PENTAGRAMS AND PENTAGONS November 2 2019

When you looked well at image 3 in Part 1 you were probably able to distill a kind of form from it.

The position of 4 crop formations with almost the same distances between them makes it possible to construct a Pentagon. 

 

These cropformations are:

22- Nielles, 9 -Torigni s. Vire, 17- Lidon and 25- Pouilloux

Distances between them:

22-9 = 297 km 

9-17 = 295 km

17-25 = 286 km

The mean distance is 292,6666....km.

To construct the Pentagon: place the “compass point” in 22-Nielles and 25-Pouilloux and measure 292,6666...km. 

On the point where they cross lies the fifth corner of the Pentagon.

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A Pentagram is drawn in the Pentagon

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The distance between 22-Nielles and 8-Menetou is 402 km. 

4-Moisselles lies exactly 201 km from 22-Nielles and 8-Menetou..... 

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A second -black- Pentagon and Pentagram can be drawn, taking a starting point at the formation near Houdain (21). The Pentagram and Pentagram have different sizes than the first ones because the distance from 9-Torigni s. Vire to 21-Houdain is greater. It is slightly more deformed than the first Pentagon. 

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The combined Pentagrams. In these images you see more information which rather astonished me but I will address this in Part 4 of this series.

 

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THEORETICAL PENTAGON AND PENTAGRAM

The pentagon and pentagram as I have drawn are not “perfect” because the length of the sides differ slightly (292, 293, 286, 295 and 297 km). The mean distance is the total of these / 5 = 292,6666....

It is interesting to see how much the found values differ from an “ideal” pentagon/gram so I put the value of 293 for one side of the pentagram in the calculator and there we have all the values:

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How much does our pentagon (with five sides of different lenght) differ from a "perfect" pentagon with five equal sides?The perimeter of the Nielles Pentagon is 1.463 km.

An “ideal” pentagon with sides of 292,666...=> 293 km has a perimeter of 1.465 km.

Our pentagon only differs 2 km or 0,1365%.....from a "perfect" pentagon.

 

Phi relationship?

It would be interesting to see if the characteristics of a theoretical pentagon/gram apply to our pentagram.

In a pentagon/-gram the line segments have a mathematical relationship to each other where Phi and Phi squared play an important role. 

In a later update of this Part 2 I will do some more measurements and see if this works for this pentagon as well.

 

There certainly is a Phi ánd a Phi squared relationship between my pentagon and pentagram:

 

Pentagon and Pentagram Nielles

Length pentagon = 1.463 km

Length pentagram = 2.362 km

Phi values in pentagram 1 : 1,61803399

Phi = 1,61803399 x 1.463 = 2.367,18 km

Difference = 5 km or 0,2%!!!

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A rather silly "mind experiment" is this:  

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Is there a Phi relationship between the total distance of Moisselles to all other crop formations in France and the total length of the pentagon/pentagram?

Total distance of Moiselles to all crop formations in France = 3.675 km.

Length pentagon = 1.463 km 

Phi squared x length pentagon = 2,61803399 x 1.463 = 3.830 km

Difference = 155 km or 4%.... 

 

Lengte pentagram 2.362 km

Phi x length pentagram = 1,61803399 x 2.362 = 3.821

Difference 3.821 - 3.675 = 146 km or 3,84%.......

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CONCLUSION

Constructing the pentagon and pentagram was an interesting "mind experiment" which came forth from the shape I meant to see in the locations and connecting lines between the French crop formations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Of course there was no crop formation on the constructed fifth corner of the pentagon but maybe in the future there will be one? 

The constructed pentagon and pentagram have the overall characteristics to be called so although they are not perfect because the distances between the four crop formations differ.

Although the difference is not much (297, 295 and 286 km) it prevents the pentagon being "perfect".

It was a great surprise to see that the total distance of Moisselles to the other French crop formations have Phi relationships with the pentagon and pentagram as well.

 

UPDATE November 4

Although the location of the crop formation near Torigni-sur-Vire compared to it's supposed location near Gieville does not have very much influence on the shape of the pentagram.

There is a slight difference though....

Here you see the white and the blue pentagram and the construction circles combined.

Note that the white and blue lines don't cover each other because of the different location of the crop formation near Torigni.

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The white and blue construction circles pass at very close distance of the crop formation near Treuzy and very close to Notre Dame de Paris......

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Treuzy

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And Notre Dame de Paris......

Please read more about the relationship between the crop formation near Moisselles , Notre Dame cathedral in Paris and........Stonehenge in Part 4 of this series. But first Part 3 Hexagon and Hexagram ......

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