**
Great Circles, Ancient Monuments, and Pi**

2018.03.14 - Happy Pi Day - This KML file includes selected study results presenting the value of pi and tau, the ratios of circumfernce of a circle to diameter and to radius respectively.

**Space Archaeology**

Celebrating a decade of space archaeology continues with this results upload. Current versions of my applet and global placemarks collection reflect recent research. The sites in this file are placemarked in the archaeogeodesy.kml file:

Archaeogeodesy Placemarks, Ancient Monuments in Google Earth v2018

Spanning the globe, more than 15,000 placemarks of ancient monuments and anthropogenic features visible in satellite imagery, reflecting a decade of space archaeology applied to ancient monument research. This file includes the 4,500+ monuments with coordinates in my Excel applet. Download - 3.8 MB Google Earth file: archaeogeodesy.kmlArchaeoGeodesy Applet v2018

Updated Excel application includes new sites from Amazon surveys and other recent research. Download - 2.3 MB Excel file: archaeogeodesy.xls

Links:

Permalinked on Pi Day 2012.Stonehenge and Pi

The Heart of Neolithic Orkney placemarks feature several intra-site pi relationships.

More archaeogeodesy study results linked in the ArchaeoBlog pages.

©2018.03.14 by James Q. Jacobs, all rights reserved.

Cite as *Great Circles, Ancient Monuments, and Pi*

http://jqjacobs.net/kml/pi.kml with access date.

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 one to pi. The ratio is precisely pi 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.

White Pyramid - Piramide del Sol - El Paraíso

pdsol-whitp arc 120.003662°

pdsol-epara arc = 38.198387°

arcs ratio @ pdsol = 1.0 : 3.141590 (+4m) ]]>

mean arc @ whitp 120.00030° = cir / 2.9999924 (+34m) ]]>

n-s : e-w @ tuchz = 1.0: 0.314175 (+89m)

n-s : e-w° = 3.143164 : 1.0

]]>

arc 11.445241° = circumference / 31.4541224 (10.01216 pi) ]]>

arc 5.729177° = circumference / 62.8362506 (20.0014 pi, -44m)

arc 5.729177° = 0.099993 radians ]]>

arcs ratio @ mptor = 1.0 : 3.1415956 (-9m) ]]>

arcs ratio @ tgpp2 = 1.0 : 0.3141600

tgpp2 - nocp e-w = asin 0.12500 ]]>

arcs ratio @ tikrp = 1.0 : 3.141480 (+27m) ]]>

arcs ratio @ malpp = 1.0 : 3.141597 (-1m) ]]>

arcs ratio @ calap = 1.0 : 3.141500 (+3m)

tikp3-calap arc 0.900060° = 0.00250017 cir (+7m)

calap-itcar arc 2.827539° = 3.1417097 grads

itcar-tikp5 arc 3.600026° = 0.03141615 d (+3m) ]]>

arcs ratio @ popma = 1.0 : 3.141551 (+23m) ]]>

e-w cosine ratio @ khugp = 1.0 : 1.273243

pi : 4.0 = 1.0 : 1.273240

khugp-chhap e-w 108.312096° cosine = -0.314193

khugp-nocga e-w 113.580922° cosine = -0.400044

chhap-khugp-khafr mean e-w 108.310372° cosine = -0.31416432 (+34m) ]]>

khugp-nocp e-w 113.578470° cosine = -0.400005 (+32m)

n-s @ khugp = 1.0 : 3,141.742

n-s @ khafr = 1.0 : 3,140.742 ]]>

e-w mean 108.31037° = asin -0.3141643

108.310067° = asin -0.314159

e-w @ khugp = 1.0 : 31,413.02 ]]>

e-w ratio @ khugp = 1.0 : 0.314158 (-13m) ]]>

e-w ratio @ khafr = 1.0 : 0.314158 (-11m)

khugp-rbrod-tausp e-w = 1.0 : 0.314158 (-13m)

khugp-sechh arc 111.469124° cosine = -0.366000 (-69m)

ld = 0.036601 lunar orbits per day

khugp-chana arc 111.485331° cosine = -0.366263 (+44m)

ro = 366.2566 rotations per orbit

secal-huass-khugp great circle @ Huascaran = 179.982° (28m) ]]>

arcs ratio @ wimbl = 1.0 : 31.416981 (-4m) ]]>

n-s ratio @ silhi = 1.0 : 314.197926 (-1m) ]]>

mean arc 36.00000 degrees = 0.3141589 diameters

mean arc = circumference / 10.000001 (-4.5m)

Newgrange A is the largest earthen circle at the Boyne complex.

The center of the henge is the stone cairn. ]]>

arcs ratio @ avocm = 1.0 : 6.282486 (+7m)

two pi = 6.2831853...

n-s ratio @ rolci = 1.0 : 3.143727 (-41m)

stonc-rolci arc : n-s = 1.0 : 0.314387

avecm-stonc-rolci arcs ratio @ rolci = 1.0 : 1.414235 (sq root of 2, -1m) ]]>

arcs ratio @ carck = 1.0 : 6.28324

arcs ratio = r : cir ]]>

e-w @ knoce = 1.0 : 0.314171 (+2m)

e-w @ rbrod = 1.0 : 1.314171 (+2m) ]]>