Plato and the Quran

An essay by Richard Heath on the numbers found in the book
“Plato and the Quran”, by Noor Bosra.


Multiplication of the consecutive numbers 1 to 6 equals 720 and this, applied, to the equal perimeter model, numerically scaled it up to the cosmic size of the Earth and Moon in miles. The Quranic formula, to instead multiply the numbers 3 to 8 and generate 20160, doubled the cosmic model’s 10080 and hence the whole geometry was doubled in scale. The further addition of the consecutive numbers 3 to 8, further signaled 33 years, pointing to the equal area model of the Solar Hero and to the Moon’s nodal period because, 33 divided by 18.618 equals √𝝅 = 1.778 and the area function squares that. This equality of a circle’s perimeter and a circle’s area to the same square can then be drawn to unite the cosmic model of Earth and Moon’s size, to the relationship of the Solar Hero period of 33 years, as the square, to a circle of radius 18.618 years, as appears quite clearly in the plan of Islam’s Dome of the Rock[1].

Chapter 23: The Seven Sleepers of the Cave

One of Noor Bosra’s key themes is that the Quran was composed out of the cultural context of the eastern Mediterranean, Arabia, the ancient Near East, and beyond. One example is the story, from different sources, of people who sleep in a cave to escape religious persecution. Waking after what appears to be a single night, they find many years have passed yet their bodies have not aged and the danger they hid from has now passed.

Noor Bosra provides comprehensive literary references, in a good order starting with the Quran’s chapter 18, the story running for 18 Suras. The situation for these verses was ironic, since they were demanded by Mohammad’s religious persecutors to demand proof that his source of knowledge was competent, or his revelations should be discredited. A further irony is that Mohammad often used to ascend to his favourite cave on Mount Hira, where many key recitations were uttered.

One previous story of the sleepers is about early Christians from Ephesus in Asia Minor. In 250 BCE the persecution was then from Rome. But a roughly similar story is found in an apocryphal Jewish text, written shortly after 110 BCE, about the prophet Jeremiah who slept in the desert alone for 66 years to escape a king. In contrast, the Christians slept for 372 years and the Quranic sleepers, 309 years.

The numbers 300 and 9:

“they remained in the cave three hundred years plus nine more”

On page 440 Noor Bosra finds, in 309, the number of lunar months in 25 solar years of 365.25 days, which was the Egyptian Sothic year (of the helical rising of Sirius) from which the Nile flood was predicted. Four Sothic years is 1461 days and the accounting for the extra quarter day per solar year might explain that, in the Quranic version, the sleepers are found with a Dog to protect their cave, just as the Jackel god Anubis protected the dead in Egyptian tombs, Sirius being the dog star.

In the ancient world, coincidences of astronomical cycles within a whole number of time periods made these “natural” numbers sacred and to be associated with archetypes such as a dog (the constellation Canis Major). 309 lunar months is just 6 days less than 25 whole solar years but what about 365 days?

The Egyptians had two other years of 360 and 365 days that, when combined, allowed them to establish historical dates for over 1000 years. And if we divide 309 lunar months (in days) by 365 days, the result is 24.99986 years, which is within 1.3 days of 25 years of 365 days. This then has a further resonance with the Venus synod of 584 days, since the latter is 8/5[2] (1.6) of 365 days, and their common factor of 73.  

Noor Bosra explains how the Apis bull, one of the deepest Egyptian traditions, was connected to this golden mean, a proportion that enables a unique division of three points as two identical proportions: of the least to the middle as of the middle to the whole – a sort of holism. We should note that Noor provides excellent resources of background information regarding astronomical numbers, numerical traditions and historical facts.

The varied accounts of the number of sleepers

Noor tells us that in no previous versions of the sleeper story were there any strong references to the number of sleepers, while in the Quran, all the numbers are playfully doubted as between 3 to 8, as if none of the locals, who remembered them emerging from the cave, could quite remember. These varied accounts were,

  • 3 [sleepers] and the 4th was their Dog and,
  • 5 [sleepers] and the 6th  was their Dog and,
  • 7 [sleepers] and the 8th was their Dog,

taking a form congruent with a rhyme-based puzzle on successive numbers between 3 and 8. Noor Bosra suggests these three couplets form a code when multiplied, to give 20160, or when added, to give 33.

The first clue for me was that, in multiplying successive numbers, a factorial process was indicated, similar to the factorial[3] for 6 (notated as 6!) that equals 720: an important harmonic prime which, when multiplied by the three numbers 3, 11, and 14, becomes the familiar geometry of equal perimeter of square and circle based upon π =22/7[4] , but here expanded by 720 in an ancient “cosmic” model of the relative size of the Earth and Moon (ratio 11/3), in units of miles containing 5280 feet. But first, what is the equal perimeter geometry of circle and square? Figure 1 shows that the approximation to π of 22/7 causes a radius r of 7 to lead to a circumference of 44 (2 πr) and that the square of equal perimeter then has a side length of 11 whose in circle is diameter 11.

Figure 1 The equal perimeter model of circle and square

  1. When 11 is multiplied by 720, the diameter of the Earth is interpreted as being 7960 miles.
  2. The circle equal in perimeter to the out square of the Earth is then to be interpreted as 14 multiplied by 720, or 10080 miles in diameter, the limits of the sub-lunary world and of sacred spaces.
  3. The diameter of the Moon is then interpreted as 3 multiplied by 720 = 2160 miles.

This cosmic geometrical model[5] [John Michell 2008] is accurately the size of the mean (spherical) Earth and of the Moon, long before the scientific revolutions of the last millennium, both Islamic and European. It suggests our planet and moon conform to a numerical plan, as an accurate overall approximation.

But the Quran appears to have used the alternative way, provided by Noor Bosra on page 443, of specifying the cosmic perimeter model, using 3 x 4 x 5 x 6 x 7 x 8 = 20160 to replace 720 x 14 = 10080. This 20160 is twice the normal 10080 of the cosmic model so that, the diameter of the Earth must also be 11/14 of that: that is, 7920 doubled to 15840. The equal perimeter length must also then double from 31680 to 63360. The results (now in half miles of 2640 feet) enabled the rhyme-form puzzle to replace the factorial expansion of the simple geometry and create numbers exactly twice that of the cosmic geometry, as shown in figure 2. By doubling the numbers of the cosmic model, the traditional numbers associated with the cosmic model of the earth were hidden, while upgrading the previous versions to become the subject for the Quranic version, the seven sleepers of the cave, all sleeping through history to avoid persecution.

Figure 2 The simplest, cosmic and Quranic geometries, the Quranic differentiating itself from the cosmic using an alternative factorial form to double the cosmic numbers.

Adding the numbers of the Sleepers

Noor then adds the numbers 3 to 8 to get 33, the number associated with the Solar Hero who are, as with Jesus and Mithras, said to die after 33 years. [6] This number has a strange relationship to the Moon’s nodal period of 18.618 years in that, the ratio between these numbers is the square root of pi as 3.141679 that is 1.77248. For this reason a square of side 33 is equal in area to the circle of radius 18.618[7] – a unique situation for a whole number as small as 33. The creation a circle and square of equal area has in fact been proven impossible to achieve by algebraic geometrical methods but 33 and 18.618 provide a practical synthesis[8].

It should be no surprise that the Quran might have referred to the nodal cycle in this way, since Mount Hira provides an approximate span, to the east, of the moon’s maximum (extreme) moonrises every 18.618 years, to the north and south, when viewed from the Kaaba, which is right angles to the lunar maximum to the north[9]. If the square side, equal to the diameter of the Earth, is reused then the required unit is one 33rd of the diameter. 15840, divided by 33, equals a unit of 480 and 18.618 x 480 equals 8936.64 as a radius, and a diameter of twice that. Figure 3 shows the radius of the circle of equal area to the square if that is 33 years and the radius 18.618 years.

Figure 3 The Quranic geometry with the nodal period added, given Noor’s clue of adding the numbers between 3 and 8 to give 33 years

This equality of a circle’s perimeter and a circle’s area, to the same square, can then be drawn to unite the cosmic model of Earth and Moon’s size, to the relationship of the Solar Hero period of 33 years, as the square, to a circle of radius 18.618 years, as appears quite clearly in the plan of Islam’s Dome of the Rock in Jerusalem.

Figure 4 left: The plan of the Dome of the Rock. Right: The Dome itself with Dome of the Chain before it, from Heath, 2021. This bedrock is the scene of Mohammad’s Journey called Miraj[10].

There appears to be some continuity between the built heritage of the subsequent Islamic empire, and the Quran’s subliminal reference to the cosmic model doubled using the story of the seven sleepers to provide the numbers 20160 and 33 through the multiplication and addition of the numbers [3, 4, 5, 6, 7, 8], respectively, centuries before. Plato and the Quran therefore appears to be both an excellent introduction to the influences acting upon the Quran when composed but also to esoteric number traditions to which the Prophet was connected, deserving of further attention.


Bosra, Noor. Plato And The Quran: Number and Allegory from Ancient Mesopotamia and Greece to Islam. London: Noor Bosra Publishing. 2023.

Heath, Richard. Sacred Geometry: Language of the Angels. Rochester, Vt.: Inner Traditions, 2021

Michell, John. Dimensions of Paradise: Sacred Geometry, Ancient Science, and the Heavenly Order on Earth. Rochester, Vt.: Inner Traditions, 2008.


[1] Heath (2021), page 201-204.

[2] The numbers 5 and 8 are early members of the Fibonacci series in which successive terms approximate the golden mean of 1.618034, in this case to 1.6.

[3] A factorial number is all the numbers up to its limit, so that factorial 3 (or 3!) equals 1 + 2 + 3 equalling 6

[4] Pronounced pi, π is the relationship between a circle’s perimeter and its diameter which if the diameter is 7 then the perimeter is accurately 22, leading to the ratio 22/7 widely adopted by early numerate cultures.

[5] See John Michell 2008, 33-35

[6] This periodicity denotes the exact location of the sun east on rising, or west on setting, since the extra quarter day is closely the fraction 32/132 which equals 0.24 days while 132 = 4 x 33.

[7] First identified by Robin Heath, personal communication.

[8] then found within astronomical time as the Solar Hero of 33 years and Nodal period of 18.618, reach into the structure of the Metonic period (19 × 19.618 × 18.618) and Saros periods (19 × 18.6182), solar year (19.618 × 18.618), and eclipse year (18.6182), all in solar days.

[9] See chapter 8: The Focal Buildings of Islam of Sacred Number: Language of the Angels, page 185

[10] The Israʾand Miʿraj( Arabic: الإسراء والمعراج, al-’Isrā’ wal-Miʿrāj) are the two parts of a Night Journey that Muslims believe the Islamic prophet Muhammad (AD 570–632) took during a single night around the year AD 621 (1 BH– 0 BH) … miʿraj means rising, or going up to a high place. – Wikipedia. To paraphrase, in the Miraj, Muhammad “ascends to heaven” whilst still alive.

The Stonehenge Crop Circle of 2002

One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it. However, metrology of feet and types of feet can hide the elegance of a design.

photo by Steve Alexander of

I received Michael Glickman’s Crop Circles: The Bones of God at the weekend and each chapter is a nicely written and paced introduction to a given years worth of crop circles generally in the noughties. The above is the second in proximity to Stonehenge reminding keen croppers of an earlier one. This cicle preceeded the late-season (August) circle at Crooked Soley that I have an analysis of soon to be posted, drawing on Allan Brown’s small book on it.

Glickman’s chapter 10 : Stonehenge Ribbons and Crooked Soley provided a tentative analysis of the Ribbons as having the ends of the ribbons measuring 58 feet. The design was observed as making use of a single half circle building block for most of the emergent six arms emerging from the center. Michael suggested that there were 13 equal units of 58 feet across the structure.

Figure 10.4 Showing thirteen divisions of one of the three diameters of ribbons. photo: Steve Alexander.

From this I was able to observe that clearly the divisions were not equal in size and the white ones were clearly smaller as was the central circle’s diameter. Scanning the picture and placing it in my Visio program, so that a rectangle of 58mm was equal to the diameter of the right hand ribbon end, it was possible to determine that the ratio between these lengths was 5 to 4, or 5/4, from which the shorter white length must be 46.4 feet and that the diameter can be seen as 9 units across, that is 104.4 feet. The unit is 104.4 feet divided by 9 which equals 11.6 feet, which is 10 feet of 1.16 feet, the root reciprocal of the Russian foot of 7/6 feet, that is 7/6 feet divided by 175/176 (= 1.16). Going down the “Russian” root led to the diagram below.

My analysis of Michael Glickman’s figure reveals a span of 580 Russian Feet.

There are parallax errors so I have had to show the ideal designed shortened across the left-hand of the design, but the design has many numerical aspects where each arm is 27 units so that two arms are 54 which, plus the center, gives 58 times 10 equaling 580 Russian feet. But then I noted that 58 feet, divided by 5, gave the unit as 11.6 English feet while 58 feet divides into the 58 unit diameter across the crop circle.

Now we see a set of multiples of 29 are there as numbers {29 58 87 116 145 174 203 232 261 … }. The reciprocal Russian at 1.16 feet and the unit of 11.6 feet are decimal echoes of the number 29. The formula of the Proto Megalithic yard is 87/32 feet and 261/8 inches.

To be continued

One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it.