Golden Mean Ratio: Egyptian Sculpture

Math in Ancient Sculpture is one of the most interesting and intriguing applications of mathematics, both formula equation and geometric structure.  This article examines the Golden Mean Ratio and Fibonacci   Sequence found in the Bust of Nefertiti in Egypt in the early 1900’s. Nefertiti literally, means, “the beautiful one has come”, and is the 14th-century BC Great Royal Wife (chief co-regent) of the Egyptian Pharaoh Akhenaten of the Eighteenth dynasty of Egypt, 1352 BC to 1336 BC.  The iconic Bust of Nefertiti is in Neues Museum of Berlin; though originally in Egypt (En.   Wikipedia.   Org / wiki/Nefertiti_Bust   (230px-Nofretete_Neues_Museum 2 .jpg)  During excavation of Nefertit’s Bust, one of the items found noted Thutmose as being the court sculptor of Egyptian Pharaoh Akhenaten, Nefertiti’s Royal Husband.  In Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science, Stakho speaks of the Berlusian philosopher Edward Soroko’s attempts to determine what mathematical ideas were used in the creation of Her Bust, “…Harmony was the perogative of the Divine order that dominated the universe, and geometry was the main tool of its expression. 

Nefertiti, playing role of Goddess, thus Her image personifying the Wisdom of the world, must have been formed with geometrical perfection and irreproachable harmony, beauty and clarity.  As a matter of fact, the main idea of ancient Egyptian aesthetic philosophy was to glorify the eternal, the measured, and the perfect in a constantly changing universe…In his analysis, he found a harmonious system of regular geometric figures such as triangles, squares, and rhombi.”  (Alekseĭ Petrovich Stakho; Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science; Scott Anthony Olsen. Book. English. 2009; pp 57-59)  Soroko believed that the Bust of Nefertiti was created based upon the Geometries of the Golden Mean Ratio and the Fibonacci Sequence.  A graphical image of Her Bust, as was drawn by Soroko is shown in this link:  http://www.pinterest.com/pin/529454499915732124/  Highly recommended to click on this link to have a finer and more detailed idea of the geometries that Thutmose is thought to have in mind when sculpting Her Bust.  One can appreciate, in particular, how the front top vertex of Her headdress is in perfect alignment with Her Heart and Breast Bone.

Depicted here, the Golden Mean Ratio, and in the geometries thought to be applied by Thutmose, the Egyptian Court Sculptor, in the creation of Nefertiti’s Bust:

n is to m, as m is to n − m,

or, algebraically,

 

n            =         m

_____            ______

m                     n – m

A more clear example of the pattern he believed Her Bust was created upon, the Fibonacci Sequence, can more easily be seen in examining nature’s pattern in pine cones, and seashells.  This ratio is also the most efficient mathematical equation for trees absorbing the most amount of sustenance from the sun’s rays, hence growing in a spiral.  In the same way, today, we can apply solar panels onto rooftops mimicking this pattern to most efficiently absorb the sun’s rays.  For further discussion on Fibonacci Sequence, visit here:  http://math-lessons.ca/fibonacci-sequence.html/

See in the photo at the top, the chamomile spiral, as well as in this link on “fibonacci-sequence” showing the pattern.  Adding two consecutive numbers from the sequence to equal the next one following, the basic mathematical sequence looks like this:

0,         1,            1,            2,            3,            5,            8,            13,            21,            34,            55,            89,            144,            233,            377, etc., etc.

That is:

0+1=1

1+1=2

2+1 (the “number” before)=3

3+2 (the number before)=5

5+3=8

8+5=13

13+8=21

34+21=55

55+34=89

89+34=144

144+233=377

etc., etc., etc.

Whereas the fibonacci sequence, cannot technically be exacted in real time, (similarly, there is no real exact end found as of yet to pi’s “3.14159265359…..”), mathematicians drew swirling squares around the spiral in the attempt to exact the formula – basically giving the left side of the human brain a way of understanding the right-brained infinite spiral, being that the left side of the brain requires finiteness / exactness to feel satisfied, shall we say.  

What kind of intriguing application can your class find to prove that math is interesting and fun?

We wonder if the geometries of Nefertiti’s Bust were also the same geometries of Nefertiti’s real-life human head.  The skulls of Ancient Egyptians, as well as those of Ancient Greece and other cultures, have definitely been shown to have geometrically perfect structures.  How can that be?

For samples of our Fun Learning Math Games, feel free to visit here:

http://butterflybooks.ca/geometry-games/ 

http://butterflybooks.ca/math-activities/