The Mathematics of the Great Pyramid


                                                    Introduction to the Great Pyramid’s Measurements

      Made of limestone and granite, the Great Pyramid is a mountain of numbers, mostly irrational numbers. These numbers are found as the measurements of all aspects of the pyramid; height, perimeter, passage system, and chambers. Some of these numbers are well known numbers like the golden proportion and its extended family of numbers, the two main upper chambers being practically hymns to the golden proportion. The square, square roots(and one very important cube root)and inverses of natural numbers like 3,5,7,10,20,75 are used often and in different parts of the pyramid. Many are more obscure like 286.2167011, which is the number of inches the entrance and passage system are eastward from the center of the pyramid’s north side, but is also a geometric ratio in its own right as are its 8th, 19.2th, and 48th parts. These are major components in the pyramids passage system as is .6787159471,(the ratio between one side of a regular triangle and one side of a regular pentagon) times ten thousand, is the inch measure of one side of the pentagon in the Great Pyramid’s circle, the radius of which being the height of the pyramid itself.

      Most numbers in the Great Pyramid are major geometric ratios, including pi, the ratio between the circle and its diameter. Although the pyramid’s exterior deals almost exclusively with the ratio between the circle and one side of its inscribed regular (equilateral) triangle, which the base perimeter represents, the length of the two meridians, and the four sides each produce different pi numbers in two simple steps of multiplication and division. Three of these are well known as they have been used at various times in mathematical history; 3.142857142 ( 22 divided by 7), 3.141640786 (the golden proportion squared times 1.2 or the square root of 1.8 plus 1.8) and the standard 3.141592654, which can be extracted from the East-West meridian.

      Many different sets of ratios between the circle and its regular polygons are used in the pyramid and have to be considered world views from different points of view. Three pi numbers can be found on the passage floors as measurements between one place to another. The King’s Chamber passage, from the Great Step through the Anti Chamber to the door of the Kings Chamber, is a veritable tour de force of pi as four separate aspects of the passage develop pi in four different ways. One formula actually develops all possible pi from 3 to 4. All this and pi is not by any means central to the purpose of the Pyramid but is just one of the ratios between the circle and lines within the circle.

      All numbers are very specific, all interact and dovetail with each other and all are intentionally used as a language to express the issue of transformation (creation) of one into two, the invisible into the visible, second dimension into third dimension, idea into form, and spirit into matter, our human matter in particular.

      These numbers have their origin in the first seven basic geometric lines; the circle, its diameter, and one side of each of the first six regular polygons. In addition to their geometric ratios between each other and the circle, each of these has an abstract symbolic meaning which represents a metaphysical concept or principle. The relationships between them and their ancillary numbers and ratios comprise the language.

      For example, the height of the Great Pyramid, which is also the radius of the two dimensional circle on whose diameter the pyramid sits, is 5773.502692 inches, the inverse of the square root of 3. As a geometric ratio, .5773502692 is the ratio between the radius of a circle and one side of the circle’s equilateral triangle. Now it is the radius that creates the circle in the first place, representing the thought or idea of the one making the circle, but is actually space and not a real line until it makes its appearance in its rightful place as sixth line in the natural order of numbers.

      Its abstract symbolic meaning as sixth line is that the created is the same as the creator ( the radius) of the circle since the radius IS one side of the circles six sided hexagon. Just as  “we are what we eat” but extended to a cosmological level, it means that the creator of the universe is not separate from the universe but IS the universe.                              

      Its inverse, 1.732050808, (the square root of 3) is the diagonal of a cube with a side of one. Just as 1.414213562,(the square root of 2), perfectly represents the second dimension by being the diagonal of a square with a side of one), the square root of 3 perfectly represents the third dimension , and is an important number in the Great Pyramid, appearing many times. The square root of 3 (1.73250808), coupled with .6787159471, the ratio between triangle side and pentagon side, are the determining factors in the heights of the upper passages and both play a major role in the Queen’s Chamber, one of which is dictating the height of the missing floor.

      Illustrating the use of the many aspects of a single number, the foot equivalent of the pyramid’s height, 481.1252243 feet, is also important as it is the first measurement encountered when entering the pyramid and the last measurement when exiting. 481.1252243 INCHES is the distance from the entrance down the Descending Passage to the famous scored lines. Multiplied by the next section (scored lines to the ascending Passage’s virtual termination on the floor of the descending passage), 628.9211044 (2 pi in the other golden proportion developed pi of 3.144605522) the product is one sixth of the Grand Gallery’s floor length of 1815.538839 inches, which, in turn, is half of that system’s ratio between the circle and its inscribed triangle side.

      The difference between 3.141592654 (actual pi) and 3.141640786 (the golden proportioned pi developed from the pyramid’s west side and actively used inside the pyramid) is but .0000000204 from being .0000481125224.   

      This is just a brief introductory illustration of the complex use of just a few of the many hundreds of numbers that are incorporated into both the outside and inside of the Great Pyramid. These numbers comprise the basic and most abstract of all languages, number itself, and are put together in the Great Pyramid with the precision of a Swiss watch. 

      These same numbers appear in both the Great Pyramid and an abstract idealized two dimensional plan of the space and time relationships between the earth, moon, and sun. Besides being composed by the same numbers, the time and space ratios and the Great Pyramid share one other major commonality in that they both show either intention or coincidence of the highest possible order.

      The base perimeter, for instance, measuring 36277.73439 inches, is not only a numerically purified half minute of the earth’s latitude, and the ratio between triangle side to circle, in one of the sets of viewpoints used in the pyramid, but also has its origin in a number as pure as the driven snow, the number 3, making the case that it is through number itself that the world manifests itself. This is one of the points The Great Pyramid was constructed to express.                                                    

      Although these constructions can be studied and appreciated just for the ingenious way they were put together to make a whole, an appreciation of their symbolic meanings more than squares that appreciation. So before looking at any of the other measurements, their origin and symbolic meanings need to be addressed.

page 5