# Giza and the quadrature of the circle in the ancient Egypt

## The problem n. 50 of the mathematical papyrus of Rhind describes a method to calculate the square of surface equal to that of a circle of diameter (D) assigned.

The problem n. 50 of the mathematical papyrus of Rhind describes a method to calculate the square of surface equal to that of a circle of diameter (D) assigned.

The scribe Ahmes says: * Divide the diameter into 9 parts. Take 8 parts and build a square 8 for 8. This square has a surface practically equal to that of the assigned circle. *

This approximate method solves the squaring of the circle with an error in the evaluation of the Greek p number (p) in excess of a part of 166, 21. approximately parts. [p * = p + (1/166, 21 ..) p = 3,16049 ...]

Many researchers have suspected that the ancient Egyptians had calculated the number (Greek p) with a more accurate precision.

Some authors, on the basis of surveys carried out on Egyptian monuments, have considered quite logical the knowledge of the 22/7 relationship that gives rise to a value of (Greek p) better than that deducible from the Rhind papyrus [p ** = p + ( 1 / 2484.48 .....) p = 3.142857 ....]

This research aims to demonstrate the possible knowledge of an even more precise method. This method is based on a geometric dynamic where a sequence of actions is activated that allow to reach a geometrical expression where a square of surface very close to that of the original circle is highlighted. [p *** = p + (1 / 29834,02 ...) p = 3,141697 ....]

-Egnet-1

-Egnet-2

-Egnet-3

-EGT-1

To support this thesis we have considered this new expression geometry of the quadrature as an essential basic element to elaborate other more complex figures. We have thus created the following geometric models:

* Planimetry: Piana di Giza - EGT-2.jpg; EGT-3.jpg; EGT-4.jpg; Gizam-3r.gif;

* Section: North-South Pyramid of Cheops - PCH-1.gif; PCH-2.gif; PCH-3.gif.

* Section: Pyramid of Chephren - CHEFREN7b.gif;

* Section: Pyramid of Meidum - MEIDUM-S.gif.

* Sections: Pyramids of Snefru to Dahshur - EGT-Snofru.gif.

These models were subsequently compared with the most accredited architectural surveys available today. Both as a single element and as a set of compared architectural elements, the differences between models and reliefs are very limited.