An ancient city has been unearthed in Egypt and dates back more than 5,000 years and contains houses, tools, pottery, and huge graves. The city lies by the River Nile, close to the temple of Seti I in Abydos. It is said to have been the city of tomb builders and architects. The rest below is from the BBC:
It is believed the city was home to important officials and tomb builders and would have flourished during early-era ancient Egyptian times.
Archaeologists have made a range of finds in the newly-discovered city including buildings, shards of pottery and tools.
It is believed that this location was home to important officials and tomb builders who may have been engaged in the construction of royal graves in the nearby sacred city of Abydos – a place of many temples, and a capital in an early period of ancient Egyptian history.
The area is in the southern province of Sohag, in Upper Egypt, home also to the city of Luxor, one of the country’s most popular tourist sites.
“About a mile behind where this material is said to be we have the necropolis with royal tombs going from before history to the period where we start getting royal names, we start getting identifiable kings,” Prof Chris Eyre, an Egyptologist based at the University of Liverpool, told the BBC.
“So, this appears to be the town, the capital at the very beginning of Egyptian history.”
1300 years before Thalès was born, Ancient Egyptians solved the famous theorem which now bears his name, Theorème de Thales in French, or Intercept theorem in English. Back then, it was called problem Number 53, and was part of the Rhind Papyrus. The value for π was already approximated as 3.16 (a 0.6% margin error, extremely good even by modern standards), 4000 years before that value was fixed at 3.14. So why are these theorems called after Pythagoras or Thales, when they had already existed thousands of years prior to their living?
The Rhind Papyrus is a famous papyrus written by the scribe Ahmes(Ahmose) around 1650 BC. It was copied from a now lost text from the reign of kingAmenemhat III (12th dynasty) 1500 years prior to Ahmose’s birth. His papyrus is one of the best known examples of advanced Egyptian mathematics; mathematician-priests of the Nile valley knew no peers. It was found during illegal excavations in or near the Ramesseum. It has been housed in the British Museum since 1865 along with the Egyptian Mathematical Leather Roll. Originally, this papyrus was 5 m long and 33 cm high. This is the most famous mathematical papyrus to have survived from Ancient Egypt.
This papyrus shows that Ancient Egyptians were very advanced mathematicians and were familiar with both roots and square roots. They could plot an arch by using offsets that were measured at regular intervals from a base line, and they could also find out areas. To find the area of a circle, the Egyptians used an area of a square on an 8/9 of the diameter, or (7/8) squared. They could also figure out the area of a triangle. They knew that the volume of a frustum of a square pyramid equaled (1/3) h (a2 + ab + b2) – modern mathematicians, 4000 years later, have still not found a better approximation. They also knew that to make right angled triangles, they had to use the ratio of 3:4:5. The Great Pyramid of Khufu, Great Pyramid of Giza, from the 4th Dynasty is a mathematical wonder: It is laid out with geometric precision – a near-perfect square base, with sides of 230 m that differ from each other by less than 20 cm, and faces that sloped upwards at an angle of 51 to reach an apex nearly 150 m above the desert floor. Khufu’s pyramid was built long before the Ahmose papyrus was written, indicating the beginning of this mathematical theory was about 1,000 years old by the year 1650 B.C.E.
The Rhind Papyrus is divided in 3 books. Book 1 includes problems 1 – 40, and is about algebra and arithmetics. Book 2 focuses on Geometry and spans problems 41 – 59, while Book 3 focuses on miscellaneous problems from number 60 – 87.
The first part of the Rhind papyrus, book 1, consists of reference tables and a collection of 21 arithmetic and 20 algebraic problems. The first part of the papyrus is taken up by the 2/n table. The fractions 2/n for odd nranging from 3 to 101 are expressed as sums of unit fractions.
Problems 41 – 46 show how to find the volume of both cylindrical and rectangular granaries. In problem 41, Ahmose computes the volume of a cylindrical granary. In modern mathematical notation (and using d = 2r) this gives V = (8/9)2 d2h = (256/81)r2h. The fractional term 256/81 approximates the value of π as being 3.1605.
Problem 47 is a table with fractional equalities which represent the ten situations where the physical volume quantity of “100 quadruple heqats” is divided by each of the multiples of ten, from ten through one hundred. The quotients are expressed in terms of Horus eye fractions, sometimes also using a much smaller unit of volume known as a “quadruple ro”. Egyptian numerals were based on 10, a precursor to our decimal system.
Problems 48–55 show how to compute an assortment of areas. Problem 48 is notable in that it succinctly computes the area of a circle by approximating π. Specifically, problem 48 explicitly reinforces the convention (used throughout the geometry section) that “a circle’s area stands to that of its circumscribing square in the ratio 64/81.” Problem number 53 is the famous Thales’s theorem, 1300 years before he was born!
Other problems show how to find the area of rectangles, triangles and trapezoids. The final six problems are related to the slopes of pyramids.
The third part of the Rhind papyrus consists of the remainder of the 91 problems, being 61, 61B, 62-82, 82B, 83-84, and “numbers” 85-87, which are items that are not mathematical in nature. This final section contains more complicated tables of data, several pefsu problems which are algebraic problems concerning food preparation, and even an amusing problem (number 79) which is suggestive of geometric progressions, geometric series, and certain later problems and riddles in history.
So, it is truly no surprise that over several thousand years later, modern-day architects still cannot reproduce the great pyramids of Egypt… well, simply because these were quite advanced mathematicians and scientists. In all ancient Egyptian mathematics, there is not a single mathematical error, not in trigonometry, algebra, geometry, arithmetic, or mechanics. No wonder we still are in awe at the Egyptian Pharaonic era. It is a pity that some of their work was “stolen” by the likes of Thales and Pythagoras and renamed after them. It is a pity that so many of us have lived in ignorance of such great science on our continent. It is sad that most African kids have been taught in their classrooms the Thales theorem or Pythagorean one or Archimede (problem 10 of the Moscow Papyrus solves Archimede’s at least 1700 years earlier) without ever being told about their famous intelligent ancestors who had the answers to all these over 3000 years earlier. So today, after looking at the Rhind Papyrus and at problem number 53, I no longer call this the Theorem of Thales or Intercept Theorem, but rather the Egyptian theorem, and Pythagorastriangle,the Egyptian triangle.
For more information, check out the works of Cheikh Anta Diop (Apport de l’Afrique à la Civilisation Universelle, 1985 – published in Presence Africaine 1987), Beatrice Lumpkin (African and African-American contributions to mathematics, PPS Geocultural Essaysbseries, 1987), Ivan van Sertima, and Elikia M’Bokolo.
I am sure every African child has read either the entire book or excerpts of ‘L’Enfant Noir‘, ‘African Child‘ by the Guinean author Camara Laye . It is a school classic. When we were in school, the teacher will often give us dictations from this book. The book focuses mostly about Camara Laye ‘s childhood and was written in the 1950s at a time when most African writers were talking about independence, negritude, panafricanism, etc. This earned Laye’s some tough remarks from Cameroonian author Mongo Beti and others about his lack of interest in panafricanism and African independences. Today, I present to you this poem, ‘A ma mère / To my mother‘ of Camara Laye to his mother (published in Coup de Pillon), which is in reality an ode to all African women, and all mothers around the globe. Good to note his mentioning of blacksmiths in this poem, especially given that Camara Laye’s family was Malinke and he was born into a caste that traditionally worked as blacksmiths and goldsmiths. The English translation is by Deborah Weagel. Enjoy!
A ma Mère
Femme noire, femme africaine,
Ô toi ma mère, je pense à toi…
Ô Daman, ô ma Mère,
Toi qui me portas sur le dos,
Toi qui m’allaitas, toi qui gouvernas mes premiers pas,
Toi qui la première m’ouvris les yeux aux prodiges de la terre,
Je pense à toi…
Femme des champs, femme des rivières femme du grand fleuve, ô toi, ma mère je pense à toi…
Ô toi Daman, Ô ma mère,
Toi qui essuyas mes larmes,
Toi qui me réjouissais le cœur,
Toi qui, patiemment, supportais mes caprices,
Comme j’aimerais encore être près de toi,
Etre enfant près de toi !
Femme simple, femme de la résignation, Ô toi ma mère, je pense à toi. Ô Daman, Daman de la grande famille des forgerons, Ma pensée toujours se tourne vers toi, La tienne à chaque pas m’accompagne, Ô Daman, ma mère, Comme j’aimerais encore être dans ta chaleur, Etre enfant près de toi…
Femme noire, femme africaine, Ô toi ma mère, Merci, merci pour tout ce que tu fis pour moi, Ton fils si loin, si près de toi.
To my Mother
Black woman, African woman, O mother, I think of you …
O Dâman, O mother,
who carried me on your back, who nursed me,
who governed by first steps,
who opened my eyes to the beauties of the world, I think of you …
Woman of the fields, woman of the rivers, woman of the great river, O
mother, I think of you …
O Dâman, O mother, who wiped my tears,
who cheered up my heart,
who patiently dealt with my caprices,
how I would love to still be near you.
Simple woman, woman of resignation, O mother, I think of you.
O Dâman, Dâman of the great family of blacksmiths, my thoughts are
always of you, they accompany me with every step,
O Dâman, my mother, how I would love to still feel your warmth,
to be your child that is close to you …
Black woman, African woman, O mother, thank you; thank you for all
that you have done for me, your son, so far away yet so close to you!
ONCE upon a time there were two men who were such great friends that they were almost always together. If one was seen the other was sure to be near. They had given one another special names, which were to be used only by themselves. One name, Maku Mawu, meant, “I will die God’s death,” and the other, Maku Fia, “I will die the King’s death.”
By and by, however, the other villagers heard these names and gradually everyone got into the habit of calling the two friends by the nicknames in preference to the real ones. Finally, the King of the country heard of them and wished to see the men who had chosen such strange titles. He sent for them to Court, and they came together. He was much pleased with the one who had chosen the name of “Maku Fia,” but he was annoyed at the other man’s choice and sought a chance of punishing him.
When he had talked to them a little while, he invited both to a great feast which he was to give in three days’ time. As they went away he gave a fine large yam to Maku Mawu and only a small round stone to his own favourite. The latter felt somewhat aggrieved at getting only a stone, while his friend got such a fine yam. Very soon he said, “Oh, dear! I do not think it is any use carrying this stone home. How I wish it were a yam! Then I could cook it for dinner.” Maku Mawu being very generous— immediately replied, “Then change with me, for I am quite tired of carrying my great yam.” They exchanged, and each went off to his own home. Maku Fia cut up his yam and cooked it. Maku Mawu broke his stone in half and found inside some beautiful ornaments which the King had hidden there. He thought that he would play a trick on the King, so told nobody what had been in the stone.
On the third day they dressed to go to the King’s feast. Maku Mawu put on all the beautiful ornaments out of the stone. Maku Fia dressed himself just as usual.
When they reached the palace the King was amazed to see the wrong man wearing his ornaments, and determined to punish him more effectually next time. He asked Maku Fia what he had done with the stone, and the man told him he had exchanged it for his friend’s yam.
At first the King could not think of any way to punish Maku Mawu, as, of course, the latter had not done anything wrong. He soon had an idea, however. He pretended to be very pleased with the poor man and presented him with a beautiful ring from his own finger. He then made him promise to come back in seven days and show the ring to the King again, to let the latter see that it was not lost. If by any chance he could not produce the ring—he would lose his head. This the King did, meaning to get hold of the ring in some way and, so get the young man killed.
Maku Mawu saw what the King’s design was, so determined to hide the ring. He made a small hole in the wall of his room, put the ring in it, and carefully plastered over the place again. No one could see that the wall had been touched.
After two days the King sent for the wife of Maku Mawu and asked her to find the ring. He promised her a large sum of money for it not telling her, of course, what would happen to her husband if the ring were lost. The woman went home and searched diligently but found nothing. Next day she tried again with no better success. Then she asked her husband what he had done with it. He innocently told her it was in the wall. Next day, when he was absent, she searched so carefully that at last she found it.
Delighted, she ran off to the King’s palace and gave the ring to him. She got the promised money and returned home, never dreaming that she had really sold her husband’s life.
On the sixth day the King sent a message to Maku Mawu, telling him to prepare for the next day. The poor man bethought himself of the ring and went to look if it were still safe. To his despair the hole was empty. He asked his wife and his neighbours. All denied having seen it. He made up his mind that he must die.
In the meantime the King had laid the ring in one of the dishes in his palace and promptly forgot about it. When the seventh morning had arrived he sent messengers far and wide, to summon the people to come and see a man punished for disobeying the King’s orders. Then he commanded his servants to set the palace in order, and to take the dishes out of his room and wash them.
The careless servants—never looking-to see if the dishes were empty or not took them all to a pool near by. Among them was the dish containing the ring. Of course, when the dish was being washed, out fell the ring into the water—without being noticed by the servants.
The palace being all in readiness, the King went to fetch the ring. It was nowhere to be found and he was obliged to go to the Assembly without it.
When every one was ready the poor man, Maku Mawu, was called to come forward and show the ring. He walked boldly up to the King and knelt down before him, saying. “The ring is lost and I am prepared to die. Only grant me a few hours to put my house in order.” At first the king was unwilling to grant even that small favour, but finally he said, “Very well, you may have four hours. Then you must return here and be beheaded before the people.” The innocent man returned to his home and put everything in order. Then, feeling hungry, he thought, “I may as well have some food before I die. I will go and catch a fish in the pool.”
He accordingly took his fish-net and bait, and started off to the very pool where the King’s dishes had been washed. Very soon he caught a fine large fish. Cutting it open, to clean it, his delight may be imagined at finding the lost ring inside it.
At once he ran off to the palace crying: “I have found the ring! I have found the ring!” When the people heard him, they all shouted in joy: “He named himself rightly ‘Maku Mawu,’ for see—the death God has chosen for him, that only will he die.” So the King had no excuse to harm him, and he went free.
Source:Barker, W. H. and Sinclair, C. West African Folk-tales. Lagos, Africa: Bookshop, 1917.
In March 1896, a well-disciplined and massive Ethiopian army did the unthinkable—it routed an invading Italian force and brought Italy’s war of conquest in Africa to an end. In an age of relentless European expansion, Ethiopia had successfully defended its independence and cast doubt upon an unshakable certainty of the age—that sooner or later all Africans would fall under the rule of Europeans. The battle of Adwa marked Ethiopia’s victory against Italian colonization. It all started with the treaty of Wuchale. The short documentary below gives you an idea about it. This indeed was the biggest, the only, African defeat of European expansionism and ugly scramble for Africa. Enjoy!
In Africa, Ethiopia is the only country which was never colonized by a European power. This was the result of the famous Battle of Adwa on March 1, 1896, which marked the Ethiopian victory against Italian colonialism. The Battle of Adwa against Italy arose from the deceitful 1889 Treaty of Wuchale between the Ethiopian Empire and Italy, a treaty whose article 17 had two different meanings in Amharic and Italian versions: The Amharic version recognized the sovereignty of Ethiopia and its relationship with Italy as just a diplomatic partnership, while the Italian version made Ethiopia Italy’s protectorate. The moment that discrepancy/trickery was uncovered, Empress Taytu Betul was the first to agitate Emperor Menelik II and other men to stand up for liberty, and dignity against Italian aggression. I am publishing here the Treaty of Wuchale. Special thanks to the Horn Affairs website for publishing the English version in its entirety. Some claim that Article 3 actually paved the way for Italians to claim Ethiopian lands (Eritrea). Well, here is the document of one of those treacherous treaties signed or rather forced upon Africans by European powers. Thank goodness for Taytu Betul,Menelik II, and their team of loyal and intelligent ministers and interpreters. I have attached the pdf version too.
Treaty of friendship and trade between the kingdom of Italy and the Empire of Ethiopia (Treaty of Wuchale)
His Majesty King Umberto I of Italy and Menelik His Majesty The King of Kings of Ethiopia, in order to make meaningful and lasting peace between the two Kingdoms of Italy and Ethiopia have agreed to conclude a treaty of friendship and commerce .
And His Majesty the King of Italy having delegated as his representative, Count Pietro Antonelli, Commander of the Crown of Italy, Knight SS. Maurice and Lazarus, his extraordinary posted by His Majesty the King Menelik, whose full powers were found in good and due form, and His Majesty the King Menelik concluded in his name as King of Kings of Ethiopia, agreed and concludes the following Articles:
Article 1. There will be perpetual peace and friendship between His Majesty the King of Italy and His Majesty the King of Kings of Ethiopia and between their respective heirs, successors, servants and protected populations.
Article 2. Each Contracting Party shall be represented by a diplomatic agent accredited to I’altra and may appoint consuls, agents and consular officers in the other. Such officials shall enjoy all the privileges and immunities according to the customs of the European governments.
Article 3. To remove any ambiguity about the limits of the territories over which the two Contracting Parties shall exercise sovereign rights, a special commission composed of two delegates and two Ethiopians will draw on Italian soil with special signals a permanent boundary line whose strongholds are established as below: a) the line of the plateau will mark the Ethiopian-Italian border; b) from the region Arafali Hala, Sagan and Asmara are villages in the Italian border; c) Adi and Adi Nefas Joannes Bogos will be on the side of the Italian border; d) by Adi Joannes a straight line extended from east to west will mark the border between Italy and Ethiopia.
Article 4. The monastery of Debra Bizen with all their possessions will remain the property of the Ethiopian government but will never use it for military purposes.
Article 5. The caravans from or to Massawa to Ethiopian territory pay on one single law of the customs entry of 8 per cent on the value of the goods.
Article 6. The trade of arms and ammunition from or through Massawa to Ethiopia will be free for the only King of Kings of Ethiopia. Whenever they want to get the passage of such kinds will make regular application to the Italian authorities, bearing the royal seal. The wagons with load of weapons and ammunition will travel under the protection and cover of Italian soldiers until alconfine Ethiopia.
Article 7. The subjects of each of the two Contracting Parties will be free to enter, travel, go out with their merchandise and effects in the other country and will enjoy greater protection of the Government and its employees. And, therefore, strictly forbidden to people on both sides armed contractors to meet many or few and pass their borders in order to impose itself on people and groped by force to provide food and livestock.
Article 8. The Italians in Ethiopia and Ethiopians in Italy or Italian possessions can buy or sell, take or lease and in any other manner dispose of their property no less than the natives.
Article 9. And fully guaranteed in both states the option for other subjects to practice their religion.
Article 10. Any disputes or quarrels between the Italians in Ethiopia will be defined by the Italian in Massawa or his delegate. The fights between Italians and Ethiopians will be defined by the Italian in Massawa or his delegate and a delegate of the Ethiopian.
Article 11. Dying in an Italian in Ethiopia or an Ethiopian in Italian territory, the local authorities were carefully kept all his property and held at the disposal of government to which the deceased belonged.
Article 12. In any event, circumstance or for any Italians accused of a crime will be judged by the Italian. That is why the Ethiopian authorities shall immediately deliver to the Italians in Massawa accused of having committed a crime. They also accused the Ethiopians of crime committed on Italian soil will be judged by the Ethiopian.
Article 13. His Majesty the King of Italy and His Majesty the King of Kings of Ethiopia is obliged to deliver criminals who may have become refugees, to escape punishment by the rulers of one on the other domains.
Article 14. The slave trade was against the principles of the Christian religion, His Majesty the King of Kings of Ethiopia is committed to prevent it with all his power, so that no caravan of slaves can cross its member.
Article 15. This Treaty shall be valid throughout the Ethiopian Empire.
Article 16. While in the present Treaty, after five years from the date of signature, one of two High Contracting Parties may wish to introduce some modifications to do so, but he must prevent the other a year earlier, while remaining firm and every single concession on territory.
Article 17.His Majesty the King of Kings of Ethiopia can  use the Government of His Majesty the King of Italy for all treatments that did business with other powers or governments.
Article 18. If His Majesty the King of Kings of Ethiopia intends to grant special privileges to nationals of third state to establish businesses and industries in Ethiopia, will always be given, under equal conditions, preference to the Italians.
Article 19. This treaty being drafted in Italian and Amharic and the two versions agree with each other perfectly, both texts shall be deemed official, and will in every respect equal faith.
Article 20. This Treaty shall be ratified.
In witness whereof, Count Pietro Antonelli on behalf of His Majesty the King of Italy, His Majesty the King of King Menelik of Ethiopia, in his own name, signed and affixed their seal to this Treaty, at the camp Uccialli of 25 miazia 1881 corresponding to May 2, 1889.
Imperial Seal of Ethiopia For His Majesty the King of Italy Pietro Antonelli
Ratification of MS, Monza, September 29, 1889
 Article 17 has an obligatory sense in the Italian language version of the Treaty.