Cheops Pyramid and Squaring the Circle
by Andras Goczey
The modern world has every right to stand amazed at the building accuracy of the Cheops pyramid of theoretically 146.7 m height. It is a well known fact that, according to the intention of builders, the perimeter of the base square of pyramid is equal to the perimeter of the great circle of a hemisphere the radius of which is equal to the height (reference to the Earth). According to our recent knowledge, the building difference compared to the calculated dimension of the base edge lies just between 20 to 30 cm!
The basic problem, however, consists of that, when building that Wonder of the World, the above tolerance can only be achieved by using Pi = 3.142 “that was unknown to them”. The use of Pi = 3.16 value attributed to their knowledge according to the Rhind papyrus predestinates an error in the base edge far exceeding one meter! Furthermore, they could not perform divisions and multiplications but only to a limited extent and they could adapt these operations by reducing them to additions! They must have known some more accurate Pi value that could be used without some particular calculations and drawing even by means of additions to solve their task!
Might it be as follows?
The most natural human measuring unit is the span (it is not this that popularized with them).
At the same place, the tenfold of stick is a mark of hairpin form, the hundredfold of it is marked by a helix while its thousandfold is represented by a mark of a lotus flower.
Thus, the mark representing thousand stick is equal to a lotus flower that might be equal even to the height of Cheops Pyramid, that is 146.7 m according to the above.
Neither places of value nor fractions were used, therefore:
if the height of Cheops Pyramid is supposed to be equal to 1000 stick unit, i.e. one lotus flower, the use of decimal system allows the bravura to be performed as follows:
1. Reference to the Sun:
It is well known that the height supposed to be equal to a lotus flower i.e. thousand sticks = 146.7 meter multiplied by thousand by thousand by thousand, i.e. by billion gives the distance to the Sun (it is well known that the minimal distance between the Sun and the Earth is equal to approx. 147 million kilometer).
2. Reference to the Earth:
If the height of 1000 units, i.e. the distance of one lotus flower is assumed to be equal to the radius of a semisphere (reference to the Earth), then the perimeter of the great circle of this semisphere shall be equal to the perimeter of the basic square of the Cheops Pyramid according to the message of the builders.
Measure a section of thousand stick length (lotus flower) on the half diagonal of this square first, then one of hundred sticks length (helix) from its end point, then one of ten sticks length (hairpin) from the end point of the previous two sections, then one of one stick length from the end point of the previous three sections; then, a simple addition of these four part sections gives the length of the half diagonal of the requested square requested to be 1111 units! — (András Goczey)
Performing the verification for a circle with radius of 1000 units i.e. r = 1000, the above drawing procedure for the diagonal of the requested basic square gives 1111
The half edge of the basic square is given by dividing 1111 by square root of two.
Multiplying this ratio by four results in the half perimeter which gives the thousands of Pi i.e. 3142!
Half of the perimeter of a circle with radius of 1000 units is equal to the Pi-fold of its radius (Pi = 3.142) i.e. 3142.
It follows that, by using the above method of drawing, the perimeter of the basic square is equal to that of the great circle. Thus, the task can be solved!.
Budapest, December 5th, 2009
Copyright by András Goczey
Did you Know?
“According to the decision adopted by the Hungarian Academy of Sciences in the mid of 19th century: „dissertations dealing with quadrature of the circle, section of circle into three sections, the invention of perpetuum mobile will be refused without consideration”