51 — Golden Numbers

John Stanley- 24th September 1355


we must not totally

Out of consideration of all four tablets we find 1,2,3, 8 and 21 amongst the other numbers

Suddenly I am quite excited

It means that we now have four numbers of the Fibonacci sequence. This series is generated by adding the last number in  the series to the next lower number. thus,1, 2, 3, 5, 8, 13, 21,34, are all members of the Fibonacci sequence.

The Fibonacci sequence is associated with what are called the golden ratios. The division of one number in the series by the previous and next numbers in the series in the sequence is known as the golden ratio, and exept for very small numbers it is a constant. either 0.681 or 1.681.  Golden ratio’s have been studied by mathematicians for at least two thousand years.

Some people would say that use of these ratios produces effects that are attractive to the human eye.

They have been used in the construction of the Acropolis in Greece and even earlier in the construction of the pyramids in Egypt.

Others say that they are more than just pleasing to the human eye, that the golden ratio’s are part of God’s plan.

Shellfish when dissected  show structures which follow the golden ratio. The petals of a flower and the  seed distribution at the centre of the flower, even the proportions of the human face and body all are examples of the golden ratio.

Of direct relevance to our search is that the numbers we have identified are associated with the construction of a pentacle, which is perhaps the ultimate application of the phenomenon of the golden ratios.

The movement of the planet Venus as observed from the earth traces the points of a pentacle in the sky.

And there is more than that here

Going back to the 1st tablet.  The number 18 is closely  associated with a perfect pentacle.  It is the origin  of a different series,  as is the sum of all the numbers of the first tablet, 36

18,36, 54, 72, 90,108. the series is made up by adding 18 to each number to generate the next number.

These all represent the angles applied in the construction of a perfect pentacle.

We have the proportions and the angles needed to construct a perfect pentacle.  Consequently, there is no doubt in my mind that the coded information in these paintings tells us that we should be looking for a pentacle as well as a triangle.

Estevan prowled round the church. John and Ximene sat on a pew waiting for him to return. I see no sign of a triangle or pentacle within this church they must therefore be external to the church. From the clues to be found here I think it is quite possible that this church marks a point of the pentacle or triangle, possibly both.

John’s eyes opened wide. Ximene jumped up and danced on the spot with excitement.

Estevan continued. ‘If you want to identify the other points, an indication of the direction in which one of the other points lies is needed.’

This information is undoubtably here. it is just a question of unravelling it.

Estevan sat on a bench, scribbled  and resorted sheet upon sheet of vellum, throwing some to one side as he became dissatisfied with the result.

We haven’t quite finised with the first two tablets

We ended up with 9+6 = 15, or 1 and 5 or 1+5 =6,   It has returned to 6 again

Now if we add the 6 from the second tablet to all the numbers derived from the first tablet

18+6= 24, or 2+4=6

8+6 = 14, or 1 and 4 or 1+4=5,

1+6 = 7

Add it to the total as well.

36+6=42, or 4+2 =6

He frowned and scratched his head. ‘So we now have  three sixes’s 666 is called the number of the beast; the devil’s number , so this may represent a  warning to those attempting to solve the puzzle not to go any further.

He shivered but continued.

If it is a warning we well ignore it. At least for now.

I am combining and recombining the numbers in many different ways.

That remarkable number 77  occurs twice more.

He drew a deep breath and walked half way down the aisle before turning

We already know are defining a pentacle and a triangle. These numbers must therefore define the size and orientation of both figures.

For the pentacle we know the internal angles but we do not know the orientation or indeeed  the length of a side. For the triangle we have lots of possibilities but no specific solutions.

Despite it being a remarkable number I don’t think 77 is involved in the solution it has simply been provided to confirm that we are on the right track. All the Fibbonachi numbers were provided to show that there was a pentacle involved but it is probable that some of the numbers are actually part of the solution

John groaned. ‘It all looked so promising  but now you are telling us that we have  learned nothing?’

Estavan smiled. ‘Not quite. on tablet 3 there were four lines of text with a large space underneath  there could have been more. Therefore 4 must have a special meaning. On all the strings I have identified and calculated two end up with the single numeral 4.  the calculted numbers in these two chains are 31 and 49. they are obviously very special numbers.

‘Let’s suppose that one leg of the pentacle is 31 degrees north of east then where would the next point of the pentacle lie? Either 72 degees in a northerly direction or 72 degrees in a southerly direction. 72 degrees in a southerly direction is 41 degrees south of east or 49 degrees east of south. 31 and 49! If I am correct  we now know the orientation of the pentacle.’

Hmm,  I am particularly interested in the number 66. It is not part of the Fibbonarchi sequence and it is in the region of what we might expect to be an angle of a triangle. the single number derived from this is 3.

Estevan’ voice rose even higher. Now suppose that the line of the triangle is 3 degrees north of the line of the pentacle that would make it 34 north of east. 34 is the sum of the prime numbers of the 3rd and 4th tablets and also one of the Fibbonachi numbers. If the angle of the triangle is 66 degrees them the southern leg of the triangle would be 32 degrees south of east which is 9 degrees away  from the 41 degees south  we identied for the next point of the pentacle  in a southerly direction  9 is the single digit number derived from the first tablet.

I have built a picture of the triangle and the pentacle in my head and the numbers I have chosen are the only numbers which fit.’

Estevan shook his head.  Now we come to the orientation of the church itself which probably has a meaning. It is approximately midday so I can see where the north lies.’

He rushed outside. When he returned he was smiling.

‘I can tell you that the orientation of the church and probably the north easterly arm of this pentacle is approximately 30 degrees north of east. Because of the work we have performed here I am very confident it will actually be 31 degrees north of east.  Thus we know that another arm of the pentacle will run at 5 degrees south of east.

He paused and looked carefully at Ximene and John.

“I do not know what has guided you here but you have found a place of great significance.

“As I said when we started, this a typical Numerology puzzle which the ancients loved and excelled in creating. When you find the other points on the pentacle you may find additional clues.

It was John and Ximene’s turn to glance at each other!

Estevan was still talking. ‘ i do not actually know the length between the points of the pentacle but they will almost certainly be fibbonachi numbers, 3 5,8? miles? leagues?’

I am now going to make a list of all the numbers and how many times they arose.

He started to make copies of the paintings. Ximene could see that he intended to continue to work on the puzzle. She took John to one side.

“I think we should show him the map.” she told him.

“I think he is right. The clues here were meant to lead a searcher to Château Mazerou but by an amazing stoke of fate we have already found what is there. Estevan works with don Fernandino. I think we should trust him. He will waste a lot of time trying to discover what we already know.’

John somewhat reluctantly agreed. It seemed to cut across the  principles of need to know, practiced by the Earl, but in the current circumstaces it seemed sensible.

Estevan agreed to accompany them back to the Château. There he was able to make a complete correlation between the clues at Brenac and the map. He produced a wooden disc around the circumference of which were marked regular subdivisions of the circle. The center of the disk had been cut away to be replaced with cross wires, which allowed him to make measurements from any point on the map using the crossed wires as a sighting device. He pointed out that the angles at the points of both the pentacles were all exactly 36 degrees, one of the numbers which had emerged from his investigations.

The northern side of the triangle was three degrees further north than the adjacent side of the pentacle, which ran from Brenac to Compagne. 31 and 34 degrees respectively. The angle between it and the southern side of the triangle was exactly 66 degrees., which meant that the southern line, The  line between Brenac and Quillian ran at 32 south of east  southern side of the triangle ran 9 degrees north of the  of the line between Brenac and Quillian

Estevan spoke in a quiet, almost reverent voice.

“All these were numbers emerged from my analysis of the Brenac paintings.

Everything on this map could have been deduced from the clues at Brenac but the map makes it much easier to visualize and therefore understand.” He put his measuring device away and looked carefully at the third side of the triangle.
“Ah!” he breathed.

“Of course! The number 666 was not a warning but a location. The north south side of the triangle is in fact the Paris Meridien. You have now had confirmed the exact location of the three sides of the triangle which the strange creatures in the paintings at Brenac were telling us we should look for. I knew that the Paris Meridien ran somewhere through here but I had never had the need to locate it precisely.

In the years when Christianity first became the official religion of the Roman Empire, all distances used to be measured from Jerusalem, the centre of Christendom. At some stage the Franks decided to measure all distances from Paris. The reference point they used was the peak of the hill of Monmartre. The line running north south through Paris became the “Frankish meridien.” It came into widespread use when the Franks ruled virtually all of Europe. It soon became common knowledge that either by plan or by accident, if a measurement is made on the same latitude as Jerusalem, the Longditude of Paris is exactly 666 leagues West of the longditude Jerusalem. It is referred to by some people as the devil’s line!

He looked back at the map.
“So, the intersections which you have started referring to as the targets, lie on the devil’s line. Now that is something to think about”

It was at that very moment, unannounced and without any warning that Thierry D’Arques returned.

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The Treasure of Trencavel

List of Characters

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Pseudo History