stonehenge  Rollright Circle stoncrolci arc : ew ratio = 1.0 : 0.314387 (+14m) 
Avebury Circles  Stonehenge  Rollright Circle avecmstoncrolci arcs ratio @ rolci = 1.0 : 1.414235 (1m) sqrt 2.0 = 1.41421356… Web Archive 
Carrowkeel K  Gran Menhir Brisé  Knowth arcs ratio @ carrk = 1.0 : 6.283248 (1m) pi * 2.0 = 6.2831853... : 1.0 : 0.159154943…
Wikimedia Commons 
Ring of Brodgar  Knowlton Central Circle  Rollright Circle ew @ knoce = 1.0 : 0.314171 (+2m) pi 3.14159265… : 1.0 : 0.3183099… The Heart of Neolithic Orkney KML includes intrasite pi relationships. 
Maes Howe  Stones of Stennes  Unstan Cairn arcs ratio @ maeho = 1.0 : 3.14183 (0.1m) pi 3.14159265… : 1.0 : 0.3183099…  
Maes Howe  Unstan Cairn maehounstc ns : ew @ maeho = 1.0 : 3.14354 (0.7m)
Web Archive 
Avebury Circles  Durrington Walls  Knowlton Henge ns ratio @ durwa = 1.0 : 1.2732210 (1.5m) ns ratio @ durwa = pi : 4.00022 (1.5m) pi : 4.0 = 1.0 : 1.2732395… Web Archive 
Poverty Point Earthworks  Observatory Circle  Woodhenge Circles arcs ratio @ popoe = 1.0 : 0.159159 (+26m) arcs ratio @ popoe = 1.0 : 6.283040 (+26m) pi * 2.0 = 6.2831853... : 1.0 : 0.159154943...

Avebury Circle  Champ Dolent Menhir ew 0.114604° = 0.002000 cir ew 0.114604° = cir / 3,141.25161 (+1.4m) pi 3.14159265… : 1.0 : 0.3183099…
Web Archive 
Newark Octagon  Eagle Mound  Avebury Circle arcs ratio @ nocp = 1.0 : 0.000314 (4m) arcs ratio @ nccm = 1.0 : 0.000314 (4m) pi 3.14159265… : 1.0 : 0.3183099… 
Newark Octagon  Avebury Circle  Thornborough South nocpavocmthosc ew ratio @ thosc = 1.0 : 0.003660 (3m) epoch hopewell ld = 0.0366010 lunar orbits per day nocpavocmthosc ew ratio @ thosc = 273.2453 : 1.0 epoch neolithic dl = 27.3216749 days per lunar orbit Wikimedia Commons 
Newark Octagon  Eagle Mound  Thornborough South arcs ratio @ nccm = 1.0 : 3,141.11144 (+0.3m) arcs ratio @ nocp = 1.0 : 3,140.98352 (+0.4m) pi 3.14159265… : 1.0 : 0.3183099…
Wikimedia Commons 
Great Circle  Observatory Circle  Knowlton Circle arcs ratio @ ncec = 1.0 : 3,141.169 (+0.2m) pi 3.14159265… : 1.0 : 0.3183099…

Avebury Circle  Stones of Stennes  Tifariti Goulet arcs ratio @ tifag = 1.0 : 1.273245 (13m) pi : 4.0 = 1.0 : 1.273240

Barnenez Tumulus  Er Grah Tumulus  Windmill Hill arcs ratio @ ergar = 1.0 : 3.141418 (+8m) pi 3.14159265… : 1.0 : 0.3183099…
Web Archive Web Archive 
St. Michel Tumulus  Table des Marchand  Le Petit Mont ns ratio @ smict = 1.0 : 3.140832 (+0.4m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive Web Archive 
Barnenez II  Table des Marchand  Le Petit Mont ns ratio @ tdmar = 1.0 : 0.031830 (0.13m) ns ratio @ tdmar = 1.0 : 31.41695 (0.13m) pi 3.14159265… : 1.0 : 0.3183099… arcs ratio @ lpemo = 1.0 : 0.036525 (0.05m) epoch neolithic do = 365.2566851 days per orbit Web Archive 
Intihuatana GPS  Avebury Cove Megalith  Thornborough arcs ratio @ avebc = 1.0 : 0.031415394 (5m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Avebury Cove  Grand Menhir Brisé  Kergadiou Menhir ns ratio @ kergas = 1.0 : 0.314154 (2m) pi 3.14159265… : 1.0 : 0.3183099…  
Avebury Obelisk  Grand Menhir Brisé  Kergadiou Menhir avebogrmebkerga ew ratio @ kerga = 1.0 : 0.618061 (+9m) phi ratio 1.0 : 0.618034... = 1.618034... : 1.0
Web Archive 
Chavin de Huantar A  Avebury Circle  Thornborough South Center arcs ratio @ avocm = 1.0 : 0.031417 (+6m) pi 3.14159265… : 1.0 : 0.3183099… Stonehenge and Pi 
Huaca Moxeke  Newark Square  Aconcagua GPS ns ratio @ acong = 1.0 : 3.141574 (+15m) pi 3.14159265… : 1.0 : 0.3183099…

Octagon Earthwork  Chavin Huaca A  Cotopaxi ew ratio @ cotop = 1.0 : 0.314166 (+3m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Newark Octagon  Machu Picchu Courtyard  Salkantay GPS arcs ratio @ mapic = 1.0 : 0.003142 (+3m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Caral Circular Plaza  Huaca de los Idolos  Huaca A Circular Plaza ew ratio @ carcp = 1.0 : 0.314047 (9m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Ring of Brodgar  Avebury Circles  Mohenjodaro East ns ratio @ avecm = 1.0 : 0.31416041 (+3m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Loma X Zanja 2100 x 1550m  Salkantay GPS  Huascarán GPS ns ratio @ lomxc = 1.0 : 0.314161 (+1m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Datong Drum Tower  Denali GPS  Huascarán GPS ns ratio @ denal = 1.0 : 0.318311 (+6m) ns ratio @ denal = 1.0 : 3.141585 (+6m) pi 3.14159265… : 1.0 : 0.3183099…

Sechin Alto  Newark Octagon  Eagle Mound ew ratio @ nocp = 1.0 : 314.18888 (0.14m) pi 3.14159265… : 1.0 : 0.3183099…  
Newark Octagon  Sechin Circular Plaza  Huaca A Circular Plaza nocpseccphuacp ew @ huacp = 1.0 : 314.21737 (0.27m)
Web Archive 
Observatory Mound  Octagon Apex  Piramide del Sol arcs ratio @ noom = 1.0 : 0.0003140 (+0.4m) pi 3.14159265… : 1.0 : 0.3183099… 
Observatory Mound  Octagon Apex  Pyramid of the Moon noomnoepmoon arcs ratio @ noom = 1.0 : 1.0003141 (0.2m) 
Newark Octagon  Observatory Mound arc 0.005735° = 0.0001001 r (+0.55m) arc 0.005735° = 0.0000159 cir (+0.55m) pi * 2.0 = 6.2831853... : 1.0 : 0.159154943… Teotihuacan, the Largest Prehistoric City in the Americas 
Llactapata Sector V  Castillo  Ingapirca ns ratio @ lla05 = 1.0 : 0.314155 (18m) pi 3.14159265… : 1.0 : 0.3183099… 
Montaña Machupicchu  Itza Nunnery Pyramid  Ingapirca mmapiitnupingap ns ratio @ mmapi = 1.0 : 0.314165 (17m) 
Urubamba Intihuatana GPS  Caracol  Ingapirca uinticaracingap ns ratio @ uinti = 1.0 : 0.314164 (+18m) Web Archive 
Newark Octagon Gateway  Chavin de Huantar A  Chupan ns ratio @ chupa = 1.0 : 0.0031415985 (+0.03m) pi 3.14159265… : 1.0 : 0.3183099…

Caral Circular Plaza  Chankillo B  Tinyash ns ratio @ tinya = 1.0 : 0.314170 (+2m) pi 3.14159265… : 1.0 : 0.3183099… Web Archive 
Chankillo A  Chupan  Tinyash ns ratio @ chana = 1.0 : 3.143262 (9m) pi 3.14159265… : 1.0 : 0.3183099…
Wikimedia Commons 