History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What...
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Transcript of History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What...
![Page 1: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/1.jpg)
History of Numbers
![Page 2: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/2.jpg)
What Is A Number?
What is a number?
Are these numbers?
Is 11 a number? 33?
What about @xABFE?
![Page 3: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/3.jpg)
35,000 BC
![Page 4: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/4.jpg)
Egyptian 3rd Century BC
![Page 5: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/5.jpg)
Additive Numeral Systems
Some societies have an additive numeral system: a principle of addition, where each character has a value independent of its position in its representation
Examples are the Greek and Roman numeral systems
![Page 6: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/6.jpg)
The Greek Numeral System
![Page 7: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/7.jpg)
Roman Numerals
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Drawbacks of positional numeral system
Hard to represent larger numbers
Hard to do arithmetic with larger numbers, trying do 23456 x 987654
![Page 9: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/9.jpg)
South American Maths
The Maya
The Incas
![Page 10: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/10.jpg)
twenties units
Mayan Maths
twenties units 2 x 20 + 7 = 47
18 x 20 + 5 = 365
![Page 11: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/11.jpg)
Babylonian Maths
The Babylonians
![Page 12: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/12.jpg)
3600s 60s 1s
BabylonIan sixties units =64 = 3604
![Page 13: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/13.jpg)
Cultures that Conceived “Zero”
Zero was conceived by these societies:
Mesopotamia civilization 200 BC – 100 BC
Maya civilization 300 – 1000 AD
Indian sub-continent 400 BC – 400 AD
![Page 14: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/14.jpg)
Hindu-Arabic
We have to thank the Indians for our modern number system.
Similarity between the Indian numeral system and our modern one
![Page 15: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/15.jpg)
From the Indian sub-continent to Europe via the Arabs
![Page 16: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/16.jpg)
Indian Numbers
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Pythagoras’ Theorem
1
1
aa2 = 12 + 12
So a2 = 2a = ?
a2 = b2 + c2
![Page 18: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/18.jpg)
Square roots on the number line
0 1 32 4 5 6 7-1-2-3-4-5
√1√4√9
√2
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Square roots of negatives
√-1=i
Where should we put √-1 ?
0 1 32 4 5 6 7-1-2-3-4-5
√1√4√9
√2
![Page 20: History of Numbers. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?](https://reader033.fdocuments.in/reader033/viewer/2022061509/56649d835503460f94a68ae3/html5/thumbnails/20.jpg)
Imaginary numbers
i2i
Real
3i
4i
Imag
inar
y
0 1 32 4 5 6 7-1-2-3-4-5
√1√4√9
√2