Updated: Jul 22, 2020
What I didn't expect, so far
So who is Saint Michael and what are these Michael lines across Europe? I set out to look into alignments first described by the Richer brothers and John Michell because Stonehenge is placed exactly at the same distance from the Mont Saint-Michel as it was from Saint Michael's Mount.
One thing that has surprised me is how important Stonehenge is to the Michael network. The Stonehenge Lundy distance is exactly 7 / 10 of the Stonehenge Michael Mount distance. Stonehenge and the two Michael Mounts make an almost perfect 6:6:7 triangle (the base is less than half a mile short of being 7 / 6 of the other two sides). Another curious find was that Saint Michael's Mount and Stonehenge are aligned along an azimuth that corresponds to sunrise on a Phi day at Saint Michael's Mount.
In fact the whole concept of Phi days was also intriguing: if you divide the 24 hour day by 1.618, or Phi, you are left with two periods of time, and if you then search for a day which has one of these periods of time of either daylight or darkness at a certain place (it is latitude dependant), you have a Phi day. What's amazing is that sunrise from these places on these days gives azimuths which match interesting alignments from these places. There are four such days in a year. For example, sunrise at Saint Michael's Mount on a Phi day in spring / summer gives an azimuth which matches the orientation of the Saint Michael's Mount - Stonehenge line. Sunrise on a autumn / winter Phi day from Saint Michael's Mount gives an azimuth which is very close to the Saint Michael Mount - Mont Saint-Michel line. The northern part of the European Michael line, which I've looked at so far, seems to be a succession of points on winter Phi day sunrise lines: Skellig Michael to Saint Michael's Mount, Saint Michael's Mount to Mont Saint-Michel, Mont Saint-Michel to Le Mans, Le Mans to Sacra di San Michele. (I haven't looked beyond here yet) And from each of these points along the winter line, there are summer Phi day sunrise lines radiating out of them, each with significant places on the line: Skellig Michael to the Rock of Cashel, Saint Michael's Mount to Stonehenge (via some interesting megalithic features such as Merrivale, Soussons Down Cairns, Grimlake Cist, and Easdon Hill), Mont Saint-Michel to Avranches and Rouen, and Le Mans to Chartres and Reims. Each of these places, with the exception of the neolithic ones such as Avebury, Stonehenge and the places I mentioned between Stonehenge and Saint Michael's Mount, has a famous cathedral. This suggests a transmission of knowledge of this network over centuries, as some of these places are definitely of Neolithic importance, and the great cathedrals are mostly Norman or French in the areas I've looked at so far. I didn't expect to find such precision with these lines over long distances, either over time or space. Was this network laid out thousands of years ago, and remembered as a whole, with its logic, or were the individual places that formed part of the network simply re-adapted to Roman, and then Christian times, but with knowledge of the system lost?
I have no idea how the precision of the network might have been achieved, but I don't doubt that it was. I feel a little like Alice, falling through the rabbit hole, a little bewildered but determined to follow the white rabbit, wherever he may go.
There have been other Michael alignments that have turned up unexpectedly, such as Skellig to Stonehenge to Brussels and Aachen, or Aix-le-Chapelle as it was known under Charlemagne, all places with Michael connections (Stonehenge has Michael connections if you think of it as part of the Saint Michael's Mount - Mont Saint Michel triangle): and the most surprising thing is that this alignment corresponds to a Michaelmas sunrise azimuth from Skellig to Stonehenge, then from Stonehenge to Brussels, then Brussels to Aachen, and then to Bonn - though Bonn has no obvious Michael connection that I can see.
There's Stonehenge to Cathedrale Saint-Michel in Carcassonne, via Notre-Dame-de Bayeux Cathedral, Saint-Patrice-du-Desert, Saint-Michel-sur-Loire, one of France's most loved places, Rocamadour, where the archangel's sword is embedded in a rock face.
And there are several 15th May alignments, for example Skellig to Dublin and Durham (and Durham Cathedral is significant in that it is the same distance from Mont Saint-Michel as is Skellig Michael, and also almost perfectly North of the Mont Saint-Michel), Saint Michael's Mount to Glastonbury and Avebury. There are also 15th May alignments from Rouens Cathedral to Amiens Cathedral, from Tumulus Saint-Michel to Kerkado Tumulus and Rennes, and from Kermario to Rennes Cathedral, and from Chartres Cathedral to Meaux Cathedral. The 15th May seems to be a point in the calendar which is at a Phi division between spring equinox and summer solstice. I've checked all the main religious calendars but there is no obvious feast on that day, the closest is on the 18th May: Vesak - Buddha Day. Saints Peter and Andrew do have their feast days on that day, though, as well as the Madrileno, Saint Isidore the Farmer, or San Isidro Labrador, whose feast day is May 15th. A kind and giving ploughman, he shared everything he had with the poor and with animals. I mention him only because he is often depicted with a staff, just like Saint Patrick and sometimes Saint Michael, or with a sickle and a sheaf of corn, or even a spade, which may be derived from an Ophiuchus image or archetype. His consort is Saint Maria de Cabeza.
They lived in XXIIth century Madrid. They had a son who fell into a well as a child, and who was saved because the water level rose enough to carry him back up. I wonder if the story of their lives was remembered through the lens of Ophiuchus and Virgo figures.
The Michael - Apollo - Artemis line through Europe connects places dedicated to Saint Michael, in North West Europe, and that there's a whole network of sites linked to these places by certain sunrise alignments. Possibly, the constellation the figure of the archangel Michael is derived from is Ophiuchus. In the tiny part of the Michael axis that was neither romanised nor invaded by the Normans (the builders of the great cathedrals), i.e. Western Ireland, one place possibly connected to this Michael axis is named after Saint Patrick, the Rock of Cashel in Tipperary. So perhaps Saint Patrick too is linked with an ancient deity connected to this line, possibly also derived from Sagittarius or Ophiuchus.
David Warner Mathisen, who has written extensively on star myths, has shown that the archangel Michael is strongly linked to Ophiuchus, with his sword and lance. Saint Patrick is also portrayed with a long stick, not quite a lance, but a staff, from top left to bottom right. David Warner Mathisen has shown that Artemis and Apollo can be understood as derived from the constellation Sagittarius, and as we move further down South along the line, there will be temples dedicated to Apollo and Artemis. See his very informative and fascinating posts: https://mathisencorollary.blogspot.com/search?q=artemis
He shows that stars, and specifically their arrangement into very old and very wide-spread figures which serve as archetypes for various heroes, deities, saints and angels, are at the root of so many stories and beliefs, that what the stars represent endures, against all odds, over hundreds of years. I think connecting a historical figure with a constellation is not only a way of understanding their power, perhaps as a rebirth of a heroic figure, be it spiritual or physical or military. It's also a way of keeping the story alive, a guarantee of longevity. Who knows, if we had a constellation for Spiderman, he might endure for thousands of years. At the moment, his longevity depends on Hollywood script writers and Chinese toy factories, i.e. market forces, not constellation stories. I hesitate to use Stalin's quote "It is not heroes that make history, but history that makes heroes" but I can't think of a better way to put it. The impact of these heroes and their stories on us, on our cultures is perhaps the single most influential thing on human minds, especially when these heroes are part of a religion. The stories that are passed on about these heroes become sources of inspiration as to how to lead our lives, how to think, what to aspire to, and how we treat others. The role of constellations in propagating and giving longevity to the stories that shape us cannot be overstated. We may no longer 'constellationise' our heroes, no more for, say, John Stuart Mill or Spiderman, whom I just mentioned, but we can hardly say that the gods, angels, prophets and saints of the religions that prevail where we live have no bearing on our lives, even if we do not hold membership of one religious group or another. When it comes to religion and myth, constellations are time.
Certain stars, together with the constellations they are part of, and the conventions with which these constellations are represented in the history of art, and referred to in myth, are crucial to important religious or mythical figures, such as Saints Michael and Patrick, and Apollo and Artemis. It is as if certain characters drawn out by the stars just won't go away and are able to survive various cultures over time under new names, as new gods or as a saint or an angel. Reincarnation is the order of the day, as much for human souls as for star figures, whose souls are poured into continually new forms, re-indeified. Gods, saints and angels appear as so many local and temporal vessels from millennia old constellation characters, and the stories that go with them. That's not to say there was never a man called Patrick in early Christian Ireland, or a man named Arthur in Roman Britain, or Isidro in Medieval Madrid, merely that the story of their lives was made to walk along a path already well trodden. The myth that followed them also preceded them.
There's a two way process I think: an already existing legend attached to a constellation is identified with a real person, perhaps during their lifetime or just after, who is then remembered as somehow pertaining to that constellation. So the constellation, as a human construct in the sky, gives the person or the god or the archangel its impetus and energy and character, and is in turn enriched by it, re-invigorated by it, changed but strengthened. From this constant play emerges an archetype, which can embody the fundamental characteristics of the mythical or religious figure, as well as the important details of the way they are portrayed. The visual element is very important, and it's thanks to the details of a certain way of standing, who a figure stands next to, and what they hold that we can piece back together the pieces of the jigsaw to see the many phases across time and place of these various archetypes. Not only is this a potentially eternal process, but eternity itself can be illustrated as a serpent biting it's tail.
Perhaps a better portrayal of this play between night sky and human story is the pair of snakes on the side of the cross at Monasterboice in Ireland, that I have mentioned already. One snake is directed upwards, one downwards, and between them, through the curvature of their entwined coils, emerge three heads. Who's is anyone's guess. The two snakes seem to give rise to these figures, just as the perpetual play between constellation, memory and imagination give rise to mythical and religious characters. For me, this snake play is the best way of illustrating the link between our oldest myths and stories with the stars.
Their stories are linked to certain times of the year because they are part of the solar year, and the movement of the planets and the constellations. What's more, their stories are linked to certain places at certain times of the year, possibly in part because of the latitude of these places. Certain feast days correspond to the perceived behaviour of the sun at a certain latitude, the dates of which are possibly dependant on latitude and its impact on the effects of the sun on Earth. Certain sacred sites correspond to a particular solar event, and are part of a network of sites all bound to each other by the design of people guided by astronomical concerns. Where the sun reveals itself at dawn, and for how long it lingers and provides light that day, determines special points in the calendar year and also determines special places on the planet. The golden ratio appears to define some of these spatial and temporal lines.
Many places dedicated to the Virgin Mary are in close proximity to places dedicated to Michael. Perhaps they are remnants of the worship of a Virgo figure, an indeification of a hearth or fertility figure, known elsewhere as Brid or Brighid for example. It has been shown very convincingly that the way the Virgin Mary is portrayed, when with child on her lap, is very similar to the way the Egyptian goddess Isis is portrayed. The antiquity of this convention of the goddess mother with a small boy on her knees, sometimes breastfeeding him, must be great. The constellation Virgo is located very close to Sagittarius, Scorpio, and Ophiuchus. She is also possibly a snake slayer. In fact, in the parish centre near where I live there is a small statue of the Virgin Mary standing on a snake, and this may is reminiscent of another aspect of the earth mother deity, but this time, Sumerian: the standing woman with a snake in each hand, though it's clear that these snakes have a positive connotation, unlike the one being trampled by the Virgin Mary.
If Scorpio is pursued by any one of these, be it Ophiuchus or Sagittarius, the idea of evil or darkness being defeated remains, and that can be associated with around about the 17th March, Saint Patrick's day, when the constellation Scorpio bites the dust and goes under the horizon. It seems to be about evil and darkness being run to the ground, or underground.
All the more so if then this happens near the spring equinox - say, if the sun rises on the spring equinox just as Antares, the brightest star in Scorpio, disappears for good (well, for a while...) Might the heliacal setting of Antares on a certain date be important? The defeat of the forces of darkness by light at the same time as the defeat of Scorpio by - well, whatever constellation it is, Sagittarius, Ophiuchus...
This would be quite impressive if you believed in reincarnation, and Scorpio's slayer (be it Sagittarius, Ophiuchus, or Hercules, or even Virgo) protecting the souls that go up and down the highway to the East. Michael is seen as a protector of people and a psychopomp. These constellations would be all the more influential if the Milky Way, which they are all close to, happened to be the equinoctial colure...
I think it all comes back to the sun and reincarnation - what constellation is the sun rising in? It seems that when the Milky Way moved along, over time, away from the East and West, other constellations took its place to ferry the souls up and down between heavens and earth - what mattered is that the souls had to go up and down in the East, where the sun rises, or in the West.
The Archangel Michael's role as a protector of souls remained fairly constant I think during the Middle Ages. In the Chanson de Roland, both Michael and Gabriel are invoked to take the soul of count Rolland to Paradise. Roland is Charlemagne's nephew, and he is killed at the battle of Roncesvalles, in Navarre, in the North of Spain, where Christians are fighting Muslims. Roland dies during the battle, and his death is told like this:
'He owns his faults, and God's forgiveness bids:
"Very Father, in Whom no falsehood is,
Saint Lazaron from death Thou didst remit,
And Daniel save from the lions' pit;
My soul in me preserve from all perils
And from the sins I did in life commit!"
His right-hand glove, to God he offers it
Saint Gabriel from's hand hath taken it.
Over his arm his head bows down and slips,
He joins his hands: and so is life finish'd.
God sent him down His angel cherubin,
And Saint Michael, we worship in peril;
And by their side Saint Gabriel alit;
So the count's soul they bare to Paradis.'
(translation by C. K. (Charles Kenneth) Moncrieff, http://www.gutenberg.org/cache/epub/391/pg391-images.html )
In the end, Charlemagne is pretty much the last man standing, and goes back to Aix-la-Chapelle, and cries.
The Michael - Apollo - Artemis line survives in part because of its place names, and because the Richer brothers studying Greece spotted a pattern. A surprising feature of this line has been the importance of the golden ratio. We've seen that in many other places actually on the Michael - Apollo - Artemis axis, if you follow a line with the same azimuth as sunrise on a day when daylight and darkness are in phi ratio, you arrive at a place named after Michael, or at a major cathedral, possibly built on a Neolithic place of importance, for example: from Saint Michael's Mount: you get to Glastonbury, or from Mont Saint-Michel, you get to Rouen and Aachen, famous for their cathedrals. (The city of Rouen had a church of Saint Michel but it's gone now). From Le Mans, on a phi day sunrise in summer line, you get to Chartres and Reims, famous for their cathedrals. In this way, the European Michael line has branches that radiate out along paths of sunrise on Phi days.
And the logic remains with winter Phi day sunrises: starting at Skellig Michael, off the coast of Kerry, the sunrise point on a winter phi day gives an azimuth which connects with Saint Michael's Mount, the next place on the line, then winter phi day sunrise at Saint Michael's Mount takes you to the Mont Saint-Michel, and so on. The European Michael line seems to be basically a series of points linked by sunrise azimuths on winter Phi days. Perhaps large parts of the world were at one time covered in this network of summer phi sunrise lines and winter phi sunrise lines criss-crossing each other. How various cultures have renewed and re-energised these sacred sites (or occasionally completely destroyed them, see Martin of Tours and Augustine) is as fascinating as how they were first envisaged.
So back on the pathways. We'll see what the Southern half of the Michael - Apollo - Artemis line holds, before returning to some of the places we've seen already in more detail.
And what about the temple of Delphi, one of the most famous 'navels' of the world? But first, a short(ish) digression: back to Stonehenge for a little geometry.
The Stonehenge Station Rectangle
There's an angle I'm interested in. After tracing all those summer Phi day and winter Phi day lines on Google Maps, I couldn't help but notice something at Stonehenge.
I wanted to check the angle between two lines: one is the North South line that runs through the station stone rectangle, from bottom left corner to top right corner. The other line is the line that runs from the top left corner straight down to the bottom right corner. (see below in black)
Trigonometry is easy on this website:
First you work out the angles on a right-angled triangle with a 5 side and a 6 side, then a couple more sums before you get to the angle in question: It's 117.574°. (see the results pasted below, or skip them!)
"Side a = 5.20684 Side b = 8.6667 Side c = 12
Angle ∠A = 22.62° = 22°37'12" = 0.39479 rad Angle ∠B = 39.806° = 39°48'22" = 0.69475 rad Angle ∠C = 117.574° = 117°34'26" = 2.05205 rad"
One of the most famous features of Stonehenge is the station stone rectangle, which stretches between four points on the Aubrey circle, framing the Sarsen circle, and with sides forming a 5:12 ratio. It is the rectangle that gave rise to Robin Heath's lunation triangle across Wales and England. The short sides of this rectangle are oriented towards summer and winter solstice and the long sides to the southernmost moonrise, two lines of sight which, uniquely at this latitude, form a right angle. The length of the diagonal of this rectangle is the same as the diameter of the Aubrey circle. Based on the fact that the north-south line runs through the top corner and the middle of the longer side of this rectangle, I worked out that the azimuth of the diagonal running between the western and eastern corners of the rectangle is 117.574°. This is very close to the value of the winter Phi day sunrise from the Mont Saint-Michel, on 15 November, 117.5°, a Phi day. It's also close to the sunrise azimuth at Stonehenge on the 11th November, which is five minutes short of being a Phi day.
And there's something else: the North-South line bissects the diagonal from top left to bottom right almost exactly at a 2/3 point. You can see above on the trigonometry results that one side is worth 8.6667. Well, the entire diagonal is worth 13 (it being a 5:12:13 triangle), and 13 / 8.6667 = 1.4999
It also says above that height c is 3.3336. So the intersection of the two lines I'm considering is 3.3336 from the longer side of the rectangle, that's equivalent to 5 / 1.49988, so almost the two third point of the 5 side.
A little more trigonometry (courtesy of the website above) shows that this intersection is on another two third point: the diagonal from top right to middle of the other side (which is also the North-South line) is divided at the two thirds point. (7.81 / 5.207 = 1.4999)
(see these figures from the website: https://www.calculator.net/triangle-calculator.html
Side a = 5.2068 Side b = 5 Side c = 4.33328
Angle ∠A = 67.38° = 67°22'48" = 1.176 rad Angle ∠B = 62.426° = 62°25'34" = 1.08954 rad Angle ∠C = 50.194° = 50°11'38" = 0.87605 rad)
Area = 9.99988
Perimeter p = 14.54009
Semiperimeter s = 7.27004
Height ha = 3.84108
Height hb = 3.99995
Height hc = 4.61538
Median ma = 3.88728
Median mb = 4.08584
Median mc = 4.6218)
And there's another interesting point that this intersection marks: the longer '12' height of the rectangle is divided at a point which is 2/3 of the height . You can see in the figures above that the height b of this triangle formed between the top right corner of the rectangle, the top left corner, and the intersection point, is 3.9995, which is close to 4.
So a segment measuring 4 is 2/3 of a line measuring 12. (4 x 3 = 12)
On the 5 by 12 rectangle above, the intersection at the various 2/3 points produces two interesting angles: 62.426° and 117.574°, and these are very close to the various sunrise azimuths for phi days at Saint Michael's Mount. In particular, the winter sunrise value is very close to 117.574°, and though the summer Phi day azimuth is a little off the value of the smaller angle, it is this same Phi day azimuth which links Saint Michael's Mount to Stonehenge in the first place. .
The actual azimuth between the two Michael Mounts is in fact a little greater:
Saint Michael's Mount to Mont Saint-Michel: 118.32°.
Here's a reminder of the Phi day values for Saint Michael's Mount:
Number of hours of daylight Azimuth sunrise
29 January 09:09:28 117.66°
4 May 14:51:45 63.63°
8 August 14:53:31 63.06°
12 November 09:12:19 117.07°
13 November 09:09:17 117.52°
So we have some interesting geometry, which produces an angle very close to the Phi day sunrises at Saint Michael's Mount, and the azimuths of these Phi day sunrises connect Saint Michael's Mount with Stonehenge and the Mont Saint-Michel. This angle also happens to be formed by a point which is at the 2/3 point along several lines: the diagonal of the 5:12 rectangle (shown in green, see above), the length of this rectangle (in pink), the width of the rectangle (in yellow) and also the diagonal of the 5:6 rectangle which is also the North South line (in blue).
Was the geometry present in the station stone rectangle being used to represent part of the Michael - Apollo - Artemis line?
At Stonehenge's latitude, the value of the winter Phi day sunrise at Saint Michael's Mount orientates the Station Stone rectangle: the North South line runs through the rectangle in such a way as to create an angle between the North-South axis and the longer side of the rectangle which closely matches Phi winter sunrise at Mont Saint-Michel. And this rectangle is itself perfectly oriented to summer and winter solstices and to lunar standstills (which, uniquely at this latitude, form a right angle with each other).
The winter Phi day at Stonehenge is between the 10th and 11th November. The closest day and corresponding sunrise azimuth I could get on sunearthtools.com to match the required nine hours and ten minutes of daylight for a winter Phi day was the 10th November 2025, and the sunrise azimuth for that date is 117.04°. The 11th November, with daylight hours of 09:06:49, has a sunrise azimuth of 117.51°, which matches the orientation of the west-east diagonal of the station stone rectangle quite well. About a minute after the first point of sunrise, when the sun is at elevation -0.833°, it then reaches about -0.45°, according to www.sunearthtools, and the azimuth has increased by about 0.52°. So I think it is correct to say that if, on a winter Phi day at Stonehenge, eg 10th November 2025, the sun is at azimuth 117.04° when it is at elevation -0.833°, then about a minute later it will be at azimuth 117.56° and elevation -0.45°. It may be that the horizon is such that the sun is actually not visible until is at about elevation -0.45° on site, or it may be that measurements were taken when a good portion of the disk was visible, i.e. five minutes after the first moment of sunrise.
117.56° is pretty much the azimuth of the diagonal in the station stone rectangle: 117.574°. So I think it is possible to put forward the idea that this diagonal corresponds to the position of the sun at dawn on a day when daylight and darkness are in Phi ratio at Stonehenge, in winter.
There are two other lines with a similar angle. Just after drawing the 12:5 rectangles above, I was watching a video, and in it something came up that grabbed my attention: it was about the silver gate and the golden gate in the sky, two portals through which the Egyptians believed souls entered and left this world. These gates are located at the intersection of two lines in the sky, the ecliptic and the galactic equator.
What's the galactic equator? The galactic plane contains the galactic equator, and the plane is the central plane of the spiral of the galaxy. There are three imaginary lines that can be drawn in the night sky: the galactic equator, the ecliptic plane and the celestial equator, and three imaginary points: the celestial north pole, the galactic north pole and the ecliptic north pole.
The celestial equator is just a projection of earth's equator into the sky. The ecliptic is the path of the sun as seen from Earth, sometimes also called the via solis. Sometimes the ecliptic is seen, in reverse, as the path of the Earth as seen from the sun.
The galactic equator is the middle of the Milky Way, our galaxy. The north celestial pole is projected from the celestial equator, and the north galactic pole is projected from the galactic equator, and the angle between them, as seen from Earth, is 62° 52' 18" (or 62.8717°).
The path of the sun is inclined at an angle of about 23° 26' 21.406" (or 23.4°) from the celestial equator. The Ecliptic Plane is tilted at 60.2° away from the North Galactic Pole. The obliquity of the ecliptic is the angle between the celestial and ecliptic north poles.
So if the angle between the galactic pole and the celestial pole is 62.87°, and therefore the angle between the celestial equator and the galactic equator is the same, can it be represented two dimensionally like this? (see below) And could a comparison be made between it and the station stone rectangle - even though the values of the angles don't match exactly? I think they are close enough to be worth spending a bit of time on, just to see if there's anything in this.
Is there some kind of correlation between the angle drawn by two imaginary sky lines connected with the Milky Way, our galaxy, and winter Phi day sunrise lines back on Earth, all neatly encased in a 5 : 12 rectangle? Is this the relative positions of the North Pole and the sun, as seen at dawn on Phi days, transposed onto the relative positions of Earth and of the Milky Way, the pathway for souls, transposed onto a rectangle? I'm not sure. If this is the intersection of celestial and ecliptic planes, what about the intersection of galactic and ecliptic planes, which is where the Egyptians believed the golden and silver gates were located in the sky? The angle between galactic and ecliptic planes, the path of the sun in relation to the plane of the Milky Way, is 60.2°. 180 - 60.2 = 119.8. It could be that further down the Michael line, we arrive at significant sunrises with these values.
Does this rectangle have any Phi properties? Well, it's not a golden rectangle as such. But there is something unexpected: if you run the North South line from the top corner at the Station Stone Rectangle in Stonehenge slightly East or West, so that instead of bissecting the long '12' side of the rectangle exactly in the middle, it bissects it at either of the phi points along the '12' side, something surprising happens.
If you divide the length of the 12 side of the rectangle by 1.618, you get 7.4166. So you have two parts to your 12 side, a 7.4166 part, and a 4.5834 part. If you draw a line from the top right corner of the rectangle down to the phi intersection of this side of the rectangle, you get a length of 6.78289 (purple rectangle) or 8.9446 (green rectangle). The intersection of the two grey lines is point O. In both cases, the point O marks a point which defines the phi proportions of the rectangle.
With the green rectangle, the ratios between the various sides and lengths are exactly 1.618, phi. And with the purple rectangle, the ratios between the various sides and lengths are 2.618, which is 1.618 x 1.618, or Phi squared. The numbers not in black below are ratios not measurements.
Fee Phi Fo Fum, it's all about the sun....
In the story of Jack and the Beanstalk, the giant roars:
"Fe, Fi, Fo, Fum.
I smell the blood of an Englishman,
Be he living, or be he dead,
I’ll grind his bones to mix my bread"
How wonderful that this story should have come from Saint Michael's Mount, the second point on the Michael line after Skellig, and that the word 'Fi', from the archaic word "fie", used to express disapproval, should also have come to express the golden ratio (named of course after the Greek letter) which is integral to the Michael-Apollo-Artemis line.
A match made in heaven, or perhaps somewhere in the Milky Way...
One last little bit of trig. If you mark out the Phi divisions on the sides of the station rectangle at Stonehenge, and link them up, you get some interesting connections, the most important of which is, I think, the fact that the diameter of the Sarsen Stone circle is worth close to the 12 side of the rectangle divided by phi. I was surprised by this.
I think it shows the importance of the golden ratio at Stonehenge. (see dimension C in pale blue on the picture below)
Also worth noting are the dimensions A and B, and how they are replicated inside the figure. (see below)
To work all this out I used the trigonometry website, and worked with the values of the sides of various triangles and their angles and heights.
12 / 1.618 = 7.41656 and 7.41656 / 1.618 = 4.58378
4.58378 + 7.41656 = 12
5 / 1.618 = 3.09023
3.09023 / 1.618 = 1.9099
1.9099 + 3.09023 = 5
This gives the dimensions of the Phi divisions on both sides of the 5 x 12 rectangle.
The diameter of the sarsen stone circle seems to correspond to the distance between two intersections of the black lines, and this length can be calculated using the values of the angles of the triangles created by the black lines.
Also worth noting is that where the black lines meet the sides of the rectangle, in red, this corresponds to 4 'Z holes', according to the plan of Stonehenge I've used. These 4 'Z holes' therefore mark the phi divisions of the sides of the 5 x 12 rectangle.
And another thing: consider the two circles created by the intersections of the black lines, one has a diameter A = 5 / 1.618 = 3.09023, see in royal blue on the diagram, and the other is in fact the sarsen stone circle, which matches the intersection of two black lines and has a diameter of C = 12 / 1.618 = 7.41674, see in pale blue on the diagram. The radius of the smaller circle is 1.54502, and the radius of the larger circle is 3.70837.
3.70837 / 1.54502 = 2.4 = 12/5.
12 and 5 are of course the proportions of the sides of the rectangle.
What about actual dimensions at the station stone rectangle? Robin Heath gives these dimensions: "The Aubrey circle is 104 MY in diameter (283 feet), whilst the Sarsen circle has an outer diameter of 104 feet." http://cura.free.fr/decem/06heath.html
(Please see this website for Robin Heath's brilliant analysis of the lunation triangle. )
and "Sarsen Circle (30 stones) Mean Diameter = 100.8 feet Sarsen Circle Outer Diameter = 104.27 feet Sarsen (Outer) circumference = 327.6 feet Mean circumference =316.8 feet Bluestone circle (59 stones?) Mean diameter 79.2 feet Aubrey circle (56 markers) Mean diameter = 283.6 feet ~ 13 x 8 MY ~ 104.2MY Aubrey circle (mean circumference) = 891 feet ~ 327.3 MY"
The longer side of the rectangle is 261.3 feet and the shorter side is 108.88 feet.
261.3 / 1.618 = 161.496 and
That means that the Phi divisions on the longer side of the rectangle are at 161.496 feet and 99.812 feet, and on the shorter side 108.88 / 1.618 = 67.293 and 67.293 = 41.59, so the Phi divisions are at 41.59 feet and 67.293 feet.
So on my diagram section A is in fact 67.293 feet, section B is 161.496 feet and section C is 99.812 feet. Section C is supposed to match the diameter of the Sarsen circle, but in fact it is about a foot out from the figures given by Robin Heath for the mean sarsen circle diameter, so perhaps you can't equate a phi division of the longer '12' side with the diameter of the sarsen circle. Perhaps you can if you can accept a mean diameter of 99.812 feet.
Gold: Autumn and Spring Phi Days
While on the subject of geometry, I just wanted to see if there was a day that corresponded to a different kind of Phi ratio: if you divide 360 by 1.618, the golden ratio, you get 222.4969.
Sunrise and sunset at a particular place always happen at the same angle either side of the North South divide, that is the 180° mark or the 0° / 360 ° mark.
Does the sun ever set at this azimuth, 222.4969°? Or rise at its counterpart 137.5031°?
( (360 / 1.618) - 180 = 42.4969, and 180 - 42.4969 = 137.5031) Yes, for example, in the North of Norway, in Hammerfest, on the 3 November, with 05:51:00 hours of daylight, the sunrise and sunset azimuths are 137.81° and 221.86° .
Or perhaps does the sun ever rise at 111.248° (222.4969 / 2 = 111.248)? Or set at its counterpart 248.75155°? The answer to this question is again yes. For example, in Hammerfest in Norway,13th October, the azimuths for sunrise and sunset are 111.22° and 248.31° . Or at a lower latitude, Durham, on the 27th October has sunrise and sunset azimuths of 111.15° and 248.6°.
Stonehenge: 30th October, 111.09° and 248.69°
Does the angle between sunrise and sunset ever get to be 222.4969° ( 360 / 1.618 = 222.4969)? Well, yes, if the sun rises at 68.75155° (180 - (222.4969/ 2) = 68.75155) or set at 291.24845° ( 180 + (222.4969 / 2) = 291.24845 )?
Or does the sun ever rise at 111.248° and set at 248.752°? (360 - 111.248 = 248.752)
Well, the most northerly place I've looked at yet is Durham Cathedral and the sunrise and sunset azimuths for summer solstice there are 44.75° and 315.25° and for winter solstice 131.98° and 228.01°. That's an angle of 256.03° for winter and 270.5° for summer. So, yes, you can get angles between sunrise and sunset worth 222.4969°, and more. Maybe a place with such an angle at summer solstice might be considered special. Maybe there's even a line of places with this angle between sunrise and sunset at various times of the year.
Let's imagine a place with 222.4969° between sunrise and sunset. What would the sunrise and sunset azimuths be? 222.4969 / 2 = 111.248. So sunrise would be at 68.752°, as180 - 111.248 = 68.752. and sunset at 291.248°, as 180 + 111.248 = 291.248.
What place would have such azimuths for its summer solstice sunrise and sunset? And what place for winter? And where might these figures be found at other times of the year?
The easiest is to find a place that I've looked at so far.
For example, at Durham Cathedral, the 20th April has sunrise and sunset azimuths of 68.66° 291.71° respectively, with 14:26:28 hours of daylight. Leeds has sunrise and sunset azimuths of 68.59° and 291.77°, on the next day, 21st April, with 14:25:22 hours of daylight. Coventry has azimuths of 68.74° and 291.6° on the next day, 22nd April with 14:22:03 hours daylight. And Stonehenge has sunrise and sunset azimuths of 68.8° and 291.53° on 23rd April, with 14:19:35 hours of daylight.
Saint Michael's Mount has sunrise and sunset azimuths of 68.76° and 291.55° on the 24th April, with 14:17:58 hours of daylight. The Mont Saint-Michel has sunrise and sunset azimuths of 68.93° and 291.37° on the next day, 25th April, with 14:14:13 hours of daylight. Carnac has sunrise and sunset azimuths of 68.89° 291.4° on the 26th April, with 14:12:32 hours of daylight.
And up North, the Farne Islands have sunrise and sunset azimuths of 68.83° and 291.55° on 19 April, with 14:26:34 hours of daylight. Aberdeen has 68.56° and 291.85° on 18th with 14:30:52 hours of daylight. Orkney has 68.81° and 291.62° on the 16th April with 14:31:40 daylight. And the northernmost tip of Shetland has sunrise and sunset azimuths of 69.03° 291.44° with 14:32:44 hours of daylight. It's interesting to note that in the UK there is nowhere that has both a phi ratio of daylight to darkness and a phi angle between sunrise and sunset on the same day.
What date might correspond to a 111.02° sunrise, at, say, the Mont Saint-Michel?
At the Mont Saint-Michel, sunrise is at 111.02° on the 1st November.
That's All Saints, the day after Halloween, when the veil between this world and the next is supposed to be a little thinner. Interesting in the context of a possible ancient belief in reincarnation linked to sunrise and sunset. That day, sunset is at 248.77°. (as per www.sunearthtools.com)
That creates an angle between sunrise and sunset which is 137.75°, and 137.75 x 1.618 x 1.618 = 360.619031
So I think we could think of this a sort of phi day, because of the angle between sunrise and sunset being loosely related to 360 by phi squared (as close as you can get in practice).
And the other possible date is the 25 April with a sunrise azimuth of 68.93° and a sunset azimuth of 291.37°. Because 291.37 - 68.93 = 222.44, and 222.44 x 1.618 = 359.908, this date shows a link between phi and the yearly cycle, also not because of a ratio between darkness and light, but because of the value of the angle between sunrise and sunset.
What about Saint Michael's Mount?
The closest match for these sunrise and sunset values at Saint Michael's Mount is the previous day, the 24th April, with 68.76° and 291.55°.
Similarly, the closest match in the autumn is also the previous day, the 31st October, with a sunrise azimuth of 111.15° and a sunset azimuth of 248.63°. Hallowe'en! Or 111.68° for the 1st November, and a sunset azimuth of 248.11°.
Are these days of special importance because of their relation to phi and the angle between sunset and sunrise at these latitudes? They are phi days of sorts, autumn and spring phi days.
What about any alignments from these Michael Mounts along these azimuths?
Well, I drew lines on Google Earth corresponding to these azimuths, and I was a bit taken a back when I saw where the lines were heading. From Mont Saint-Michel, the line corresponding to sunrise on an autumn phi day, azimuth 111.02°, runs a few miles from the Temple of Apollo at Delphi.
Mont Saint-Michel - Delphi Temple of Apollo: 111.50°, 1385.79 miles. That's very close.
And from Saint Michael's Mount, the sunrise line for an autumn phi day, 111.15°, goes close to the Monte Sant'Angelo.
Saint Michael's Mount - Monte Sant'Angelo 111.35°, 1,179.16 miles
Over such long distances, more than a thousand miles, that's pretty close. The 30th October at Saint Michael's Mount gives a sunrise azimuth of 110.62° , so in fact the 31st October (111.15°) or 1st November (111.68°) is the best match for a Saint Michael's Mount - Monte Sant'Angelo connection . The ideal autumn phi day values would be sunrise at 111.248° and sunset at 248.752°, which straddles the 1st November and 31st October.
And Mont Saint-Michel to Delphi being 111.50°, such an azimuth is close to the sunrise azimuth on 1st November, which is 111.04°. The next day, 2nd November, is better though for the actual geographical relation with 111.54°. Again, though, the value of a phi autumn sunrise, arrived at mathematically rather than by looking for the closest match on www.sunearthtools.com, is 111.248°, and this comes close to the line between Mont Saint-Michel and Delphi, the difference is just over a quarter of a degree.
I don't know if there's anything in these two connections, Mont Saint-Michel to Delphi and Saint Michael's Mount to Monte Sant'Angelo. Maybe it's just a coincidence. The more connections I find, the more improbable the whole thing seems.
By the way, I came across this very interesting observation on the Graham Hancock website, by a contributor called engbren, on a discussion forum. http://grahamhancock.com/phorum/read.php?1,1184129,1185519#msg-1185519
Khafres Pyramid is 411 Cubits or 3 x 137 cubits of 20.62 inches. Of course we know the baselength of the Great Pyramid as 440 Royal Cubits but was it intended to be 444 or 2 x 222? The Ancient Egyptians used 360 degrees in their astronomy to determine the decan stars. Perhaps they were aware of the golden angle and encoded it into their Pyramids?
When you look at the calculation of earth radius/diameter, it is possible if we allow for the 222 x 2 = 444 Royal Cubit baselength to calculate the radius of earth from parameters in the great pyramid baselength and Khafres Pyramid baselength.
88,888 = 444.44 x 2 x 100
88,888 x 137 Cubits of 20.62 inches = 6,378,022m. The generally accepted equatorial radius is 6,378,137m. A 15m difference or 0.00023%
So much for these new Phi days then. Are there any more, I wonder?
There may be other ways to think of dividing the year into Phi parts..., to divide a circle by Phi. There's an infinity of ways really, you can divide by Phi, by 2xPhi, by 3xPhi, Phi squared, you can subdivide the angles you get by phi ad infinitum, you can use the greater or the smaller angle created by dividing your circle into two parts....
Simply dividing a circle into ten equal parts is down to Phi.
Phi can be used to create angles of 36 degrees. 36 degrees is 1/10th of a full 360 and therefore can be used to divide a circle into 10 parts. Dividing the circle into tenths requires that you construct two lengths having a proportion of Phi. In other words you must be able to create the constant Phi in order to divide the circle into 10 parts.
So what about a ten month year?
In one of my earlier posts, I showed that there were common numerical links between the solar and lunar cycles, involving Phi and the number 20. Let's assume someone likes Phi and divides the solar year into 10 or 20, to honour the phi relationship between solar and lunar cycles might they design a ten month year, and dividing a circle into ten parts. That's because: a solar year in days / 20 is almost equal to 1 lunation in days / phi. Which means that a phi part of a lunation is pretty much one twentieth part of a solar year.
Not only would this reflect the solar and lunar parts of a year, but it would in fact be true to phi anyway, in that it is central to a division of a circle into ten equal parts. There's a difference of 0.2164 days between 20 phi parts of a lunar month and an actual solar year of 365.242199 days, that's just over 5 hours and 11 minutes. These 5 hours and 11 minutes go into 24 hours almost exactly 4.6 times, which is 23/5.
Here are some of the conclusions I came to in the third post, involving Phi:
Basically, the sun and moon cycles are (imperfectly) related to each other by Phi and 20, and a circle can be divided into ten equal parts by drawing a circle and lines based on a line divided into three points, at Phi ratios from each other. So it seems that a circle divided by ten would be a phi-phile way to go, if you wanted to pin point special days in the calendar. If a year is 365.242199 days long, then every 36.5242199 day could be marked as special. Or every 18.2621 days, which happens to be very close to 18.2513, which is 29.53059, the number of days in a lunation, divided by 1.618, phi. So that would in effect be every 36 or 18 days, with a few left over at the end of the year. Or with 3 extra days between the summer solstice and midsummer ( 24th June, in the Christian world, the feast of St John) and another 3 between the winter solstice and midwinter, or Christmas Eve (24th December). This would in fact make sense of the fact, or at least be reflected in the fact that today midsumm