**4.1 GIZA (Egypt) Great Pyramid of Cheops, dd. ca. 2570 BC, monumental tomb**

Long before the Pythagorean philosophers, the design of this monumental tomb expresses a stupefacient simplicity and coherency in geometry and dimension, fully compatible with the Egyptian vision on the society and the cosmos, witnessing the exceptional culture and knowledge of some 5.000 years ago (**Figure 3a-c**).

The symbolic geometry is obvious: the combination of a square ground floor, symbolizing the flat plane of the earth, and the upwards rising triangular flanks directed versus the celestial globe, with the mummy of the pharaoh and his wife, waiting for rebirth, at the center of the monument. The sides of the square are closely aligned to the four cardinal points. According to some researchers, inside passages and corridors are orientated versus astrologic constellations at the time of building. The King's and Queen's tomb chambers are located in the geometric gravity center of the construction, on emplacement and distances of interior corridors related to the golden mean proportion ϕ([9], I, pl.XLIV).

The physical environment of the pyramid, the access way, the sphinx statue and the position of other monumental tombs of pharaoh related people or animals show a well-considered geometric and measured design.

The pyramid's external dimensions witness an equally exceptional design with a selection of most allegorical and harmonious numbering, combining length of sides, diameter, vertical and sloping heights, including also particular prime numbers and the irrational ratio'sπ and ϕ(**Figure 3b,c**):


#### **Figure 3.**

*Pyramid of pharaoh Cheops at Giza a. general view [8], photo: Giza-legacy.Ch; b + c: Geometries (drawings: Pinterest).*

**153**

**Figure 4.**

*general view rotunda inside (Wikimedia).*

*Architectural Design Canons from Middle Ages and Before: An Inspiration for Modern...*

isosceles profile signs = Erc (280/220) = 1,272727…= √

mental (according Plato) of all terrestrial matter.

ϕ

280) also include (unknown) allegorical messages. [8]; [Wikipedia].

**4.2 ROMA, pantheon - founded ca. 23 b.C.; present structure dd.** 

• the ratio (height: ½ side) or the ratio between both cathedes of half of the

number 27 (=3x3x3) after comma, also being easy to draw as it equals the ratio (14:11). This property illustrates the value of number three, being the funda-

• ratio (perimeter: height) = 1760/280 Erc = 6,2857 equates to 2π to an accuracy of better than 0.05 percent (corresponding to the approximation of π as 22:7).

• other surprising arithmetic ratios and golden- mean- related dimensions are

The integer dimensions (440 and 280 Erc) as well as the irrational ratio's 5:8 and

= 2(44:14); (note the numeric resemblances between 44 ↔440 and 2(14) ↔

This ancient Roman temple, dedicated to all God's, is a most interesting monument for many reasons, a.o. for his unusual design showing a multilayered intangible content(**Figure 4a-d**). The building was founded as a rectangular temple about

*Roma, pantheon: (a) aerial view (photo Pinterest); (b) ground floor of rotunda and so-called portico (Wikimedia & author); (c) transversal section (Pinterest); (d) longitudinal section (Getty images); (e)* 

ϕ

, and with the exceptional sequence of a repeated

which results as

*DOI: http://dx.doi.org/10.5772/intechopen.95391*

double irrational by √ and

signed in **Figure 3c**.

**ca. 125 a.C. - temple**

2π *Architectural Design Canons from Middle Ages and Before: An Inspiration for Modern... DOI: http://dx.doi.org/10.5772/intechopen.95391*


The integer dimensions (440 and 280 Erc) as well as the irrational ratio's 5:8 and 2π = 2(44:14); (note the numeric resemblances between 44 ↔440 and 2(14) ↔ 280) also include (unknown) allegorical messages. [8]; [Wikipedia].
