Amenhotep II

Amenhotep II (Amun is Satisfied) was the seventh Pharaoh of the 18th dynasty of Egypt. Amenhotep inherited a vast kingdom from his father Thutmose III.  His reign is usually dated from 1427 to 1401 BC.

Museo Egizio Torino

How to measure the stair angle

According to the site of Duradek http://duradekmidatlantic.com/durarailchecklisthelp.html you can
use a protractor (available at most hardware stores) to determine this angle.

Lay a straightedge across a minimum of 3 stair nosings. Put your universal protractor on the straightedge and measure the angle. Note that the more stair nosings you have under the straightedge, the more accurate the angle will be. In the case that the run of stairs is very long, measure the stair angle at 2 or 3 places along the run to check that the angle remains constant along the full run.


I am proposing that Kha the architect at Deir El-Medina, Egypt, supervisor of the projects of three kings of the 18th Dynasty used his protractor to check the inclination of stairs for instance. You can see it at the Egyptian Museum of Torino. Read more at http://stretchingtheboundaries.blogspot.com/2011/08/khas-protractor.html

A modern universal protractor for building is that shown in the following figure.

Kha

 

Kha, the architect

Museo Egizio, Torino 

Back to Kha's protractor

In the post "Kha's protractor", I have discussed an object found in the tomb of  an ancient egyptian architect, Kha.  It can be used to measure angles.Plums, levels, protractors , compasses and so on are instruments for surveying. See http://en.wikipedia.org/wiki/Surveying and the table http://en.wikipedia.org/wiki/File:Table_of_Surveying,_Cyclopaedia,_Volume_2.jpg
In this table there is the image of a compass rose. We can start from it and go back to the Kha's rose.

Kha's protractor

Kha was an architect at Deir El-Medina, Egypt, supervisor of some projects completed during the reigns of three kings of the 18th Dynasty (approximately 1440-1350 BC). Buried with his wife Merit, the items of their tomb are exposed at the Egyptian Museum, Torino. The papers at http://arxiv.org/abs/1107.4946 describes some devices of the ancient Egypt masonry (cubits, cords, plumb, levels and squares), that Kha used during his activity. An object among those found in his tomb could be used a protractor.

The figure shows an object from the Kha’s Tomb supposed to be the case of a balance scale, or the scale itself as reported by the corresponding label. In a previous preparation of the items of Kha’s Tomb, it was possible to see the front and back of the object. They are the same, with the same complex decoration.

The tool has a complex decoration, that suggested me the case could be used as a protractor, to determine directions and measure angles. The detail of decoration is shown in the following figure. 

 We see the 16-fold symmetry of a compass rose with 16 leaves as an inner decoration. Outside this rose there is a polygonal line with 18 corners and then 36 sides. In the inner decoration we can see the fraction 1/16 corresponding to one leaf. The Egyptian knew  and used the fractions as the sum of distinct unit fractions. That is, a fraction was written as a sum of fractions, each fraction having a numerator equal to 1 and a denominator equal to a positive  integer. Every positive rational number can be represented by an Egyptian fraction. In this ancient system of calculus, the Eye Of Horus defined the Old Kingdom number one, such as, 1 =  1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64, rounded-off at the six-term. A 1/64 is needed to have the exact value 1. The separated parts of the Eye of Horus were used to write describe the fractions. May be, Kha used the balance case for calculations, or simply as a protractor when he was using a plumb, a level or a scale, to find vertical or equilibrium positions, but also to measure the deviation from vertical or horizontal directions. 

Is there anything we can tell about number 36, the number of corners of the external decoration of the architect’s case? Let us remember that the Egyptians has the Decans, 36 groups of stars which rise in succession from the horizon due to the earth rotation. The rising of each decan marked the beginning of hours of the night. In the ancient Egypt, the decans were used as a sidereal clock beginning by at least the 9th or 10th Dynasty (ca 2100 BC). Probably, the object found in the Kha’s tomb had simply a geometrical decoration, such as that on another object of the tomb, which seems to be a “rose of direction”. 

The use of 1/16 fraction, the coincidence of the number of corners with that of decans, and the fact that the decoration was engraved on the instrument of an architect, suggest me that this object had been used as a protractor instrument with two scales, one based on Egyptian fractions, the other based on decans. Assuming this tool used to evaluate angles, let me show a possible set-up to measure the angle of an inclined plane. Note that the case has a lid. Let us imagine to remove the lid; the case has a perfectly linear side, that can be put on a smooth surface, as shown in the following figure.

 

(http://arxiv.org/abs/1107.4946)

When the surface is horizontal, using a plumb to have the vertical direction, one of the directions of the rose of the case coincides with the direction of the plumb (the line between leaves 1-16 or 8-9 seems to be perpendicular to the side of the case). If the surface is inclined, the direction of the rose is inclined forming a certain angle with respect to the vertical. This angle has the same value of the angle of the inclined plane.  Geometry originated as a practical science, to measure lengths, surfaces and volumes. In my opinion, Kha could have used his tool, with the contemporary use of a plumb to have a reference direction, to create a set-up able to provide a practical measurement of inclination. The Kha’s protractor could be one of the first devices to measure angles. 

References 

TT8, http://en.wikipedia.org/wiki/TT8

Turin Egyptian Museum: the tomb of Kha 

Deir El Medina: The Painted Tombs, Christine Hobson, Exploring the World of the Pharaohs: A 

complete guide to Ancient Egypt, Thames & Hudson, 1993. 

Building in Egypt; Pharaonic Stone Masonry, Dieter Arnold, Chapter 6, Tools and their 

applications, New York and Oxford, 1991 

Cubits, http://en.wikipedia.org/wiki/Cubit

E. Robens and R.S.H. Mikhail, The ancient Egyptian balance, Thermochimica Acta, Volume 

82(1), 1 December 1984, Pages 63-80. 7. Egypt Plumb Bobs, Wolfgang Ruecher, Wolf’s Plumb Bob News, Issue 02, Feb.2010, 

http://www.plumbbob.de/media//DIR_42117/DIR_120101/309a7eac7359df18ffff818cac14422e.pdf

http://en.wikipedia.org/wiki/Eye_of_Horus

http://en.wikipedia.org/wiki/Egyptian_fraction

http://en.wikipedia.org/wiki/Decans

Scarab seal

"Ancient Egyptian scarabs were popular amulets in ancient Egypt. According to ancient Egyptian myths, the sun  rolls across the sky each day and transforms bodies and souls. Modeled upon the Scarabaeidae family dung beetle, which rolls dung into a ball for the purposes of eating and laying eggs that are later transformed into larva, the scarab was seen as an earthly symbol of this heavenly cycle. This came to be iconographic, and ideological symbols were incorporated into Ancient Egyptian society."

From Wiki

Heart-scarab with a decoration on the back

(Egyptian Museum, Torino)

See my book

http://www.scribd.com/doc/42000776/Ancient-Egyptian-Seals-and-Scarabs-by-A-C-Sparavigna-2009

Painted ostraca

Painted ostraca

Egyptian Museum, Torino

Primo Maggio - Festa del Lavoro

Museo Egizio - Torino

Egyptian faience

"Egyptian faience is a non-clay based ceramic displaying surface vitrification which creates a bright lustre of various blue-green colours. Having not been made from clay it is often not classed as pottery. It is called "Egyptian faience" to distinguish it from faience, the tin glazed pottery associated with Faenza in northern Italy. Egyptian faience, both locally produced and exported from Egypt, occurs widely in the ancient world, and is well known from Mesopotamia, the Mediterranean and in northern Europe as far away as Scotland." Wiki

Faience bowl blue-glazed decorated with lotus flowers and the face of the goddess Hathor, symbol of rebirth are the decoration.

Faience. Provenance unknown. New Kingdom, dynasty XVIII-XX (1350-1070 B.C.)
Egyptian Museum, Turin.

Weighing of the Heart

"In Egyptian religion, the heart was the key to the afterlife. It was conceived as surviving death in the nether world, where it gave evidence for, or against, its possessor. It was thought that the heart was examined by Anubis and the deities during the Weighing of the Heart ceremony. If the heart weighed more than the feather of Maat, it was immediately consumed by the monster Ammit."
Wiki

Egyptian Museum Torino

Four sons of Horus

Statuette dei quattro figli di Horus: Duamutef, a testa di sciacallo, Hapi, a testa di babbuino, Qebehsebuf, a testa di falco, Amset, a testa umana erano i protettori delle viscere del defunto, XXV-XXXI dinastia. Statuettes of the four sons of Horus:  Duamutef, jackal headed, Hapi, baboon headed,  Qebehsebuf, falcon headed, and human headed Amset, protectors of the deceased's viscera,  Dinasty XXV-XXXI
(712-332 BC)

Eye of Horus

The Eye of Horus is an ancient Egyptian symbol of protection, royal power and good health. The eye is personified in the goddess Wadjet. The name Wadjet is derived from 'wadj' meaning 'green' hence 'the green one' and was known to the Greeks and Romans as 'uraeus' from the Egyptian 'iaret' meaning 'risen one' from the image of a cobra rising up in protection. More at Wiki
Wadjet was one of the earliest of Egyptian deities who later became associated with other goddesses such as Bast, Mut, and Hathor, who is also depicted with this eye. Burial amulets were often made in the shape of the Eye of Horus, to protect the owner in the afterlife and to ward off evil. Ancient Egyptian and Near Eastern sailors would frequently paint the symbol on the bow of their vessel to ensure safe sea travel (Charles Freeman, The Legacy of Ancient Egypt, Facts on File, Inc. 1997. p.91).
"Horus was the ancient Egyptian sky god who was usually depicted as a falcon. His right eye was associated with the sun Ra. The eye symbol represents the marking around a Peregrine Falcon's eye that includes the "teardrop" marking sometimes found below the eye."
It is interesting to note that, in the ancient egyptian calculus, the Eye Of Horus defined number one (1) = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64, by throwing away 1/64. The parts of the Eye were used to represent fractions.

Amulets on display at the Egyptian Museum, Torino

Ozymandias

I met a traveller from an antique land
Who said: Two vast and trunkless legs of stone
Stand in the desert. Near them, on the sand,
Half sunk, a shattered visage lies, whose frown
And wrinkled lip, and sneer of cold command
Tell that its sculptor well those passions read
Which yet survive, stamped on these lifeless things,
The hand that mocked them and the heart that fed.
And on the pedestal these words appear:
"My name is Ozymandias, king of kings:
Look on my works, ye Mighty, and despair!"
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare
The lone and level sands stretch far away.

- Percy Bysshe Shelley, 1818

Questa poesia parla di Ozymandias, altro nome di Ramses II.

Ramses II, Egyptian Museum, Torino

Testa osiriaca danneggiata

"Uno dei pezzi esibiti alla mostra di antichità del Museo Egizio di Torino a Shizuoka (Giappone), durante i lavori di imballo/trasporto, ha subito un grave danno. Si tratta della testa osiriaca che era a suo tempo stata riparata con l'aggiunta di una corona bianca, non sua. Viva preoccupazione degli Egittologi italiani."
http://www.archaeogate.org/egittologia/article/1277/1/danneggiata-la-testa-osiriaca-del-museo-egizio-di-torin.html

Egyptian Museum, Torino

This head has been damaged during the packaging after an exhibition in Japan

Night at the Museum - 4 - Egypt

Wood and faience objects at the Egyptian Museum

Isis and Harpocrates

In late Greek mythology as developed in Ptolemaic Alexandria, Harpocrates is the god of silence, adapted from the Egyptian child god Horus. To the ancient Egyptians, Horus represented the new-born Sun, rising each day at dawn. When the Greeks conquered Egypt under Alexander the Great, they transformed the Egyptian Horus into their Hellenistic god known as Harpocrates, a rendering from Egyptian Har-pa-khered or Heru-pa-khered (meaning "Har, the Child"). Horus was conceived by Isis, the mother goddess, from Osiris, the original god-king of Egypt, who had been murdered by his brother Set.  Among the Egyptians the full-grown Horus was considered the victorious god of the Sun who each day overcomes darkness. In this way Harpocrates, the child Horus, personifies the newborn sun each day, the first strength of the winter sun, and also the image of early vegetation. Egyptian statues represent the child Horus, pictured as a naked boy with his finger on his mouth, a realization of the hieroglyph for "child" , or with the mother Isis.
From Wiki

Isis and the child Harpocrates - Museo Egizio

Amun

The king and the god Amun. This sculpture represents the king's allegiance to the Theban god Amun. The sides of the throne are decorated with hieroglyphs forthe unification of Upper and Lower Egypt. Limestone, Dinasty XVIII,reign of Horemheb (1319-1292 BC), Temple of Amun, Thebes.

Hathor

"Hathor was an Ancient Egyptian goddess who personified the principles of love, beauty, music, motherhood and joy. She was one of the most important and popular deities throughout the history of Ancient Egypt. Hathor was worshipped  ... as "Mistress of the West" welcoming the dead into the next life. In other roles she was a goddess of music, dance, foreign lands and fertility who helped women in childbirth, as well as the patron goddess of miners. The cult of Hathor predates the historical period and the roots of devotion to her are, therefore, difficult to trace, though it may be a development of predynastic cults who venerated the fertility, and nature in general, represented by cows.
Hathor is commonly depicted as a cow goddess with head horns in which is set a sun disk with Uraeus."
Source: Wiki

Museo Egizio, Torino

Night at the Museum - 1 - Egypt

Here a film showing some statues you can see visiting the Egyptian Museum, Torino

In occasion of the Winter Olympic Games, Torino 2006, the exibition space of the  Museum hosting the statues gained a new stage design created by Dante Ferretti (two times awared by the Academy for Best Art Direction).  Visitors entering the room were  plunged in a dark space where only the statues were lighted. Dark walls and mirrors on them, background music of flutes with the rattling of a sistrum, created a suggestive feeling of being in Egypt.