3,700-year-old Babylonian tablet rewrites the history of maths

[EgyptianAmerican]

3,700-year-old Babylonian tablet rewrites the history of maths - and shows the Greeks did not develop trigonometry

The tablet is broken and probably had more rows, experts believe CREDIT: UNSW

A 3,700-year-old clay tablet has proven that the Babylonians developed trigonometry 1,500 years before the Greeks and were using a sophisticated method of mathematics which could change how we calculate today.

The tablet, known as Plimpton 332, was discovered in the early 1900s in Southern Iraq by the American archaeologist and diplomat Edgar Banks, who was the inspiration for Indiana Jones.

The true meaning of the tablet has eluded experts until now but new research by the University of New South Wales, Australia, has shown it is the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, palaces, and canals.

However unlike today’s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate.

“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.

“It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.


“This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics and education.

“This is a rare example of the ancient world teaching us something new.”

The Greek astronomer Hipparchus, who lived around 120BC, has long been regarded as the father of trigonometry, with his ‘table of chords’ on a circle considered the oldest trigonometric table.

A trigonometric table allows a user to determine two unknown ratios of a right-angled triangle using just one known ratio. But the tablet is far older than Hipparchus, demonstrating that the Babylonians were already well advanced in complex mathematics far earlier.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC. It is now in the Rare Book and Manuscript Library at Columbia University in New York.

“Plimpton 322 predates Hipparchus by more than 1000 years,” says Dr Wildberger.

“It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.


“A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us.”

The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

The left-hand edge of the tablet is broken but the researchers believe t there were originally six columns and that the tablet was meant to be completed with 38 rows.

“Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids,” added Dr Mansfield.

The new study is published in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.

http://www.telegraph.co.uk/science/...bylonian-tablet-rewrites-history-maths-could/

 

[StraightShooter]

Mitanni
Definition

by Joshua J. Mark
published on 28 April 2011

The Kingdom of Mittani, known to the people of the land, and the Assyrians, as Hanigalbat and to the Egyptians as Naharin and Metani, once stretched from present-day northern Iraq, down through Syria and into Turkey and was considered a great nation. Few records of the people themselves exist today but correspondence between kings of Mitanni and those of Assyria and Egypt, as well as the world’s oldest horse training manual, give evidence of a prosperous nation which thrived between 1500 and 1240 BCE. In the year 1350 BCE Mitanni was powerful enough to be included in the 'Great Powers Club' along with Egypt, the Kingdom of the Hatti, Babyloniaand Assyria.

THE PEOPLE OF MITANNI
The Mitanni dynasty ruled over the northern Euphrates-Tigris region between c. 1475 BCE and c. 1275 BCE. While the Mitanni kings were Indo-Iranians, they used the language of the local people which was at that time a non Indo-Iranian language, Hurrian (and so the land is sometimes referred to in ancient records as the Land of the Hurrians). The historian Leick writes, "The population of Mitanni was predominantly Hurrian, but the ruling elites were Indo-European warriors who called themselves Mariannu and who worshipped deities with Vedic names such as Indar, Uruwana, and the collective Devas. This elite was to intermarry with the local population, as the names of their children testify" (120). The capital of Mitanni was Wassukanni, located on the headwaters of the River Habur, a tributary of the Euphrates.

The name Washukanni is similar to the Kurdish word 'bashkani', 'bash' meaning good and 'kanî' meaning well or source, and so is translated as 'source of good' but also as 'source of wealth'. Some scholars have claimed that the ancient city of Sikan was built on the site of Washukanni, and that its ruins may be located under the mound of Tell el Fakhariya near Gozan in Syria.

AT ITS HEIGHT, THE MITANNI DYNASTY CONTROLLED TRADE ROUTES DOWN THE HABUR TO MARI AND UP THE EUPHRATES FROM TO CARCHEMISH.
THE GREAT KINGDOM
At its height, the Mitanni Dynasty controlled trade routes down the Habur to Mari and up the Euphrates from to Carchemish. They also controlled the upper Tigris and its headwaters at Nineveh. Their allies included Kizuwatna in south eastern Anatolia, Mukish, which stretched between Ugarit and Quatna west of the Orontes to the sea, and the Niya which controlled the east bank of the Orontes from Alalah down through Aleppo, Ebla and Hama to Quatna and Kadesh. To the east the Mitanni had good relations with the Hurrian-speaking Kassites whose territory corresponds to present-day Kurdistan. The lands of the Mitanni in northern Syria bordered eastern Anatolia to its west and extended east as far as Nuzi (present-day Kirkuk) and the river Tigris in the east. In the south it extended from Aleppo across to Mari on the Euphrates in the East. The entire region allowed agriculture without artificial irrigation. Herds of cattle, sheep, horses and goats were raised and the Mitanni were famed horsemen and charioteers. It is recorded that they were the innovators who spearheaded the development of the light war chariot with wheels that used spokes rather than the solid wood wheels, such as those used by the Sumerians, so that the chariots were faster and easier to maneuver. Excavations of the Hittite archives of Hattusa, near present-day Boğazkale (Turkey), found the oldest surviving horse training manual in the world. The work was written in 1345 BCE on four tablets and contains 1080 lines by a Mitanni horse trainer named Kikkuli, beginning with the words, "Thus speaks Kikkuli, master horse trainer of the land of Mitanni” and exhaustively describes the proper methods of training horses.

KING TUSHRATTA & THE COMING OF THE HITTITES
Little is known of the early kings of Mitanni owing to the later destruction of the culture by the Assyrians but the names of the early rulers are known through the correspondences with other countries. In the 16th century BCE the most prominent kings seem to have been Kirta, Shuttarna, and Barratarna. King Shaushtatar (ruled c. 1430) extended the boundaries of Mitanni through the conquest of Alalakh, Nuzi, Assur, and Kizzuwatna. Egypt, under Tuthmosis III (1479-1425 BCE), defeated the Mitanni at Aleppo after a long period of contention over control of the region of Syria. Later Egyptian dynasties entered into pacts and treaties with Mitanni and the daughter of the Mitanni King Tushratta, the princess Taduhepa, was given in marriage to Amenhotep III (1391-1353 BCE) as part of a treaty which balanced power between the two nations.This treaty was put to the test during a power struggle in Washukanni between Tushratta and a relative of the previous king, Shuttarna, known as Artatama II. Egypt backed Tushratta in this conflict while the Hittite king Suppiluliuma I backed Artatama II. Tushratta seemed poised to succeed when Egypt, fearing the growing power of the Hittites, withdrew its support. Suppiluliuma I, tired of diplomacy and now free to do as he pleased without fear of Egyptian reprisal, led his forces on Washukanni and sacked it. Tushratta was assassinated by his son, perhaps in an effort to save the city. Following this conquest, Mitanni was ruled by Hittite kings.



Stone Foundation Document of King Adad-Nirari I


THE ASSYRIAN CONQUEST OF MITANNI
Suppiluliuma I divided the former kingdom into two provinces with their capitals at Aleppo and Carchemish. The remainder of the region kept some degree of autonomy, though still a vassal state, and was known as Hanigalbat. At some point the region which was once Mitanni fell under the yoke of the Assyrian Empire. Exactly when is not clear but possibly during the reign of the Hittite king Mursili II, (1321-1295 BCE) and definitely before the reign of Tudhaliya IV and the Battle of Nihriya in 1245 BCE (which marks the beginning of the decline of the Hittite Empire). The Assyrian king Adad-Nirari I (ruled 1307-1275 BCE) left inscriptions telling of how an upstart Hittite king Shattuara I challenged his might and so Adad-Nirari I marched on Mittani, crushed their forces in battle, and carried Shattuara I back to Ashur in chains where he was forced to swear an oath of allegiance to the Assyrian ruler. While still an autonomous state, the kingdom now owed tribute and allegiance to Assyria and was no longer considered an equal of the other powers of the region.

Ancient Assyrian records further tell how, in the reign of King Shalmaneser I (1270's-1240's BCE), King Shattuara II of Mitanni rebelled against Assyria with the aid of a nomadic tribe known as the Ahlamu around 1250 BCE. Shattuara’s forces were well organized, fully armed, and had occupied all the mountain passes and waterholes to effectively cut off the Assyrian army’s water supply and severely hamper their attempts at foraging. Even so, hungry and thirsty, Shalmaneser’s army won a crushing victory. He claims in the records to have slain 14,400 men and the survivors were blinded and carried away. His inscriptions mention the conquest of nine fortified temples, 180 Hurrian cities were "turned into rubble mounds" and Shalmaneser "…slaughtered like sheep the armies of the Hittites and the Ahlamu his allies…". The cities from Taidu (also known as Taite) to Irridu were captured (an area which today comprises northern Iraq through Syria), as well as all of the region of the Mount Kashiyari range down to, and including, the city of Eluhat (also known as Eluhut which was located south-east in modern-day Turkey). A large part of the population of the conquered regions were sold into slavery and deported. Mitanni was then completely absorbed into the Assyrian Empire and gradually forgotten by history.

MAP
LEARN MORE
RELATED ARTICLES BOOKS BIBLIOGRAPHY CITE THIS WORK LICENSE

ABOUT THE AUTHOR

Joshua J. Mark
A freelance writer and former part-time Professor of Philosophy at Marist College, New York, Joshua J. Mark has lived in Greece and Germany and traveled through Egypt. He has taught history, writing, literature, and philosophy at the college level.

http://www.ancient.eu/Mitanni/

 

[EgyptianAmerican]

Mitanni
Definition

by Joshua J. Mark
published on 28 April 2011

The Kingdom of Mittani, known to the people of the land, and the Assyrians, as Hanigalbat and to the Egyptians as Naharin and Metani, once stretched from present-day northern Iraq, down through Syria and into Turkey and was considered a great nation. Few records of the people themselves exist today but correspondence between kings of Mitanni and those of Assyria and Egypt, as well as the world’s oldest horse training manual, give evidence of a prosperous nation which thrived between 1500 and 1240 BCE. In the year 1350 BCE Mitanni was powerful enough to be included in the 'Great Powers Club' along with Egypt, the Kingdom of the Hatti, Babyloniaand Assyria.

THE PEOPLE OF MITANNI
The Mitanni dynasty ruled over the northern Euphrates-Tigris region between c. 1475 BCE and c. 1275 BCE. While the Mitanni kings were Indo-Iranians, they used the language of the local people which was at that time a non Indo-Iranian language, Hurrian (and so the land is sometimes referred to in ancient records as the Land of the Hurrians). The historian Leick writes, "The population of Mitanni was predominantly Hurrian, but the ruling elites were Indo-European warriors who called themselves Mariannu and who worshipped deities with Vedic names such as Indar, Uruwana, and the collective Devas. This elite was to intermarry with the local population, as the names of their children testify" (120). The capital of Mitanni was Wassukanni, located on the headwaters of the River Habur, a tributary of the Euphrates.

The name Washukanni is similar to the Kurdish word 'bashkani', 'bash' meaning good and 'kanî' meaning well or source, and so is translated as 'source of good' but also as 'source of wealth'. Some scholars have claimed that the ancient city of Sikan was built on the site of Washukanni, and that its ruins may be located under the mound of Tell el Fakhariya near Gozan in Syria.

AT ITS HEIGHT, THE MITANNI DYNASTY CONTROLLED TRADE ROUTES DOWN THE HABUR TO MARI AND UP THE EUPHRATES FROM TO CARCHEMISH.
THE GREAT KINGDOM
At its height, the Mitanni Dynasty controlled trade routes down the Habur to Mari and up the Euphrates from to Carchemish. They also controlled the upper Tigris and its headwaters at Nineveh. Their allies included Kizuwatna in south eastern Anatolia, Mukish, which stretched between Ugarit and Quatna west of the Orontes to the sea, and the Niya which controlled the east bank of the Orontes from Alalah down through Aleppo, Ebla and Hama to Quatna and Kadesh. To the east the Mitanni had good relations with the Hurrian-speaking Kassites whose territory corresponds to present-day Kurdistan. The lands of the Mitanni in northern Syria bordered eastern Anatolia to its west and extended east as far as Nuzi (present-day Kirkuk) and the river Tigris in the east. In the south it extended from Aleppo across to Mari on the Euphrates in the East. The entire region allowed agriculture without artificial irrigation. Herds of cattle, sheep, horses and goats were raised and the Mitanni were famed horsemen and charioteers. It is recorded that they were the innovators who spearheaded the development of the light war chariot with wheels that used spokes rather than the solid wood wheels, such as those used by the Sumerians, so that the chariots were faster and easier to maneuver. Excavations of the Hittite archives of Hattusa, near present-day Boğazkale (Turkey), found the oldest surviving horse training manual in the world. The work was written in 1345 BCE on four tablets and contains 1080 lines by a Mitanni horse trainer named Kikkuli, beginning with the words, "Thus speaks Kikkuli, master horse trainer of the land of Mitanni” and exhaustively describes the proper methods of training horses.

KING TUSHRATTA & THE COMING OF THE HITTITES
Little is known of the early kings of Mitanni owing to the later destruction of the culture by the Assyrians but the names of the early rulers are known through the correspondences with other countries. In the 16th century BCE the most prominent kings seem to have been Kirta, Shuttarna, and Barratarna. King Shaushtatar (ruled c. 1430) extended the boundaries of Mitanni through the conquest of Alalakh, Nuzi, Assur, and Kizzuwatna. Egypt, under Tuthmosis III (1479-1425 BCE), defeated the Mitanni at Aleppo after a long period of contention over control of the region of Syria. Later Egyptian dynasties entered into pacts and treaties with Mitanni and the daughter of the Mitanni King Tushratta, the princess Taduhepa, was given in marriage to Amenhotep III (1391-1353 BCE) as part of a treaty which balanced power between the two nations.This treaty was put to the test during a power struggle in Washukanni between Tushratta and a relative of the previous king, Shuttarna, known as Artatama II. Egypt backed Tushratta in this conflict while the Hittite king Suppiluliuma I backed Artatama II. Tushratta seemed poised to succeed when Egypt, fearing the growing power of the Hittites, withdrew its support. Suppiluliuma I, tired of diplomacy and now free to do as he pleased without fear of Egyptian reprisal, led his forces on Washukanni and sacked it. Tushratta was assassinated by his son, perhaps in an effort to save the city. Following this conquest, Mitanni was ruled by Hittite kings.



Stone Foundation Document of King Adad-Nirari I


THE ASSYRIAN CONQUEST OF MITANNI
Suppiluliuma I divided the former kingdom into two provinces with their capitals at Aleppo and Carchemish. The remainder of the region kept some degree of autonomy, though still a vassal state, and was known as Hanigalbat. At some point the region which was once Mitanni fell under the yoke of the Assyrian Empire. Exactly when is not clear but possibly during the reign of the Hittite king Mursili II, (1321-1295 BCE) and definitely before the reign of Tudhaliya IV and the Battle of Nihriya in 1245 BCE (which marks the beginning of the decline of the Hittite Empire). The Assyrian king Adad-Nirari I (ruled 1307-1275 BCE) left inscriptions telling of how an upstart Hittite king Shattuara I challenged his might and so Adad-Nirari I marched on Mittani, crushed their forces in battle, and carried Shattuara I back to Ashur in chains where he was forced to swear an oath of allegiance to the Assyrian ruler. While still an autonomous state, the kingdom now owed tribute and allegiance to Assyria and was no longer considered an equal of the other powers of the region.

Ancient Assyrian records further tell how, in the reign of King Shalmaneser I (1270's-1240's BCE), King Shattuara II of Mitanni rebelled against Assyria with the aid of a nomadic tribe known as the Ahlamu around 1250 BCE. Shattuara’s forces were well organized, fully armed, and had occupied all the mountain passes and waterholes to effectively cut off the Assyrian army’s water supply and severely hamper their attempts at foraging. Even so, hungry and thirsty, Shalmaneser’s army won a crushing victory. He claims in the records to have slain 14,400 men and the survivors were blinded and carried away. His inscriptions mention the conquest of nine fortified temples, 180 Hurrian cities were "turned into rubble mounds" and Shalmaneser "…slaughtered like sheep the armies of the Hittites and the Ahlamu his allies…". The cities from Taidu (also known as Taite) to Irridu were captured (an area which today comprises northern Iraq through Syria), as well as all of the region of the Mount Kashiyari range down to, and including, the city of Eluhat (also known as Eluhut which was located south-east in modern-day Turkey). A large part of the population of the conquered regions were sold into slavery and deported. Mitanni was then completely absorbed into the Assyrian Empire and gradually forgotten by history.

MAP
LEARN MORE
RELATED ARTICLES BOOKS BIBLIOGRAPHY CITE THIS WORK LICENSE

ABOUT THE AUTHOR

Joshua J. Mark
A freelance writer and former part-time Professor of Philosophy at Marist College, New York, Joshua J. Mark has lived in Greece and Germany and traveled through Egypt. He has taught history, writing, literature, and philosophy at the college level.

http://www.ancient.eu/Mitanni/

Why are you de-railing my thread?

 

[Ceylal]

Why are you de-railing my thread?

He is adding to it..relax..interesting read..