Golden Kilometres

Navigational system


From the earlier work I came to the conclusion that there was a high probability of a viable navigation system covering the whole of this area and quite possibly a much wider area. The system could then have been used to produce maps using the myriad of points created by the pentacles themselves and the alignment lines running in every direction. To create maps, however, the measurements of the pentacles would have to be known.

Fibonacci Proportions

build-10-12 Thus using 1,2,3,5,8 etc as dimensions of the various components of a pentacle will not work, it will not be possible to predict the size of other components.

What is always true is that the dimensions are still related to the golden number. Thus in this diagram A/B is always 1.618(….)even though the individual lengths may not be Fibonacci numbers.

build-2-9 This diagram shows Fibonacci numbers which are sufficiently high in the series to make this possible.
Using the numbers 34,55,89,144,233,etc will make it possible to predict the size of other components.

All the main dimensions will be numbers from the Fibonacci Sequence.


build-4-1 it would then be possible to predict the distance between North-South alignment lines (and every other set of alignment lines)

build-4-2 By the successive use of the properties of triangles more and more information about distances between the alignments be obtained . Here the distance between two points of a pentacle ,and therefore the side of the enclosing pentagram can be calculated. now howe.ver we are using the other side of the use of pentacles , that the size of angles is known and repeatable

build-10-13 Here distances between N-S alignment lines and E-W alignment lines are being calculated.

build-4-4 It would have been within the capability of many of those carrying out surveying work to carry out these calculations.

cassini-triangulation However unlike triangulation, surveyors in the field would not have to work out these dimensions in the way shown here , they could be read from tables. These calculations only had to be performed once as all the pentacles are specifically constructed to be identical. Here for comparison is another look at the preliminary notes made by Cassini, showing the enormous variation in the measurements and triangles he was using.


internal-alignments And then another look at the criss crossing lines of the pentacles themselves and the alignment lines, an absolute lacework available in which every dimension is known. extremely useful in the production of maps but giving no clear clues as to the location of the Treasure. Perhaps putting a X on a map did not give adequate protection. The location would have to be hidden in some cryptic clue but could that be based on a knowledge of the navigation system?

Wouldn’t it be wonderful if there was a unit of measurement which gave a match for these higher fibonacci numbers and could be used to construct pentacles “on the ground”


google-measure-6-11 Armed with the knowledge that there is a “golden number” relationship between kilometres and royal french miles, the measurement tool in google earth was switched from Miles to Kilometers. I had been previously been measuring distances in miles because several writers had talked in favour of the real measurements having been made in chains, rods or perches which are all subdivisions of a mile.

Now I concentrated on Kilometres and took the very first measurement across the side of a pentacle. It is displayed as a yellow measurement lineof value 6.11 Kilometers * 0.6172 =3.77 miles =377 Centi-milles. 377 is a Fibonacci number and sufficiently large for the golden number relationships to apply.

Why is the Conversion number not a perfect golden number? it is all to do with the use of decimal places. I believe it is the 6.11 measurement which is slightly wrong not the centi-milles.


google-measure-3-78 It should come as no surprise that this second measurement also converts to a member of the fibonacci series.

The numbers are high enough in the series for the relationship to be valid. 3.78 Kilomenters * 0.6172 = 233 centi-miles

google-measure-2-33 And so it continues. A centi-milles is one hundredth of a French Royal mille. I can find no confirmation for it’s existence but it seems a reasonable assumption that it would have been used was used.


google-measure-1-44 2.33 Kilometers converts to another Fibonacci number(144) In fact every measurement converts to a Fibonacci number.

In this case 1.44 converts to 89 Centi-Milles.

google-measure-3-78-and-table The side of the enclosing pentagram is also a Fibonacci number. Now another relationship is revealed.

If the metric distances had been measured in Centi-Kilometers (a unit of 10 meters) then the metric measurements would also be Fibonnaci numbers but always on higher in the series that the cent-mille equivalent!

build-2-12 These metric numbers therefore give rise to the Fibonacci relationship which applies to every pentacle including the Rennes pentacle.

All the distances in alignments, calculated at the bottom of the navigation construction page, apply to all the alignment lines running in every direct without any further conversion.

Nesting Pentacles

google-measure-2-33-small The Fibbonaci numbers also dictate the dimensions of the smaller pentacles.

In this case 2.33 kilometres is the side of the middle sized pentacle, is the same as the side of one of the points of the larger pentacle of value 144.

google-measure-1-44-small Obviously once once key dimension of the middle sized pentagon is found to be a Fibonacci number all the other key dimensions will also be Fibonacci numbers.

Every dimension is predictable.

google-measure-0-55-small This dimension is the side of the pentagon enclosing the smallest pentacle.

Therefore key dimensions of the smallest pentacle should also be Fibonacci numbers or should they?

google-measure-0-34-v-small Certainly the side of the point seems to comply

System Breakdown

google-measure-0-22-v-small But here finally the relationship breaks down. As can be seen from the table to generate the fibonacci number 13 as a centi-mille measurement. The dimension should be 0.21 Kilomenters but in fact it is 0.22. this is because we have now come to low in the series for the golden relationship to be valid.


I find all this interesting and surprising. It means that it is possible that there was a viable navigation system which could be used to draw maps on which the location of the treasure could be marked. Alternatively the system of pentacles itself could be used to locate the hiding place. This second method could be codified and without a knowledge of how the navigation system works be difficult to penetrate. But does any of this give us a clear idea of where the treasure is or might be? No! emphatically not!

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The most dangerous woman in the world

The Treasure of Trencavel

List of Characters

Table Of Contents



List of Places

Table of Contents

Pseudo History


Extract from The Prisoner of Foix--Chapter 43 -The EntranceNo need to buy a Kindle. Read it on your computer or tablet

John Stanley-26th April 1355


'Looks like we are going to see a bit of excitement, John. The Captain tried to get an agreement from the Prince that if there is surf running across the channel to Arcachon we will turn back to Bordeaux, but the Prince would hear none of it. Instead, he has offered to provide insurance for all three ships. If they are damaged or sunk, the owners will be compensated and every sailor who makes the passage will be given a bounty payment. What none of this seems to take into account is that if we sink in rough, fast-flowing waters we might all drown.'

John raised his eyebrows. 'But that is what we are going to do?'

'Yes, despite the fact that surf running accross the entrance is not uncommon and the deep water channel moves continually. In the end, the Prince attacked their captains on their weakest point, their professional pride! He threw down the gauntlet. He offered to take the Sally first through the channel, and to take control during the passage.' He raised his brow. 'We are going into the Bay of Arcachon, come what may! '

Extract from The Eagle of Carcassone -- Chapter 24-- A Real GoddessNo need to buy a Kindle. Read it on your computer or tablet

John Stanley - 22 July 1355

An hour later John walked with Ximene close to the river along the valley below St Feriole. It was the very essence of a summer’s day. The sun was fierce but in the shadow of the trees, it was cool and fragrant. The trees and shrubs along the riverbank hid their progress, from the Château, from St Feriole.

Eventually they reached a point where John thought it was safe to emerge from cover. To his satisfaction the stream extended into a pool with a sandy beach, shaded by trees. Where the stream entered the pool there was a flat grassy area, almost circular. Behind this, the bulk of two mountain ridges provided a splendid backdrop. He looked around once more ‘Not just a good training ground but a great training ground. If the Greek heroes knew about this they might be tempted to join me, to train with me’

Ximene laughed out loud. He turned to look at her. She had removed her outer clothes and was wearing a white chemise, cut short so that it barely reached her knees. Around her waist, she wore a plaited leather belt, obviously fashioned from the multitude of leather straps to be found in the tackle room.

She ran her hands down over her breasts. ‘When you were unconscious I heard you muttering about gods and goddesses, so  I have decided that from now on, for you, I will be the goddess.’

The Prisoner of FoixVol 1 of the series—The Treasure of Trencavel

Aquitaine, an English possession, is in crisis. It is under threat from neighbouring nations and internal dissension.

The Black Prince, King Edward III’s eldest son has been given the task of taking command in Aquitaine.

Suddenly there is an opportunity. Ximene Trencavel is the heiress to the lands of Occitan, to the east of Aquitaine: lands controlled by the Franks. Ximene wants independence, both for herself and for Occitan.

A union between Aquitaine and Occitan would be mutually beneficial. The Black Prince undertakes a secret journey to meet Ximene to negotiate a marriage contract. It is, however, a marriage neither of them really wants.

Meanwhile, the  Franks plot to murder Ximene to prevent ,not just the marriage, but any kind of union between England and Occitan.

The Eagle Of CarcassonneVol II of the series—The Treasure of Trencavel

The loose alliance between Ximene Trencavel and the Black Prince is under threat.

The Prince invades Occitan, to show his support for Ximene but it becomes an invasion which creates more problems than it solves.

The Prince has fallen hopelessly in love with Joan of Kent and Joan is now determined to marry him and become the next Queen of England.

Joan is therefore  determined to convince Ximene that she should not marry the Prince.

Part of her strategy is to encourage Ximene’s relationship with John Stanley—one of the Princes bodyguards—not an easy task as both John and Ximene have doubts about their compatibility.

However, John is grievously injured in a battle and Ximene commits herself to nurse him back to health.