Dharma Initiative - Mathematical Forecasting Initiative

Sacred Geometries powered by Google Maps

Locate weird geometrical shapes on the places you love

Tool created by Mariano Tomatis

The tool here provided can be used to find weird (maybe sacred?) geometries on maps provided by Google®, starting from two points defined by the user.

1) Specify in decimal format latitudes and longitudes of the two key points of your geometry (use a DMS-to-decimal converter if you need it).

You can verify the correctness of your coords by clicking "View" buttons.

2) Select one of the four shapes from the icons on the left and click on it, to draw it on the map starting from the two points.

		° Latitude	View »
		° Longitude

		° Latitude	View »
		° Longitude

How to get latitude and longitude from Google Maps

Center the map on the point you want and paste in the URL bar of your browser this command:

javascript:void(prompt('',gApplication.getMap().getCenter()));

Default settings

Default settings refer to the Magdala Tower in Rennes-le-Château and the Blanchefort Castle, both in the French region of Aude. According to Henry Lincoln, the mountain top of Rennes-le-Château and of four other adjacent mountain tops precisely mark out a pentagram, the tips of a five-pointed star that stretches across the landscape.

Coordinates

Starting from the two points specified by the user, the calculation of vertices is performed with trigonometrical formulas, with a proper correction because of the spherical surface of the Earth.

At first, the longitude of each point is divided by cosine of latitude. Then, the coordinates of other points are calculated. At the end, all points are multiplied by cosine of latitude.

Triangles

Two points on a map define two distinct equilateral triangles.

Given the coordinates of the two points (ll1,lt1) and (ll2,lt2), points #3 are defined this way:

Triangle A

Point #A3

ll3 = cos(120°)×(ll2-ll1) - sin(120°)×(lt2-lt1) + ll2

lt3 = sin(120°)×(ll2-ll1) + cos(120°)×(lt2-lt1) + lt2

Triangle B

Point #B3

ll3 = cos(120°)×(ll1-ll2) - sin(120°)×(lt1-lt2) + ll1

lt3 = sin(120°)×(ll1-ll2) + cos(120°)×(lt1-lt2) + lt1

Squares

Two points on a map define three distinct squares (they may define a side in two different ways A,B or its diagonal in one way C).

For triangle C, it is useful to define the median point (llM,ltM) as ((ll1+ll2)/2,(lt1+lt2)/2).

Square A

Point #A3

ll3 = cos(90°)×(ll2-ll1) - sin(90°)×(lt2-lt1) + ll2

lt3 = sin(90°)×(ll2-ll1) + cos(90°)×(lt2-lt1) + lt2

Point #A4

ll4 = cos(90°)×(ll3-ll2) - sin(90°)×(lt3-lt2) + ll3

lt4 = sin(90°)×(ll3-ll2) + cos(90°)×(lt3-lt2) + lt3

Square B

Point #B3

ll3 = cos(90°)×(ll1-ll2) - sin(90°)×(lt1-lt2) + ll1

lt3 = sin(90°)×(ll1-ll2) + cos(90°)×(lt1-lt2) + lt1

Point #B4

ll4 = cos(90°)×(ll3-ll1) - sin(90°)×(lt3-lt1) + ll3

lt4 = sin(90°)×(ll3-ll1) + cos(90°)×(lt3-lt1) + lt3

Square C

Point #C3

ll3 = cos(90°)×(llM-ll1) - sin(90°)×(ltM-lt1) + llM

lt3 = sin(90°)×(llM-ll1) + cos(90°)×(ltM-lt1) + ltM

Point #C4

ll4 = cos(90°)×(llM-ll2) - sin(90°)×(ltM-lt2) + llM

lt4 = sin(90°)×(llM-ll2) + cos(90°)×(ltM-lt2) + ltM

Pentacles

Two points on a map define four distinct pentacles.

Pentacle A

Point #A3

ll3 = cos(72°)×(ll2-ll1) - sin(72°)×(lt2-lt1) + ll2

lt3 = sin(72°)×(ll2-ll1) + cos(72°)×(lt2-lt1) + lt2

Point #A4

ll4 = cos(72°)×(ll3-ll2) - sin(72°)×(lt3-lt2) + ll3

lt4 = sin(72°)×(ll3-ll2) + cos(72°)×(lt3-lt2) + lt3

Point #A5

ll5 = cos(72°)×(ll4-ll3) - sin(72°)×(lt4-lt3) + ll4

lt5 = sin(72°)×(ll4-ll3) + cos(72°)×(lt4-lt3) + lt4

Pentacle B

Point #B3

ll3 = cos(72°)×(ll1-ll2) - sin(72°)×(lt1-lt2) + ll1

lt3 = sin(72°)×(ll1-ll2) + cos(72°)×(lt1-lt2) + lt1

Point #B4

ll4 = cos(72°)×(ll3-ll1) - sin(72°)×(lt3-lt1) + ll3

lt4 = sin(72°)×(ll3-ll1) + cos(72°)×(lt3-lt1) + lt3

Point #B5

ll5 = cos(72°)×(ll4-ll3) - sin(72°)×(lt4-lt3) + ll4

lt5 = sin(72°)×(ll4-ll3) + cos(72°)×(lt4-lt3) + lt4

Pentacle C

Point #C3

ll3 = cos(144°)×(ll2-ll1) - sin(144°)×(lt2-lt1) + ll2

lt3 = sin(144°)×(ll2-ll1) + cos(144°)×(lt2-lt1) + lt2

Point #C4

ll4 = cos(144°)×(ll3-ll2) - sin(144°)×(lt3-lt2) + ll3

lt4 = sin(144°)×(ll3-ll2) + cos(144°)×(lt3-lt2) + lt3

Point #C5

ll5 = cos(144°)×(ll4-ll3) - sin(144°)×(lt4-lt3) + ll4

lt5 = sin(144°)×(ll4-ll3) + cos(144°)×(lt4-lt3) + lt4

Pentacle D

Point #D3

ll3 = cos(144°)×(ll1-ll2) - sin(144°)×(lt1-lt2) + ll1

lt3 = sin(144°)×(ll1-ll2) + cos(144°)×(lt1-lt2) + lt1

Point #D4

ll4 = cos(144°)×(ll3-ll1) - sin(144°)×(lt3-lt1) + ll3

lt4 = sin(144°)×(ll3-ll1) + cos(144°)×(lt3-lt1) + lt3

Point #D5

ll5 = cos(144°)×(ll4-ll3) - sin(144°)×(lt4-lt3) + ll4

lt5 = sin(144°)×(ll4-ll3) + cos(144°)×(lt4-lt3) + lt4