A bit of story background: Egipt

 

                                                           Welcome back geometricians!

As we saw in the first entry, geometry is a fundamental tool for understanding and ordering the world around us, and what would great buildings be without geometry? 

And speaking of great buildings, could anyone tell me the name of this gigantic one? 

The Great Pyramid of Giza in Egypt is nothing more and nothing less, it fascinates many of us. It is an amazing construction with an incredible precision, much greater than can be achieved with our current technology. In this article we discuss some important properties of its design that are directly related to Sacred Geometry. We will show that the ratio of its apothem to half its base obeys the Golden Ratio, and that the perimeter of its base is equal to that of a circle with a radius equal to its height. We will also see that the angles of the Great Pyramid hide Euler's number. In preparation we need to remember the properties of Kepler's triangle, as well as the problem of the Quadrature of the Circle. Then we will show that the dimensions of the Earth and the Moon obey the same proportions as the dimensions of the Great Pyramid, and that they can be obtained directly using the Pythagorean triangle 3-4-5. And finally we will show that the exact dimensions of the Great Pyramid respond to a simple formula related to the cubes of certain integers.

The word Geometry in Egypt refers to "measuring the earth".  Egyptian geometry together with Babylonian geometry was the forerunner of the powerful Greek geometry.

The Egyptians mastered:

• Triangles, measured with equidistant knots.
• They achieved a right angle and therefore right-angled triangles.
• They differentiated hypotenuse from legs.
• They found areas of squares, rectangles, rhombuses and trapezoids.
• They gave the area of the circle an approximate value, because for Π they assumed 3,16.
• They knew the cylinder, the truncated cone, the truncated pyramid and pyramid.

This papyrus begins with the sentence: "exact calculation to enter into the knowledge of all existing things and of all dark secrets and mysteries". It provides information on:

• Basic arithmetic.
• Fractions.
• Progressions.
• Proportional divisions.
• Rules of three.
• Linear equations.
• Basic trigonometry.
• Division problems.
• Problems with the area of an isosceles triangle.
• Area of an isosceles trapezium.
• Area of a circle, with a shape similar to the present one, but with π=3+1/6.
• The volume of a pyramid with a square base.In other papyri we find the numeration.
• The volume of a truncated cone.
• A good approximation of the volume of a sphere.

If the Egyptians were able to reach these conclusions by exploring the natural environment, how far will human beings go in the face of so much progress, discovery and change?