Babylonian mathematics Eleanor Robson University of Cambridge.
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Transcript of Babylonian mathematics Eleanor Robson University of Cambridge.
![Page 1: Babylonian mathematics Eleanor Robson University of Cambridge.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649dda5503460f94ad023a/html5/thumbnails/1.jpg)
Babylonian mathematics
Eleanor RobsonUniversity of Cambridge
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Outline
• Introducing ourselves• Going to school in ancient Babylonia• Learning about Babylonian numbers• Learning about Babylonian shapes• Question time
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Who were the Babylonians?
• Where did they live?• When did they live?• What were their lives like?
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We live here
The Babylonians lived here, 5000-2000 years ago
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• Cities and writing for 1500 years already
• Brick-built cities on rivers and canals
• Wealth through farming: barley and sheep
• Central temples, to worship many gods
• King Hammurabi (1792–1750 BC)
• Most children didn’t go to school
Babylonia, 1900–1650 BC
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Babylonian men and women
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Cuneiform writing
• Wedges on clay– Whole words– Syllables – Word types– 600 different signs
• Sumerian language– No known relatives
• Akkadian language– Related to Hebrew, Arabic,
and other modern Middle Eastern languages
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Cuneiform objects
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Professional scribes• Employed by:
– Temples– Palaces– Courts of law– Wealthy families
• Status:– Slaves– Senior officials– Nobility
• In order to write:– Receipts and lists– Monthly and annual accounts– Loans, leases, rentals, and
sales– Marriage contracts, dowries,
and wills– Royal inscriptions– Records of legal disputes– Letters
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I’m an archaeologist of maths
• Archaeology is the study of rubbish– To discover how people lived and died– To discover how people made and used
objects to work with and think with
• Doing maths leaves a trail of rubbish behind
• I study the mathematical rubbish of the ancient Babylonians
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Imagine an earthquake destroys your school in the
middle of the night …
• An archaeologist comes to your school 500 years from now …
• What mathematical things might she find in your school?
• What would they tell her about the maths you do?
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Some mathematical things in modern schools
• Text books and exercise books• Scrap paper and doodles• Mathematical instruments from rulers to
calculators• Mathematical displays from models to
posters• Computer files and hardware
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But isn’t maths the same everywhere?
• Two different ways of thinking about maths:
• Maths is discovered, like fossils– Its history is just about who discovered
what, and when
• Maths is created by people, like language– Its history is about who thought and used
what, and why
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The archaeology of Babylonian maths
• Looking at things in context tells us far more than studying single objects
• What sort of people wrote those tablets and why?
• Tablets don’t rot like paper or papyrus do
• They got lost, thrown away, or re-used
• Archaeologists dig them up just like pots, bones or buildings
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The ancient city of Nippur
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Maths at school: House F• A small house in Nippur,
10m x 5m• Excavated in 1951• From the 1740s BC• 1400 fragments of tablets
with school exercises– Tablets now in Chicago, Philadelphia,
and Baghdad
• Tablet recycling bin• Kitchen with oven• Room for a few students
19 tablets48 tablets29 tablets348tablets
3 tablets11 tablets967 tablets+ 46 tablets?tanour
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The House F curriculum• Wedges and signs• People’s names• Words for things (wood,
reed, stone, metal, …)• How cuneiform works• Weights, measures,
and multiplications• Sumerian sentences• Sumerian proverbs• Sumerian literature
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Babylonian numbers
• Different: cuneiform signs pressed into clay– Vertical wedges 1–9– Arrow wedges 10–50
• Different/same: in base 60– What do we still count in
base 60?
• Same: order matters– Place value systems• Different: no zero
– and no boundary between whole numbers & fractions
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1 52 30
1 52 30 Base 10 equivalent
1 x 3600 52 x 60 30 6750
1 x 60 52 30/60 112 1/2
1 52/60 30/3600 1 7/8
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Playing with Babylonian numbers
• Try to write:– 32– 23– 18– 81– 107– 4 1/2
• Think of a number for your friend to write. Did they do it right?
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Multiplication tables • 1 30• 2 1• 3 1 30• 4 2• 5 2 30• 6 3• 7 3 30• 8 4• 9 4 30• 10 5• 11 5 30• [12] 6• 13 6 30 …
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… continued• [14 7]• [15 7 30]• 16 [8]• 17 [8 30]• 18 9• 20-1 9 30• 20 10• 30 15• 40 20• 50 25
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Practicing calculations
5 155 1527 33 45
5.25x 5.25 27.5625
or 325
x 325= 105,625
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Was Babylonian maths so different from ours?
• Draw or imagine a triangle
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Two Babylonian triangles
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Cultural preferences
• Horizontal base• Vertical axis of symmetry• Equilateral
• Left-hand vertical edge• Hanging right-angled triangle or
horizontal axis of symmetry• Elongated
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A Babylonian maths book
front back
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What are these shapes?
• The side of the square is 60 rods. Inside it are: o 4 triangles, o 16 barges, o 5 cow's noses.
• What are their areas?
"Triangle" is actually santakkum "cuneiform wedge" — and doesn't have
to have straight edges
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Barge and cow’s nose
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A father praises his son’s teacher:
• “My little fellow has opened wide his
hand, and you made wisdom enter
there. You showed him all the fine
points of the scribal art; you even made
him see the solutions of mathematical
and arithmetical problems.”