수의 세계

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수의 세계

1주차. Early Number

Systems and Symbols

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1. Early number systems 2. Symbols of numbers

• 고대문명의 수체계와 기호 체계

• 고대문명의 계산 방식 학습내용

학습목표

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1. The history of mathematics, 6^th edition, David M. Burton

2. 수학의 세계, 박세희

3. (눈으로 보며 이해하는) 아름다운 수학, 클라우디 알시나 외

교재

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수의 세계

Systems and Symbols

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1 Numbers 1

(1) Mathematics

Mathematics <--- Mathematica (Greek

word): any subject of instruction or study To think the thinkable - that is the

mathematician’s aim. --- C.J. Keyser 1) Mathematics and Numbers

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1 Numbers 1

(2) Primitive counting - One, two, many

- tally --- to scratch, to notch - fingers --- five

- The peruvian Quipus: Knots as Numbers 1) Mathematics and Numbers

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1 Numbers 1

1) Mathematics and Numbers

Ishango Bone,

Museum of Natural Sciences, Brussels

Quipu from Inca Empire, Larco

Museum Collection

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1 Numbers 1

(3) Egyptian Numerals

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1 Numbers 1

+

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1 Numbers 1

-

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1 Numbers 1

(4) Egyptian Hieratic Numeration 1) Mathematics and Numbers

=

^{= 37}

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1 Numbers 1

(5) Babylonians’ number recording - Positional Number system

- Sexagesimal, base 60, system 1) Mathematics and Numbers

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1 Numbers 1

(6) Ancient chinese numerals 1) Mathematics and Numbers

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1 Numbers 1

(7) Roman numerals

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1 Numbers 1

(8) Positional systems

- Egyptian, Greek, Roman, Chinese systems are not positional

- Babylonians developed sexagesimal positional system

- Zero was not used until Middle age in western Europe, which partially explains why we do not have a year 0 in our

calendar system

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1 Numbers 1

(9) Greek Numerals

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1 Numbers 1

(10) 0

- Ancient mayans used 0

- But 0 was first used in India 1) Mathematics and Numbers

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수의 세계

Systems and Symbols

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2 1

1) Egyptian Arithmetic

Arithmetic

Rhind Papyrus, British Museum

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2 1

Arithmetic

Product of 19 and 71

1349 = 71 + 142 + 1136 = (1 + 2 + 16) x 71 = 19 x 71

or

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2 1

Arithmetic

Divide 91 by 7 (doing multiplication in reverse)

1+4+8=desired quotient

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1 Arithmetic 2

(1) Solving an equation

- A certain man buys eggs at the rate of 7 for 1 denarius and sells them at a rate of 5 for 1 denarius, and thus makes a profit of 19 denarii. The question is: How much

money did he invest?

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1 Arithmetic 2

(1) Solving an equation—False position 1) Egyptian Arithmetic

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2 1

2) Egyptian Geometry

Arithmetic

(1) Approximating the area of a circle

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2 1

2) Egyptian Geometry

Arithmetic

(1) Approximating the area of a circle

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2 1

3) Babylonian Mathematics

Arithmetic

(1) Solving quadratic equation

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2 1

Arithmetic

(2) Quadratic equation ax²+bx+c=0 Cubic equation ax³+bx²+cx+d=0 …

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2 1

Arithmetic

(3) Number triple

Integers satisfying x²+y²=z²

Babylonians knew the Pythagorean Theo rem

Plimpton 322

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2 1

Arithmetic

(4) Diophantus

Integers satisfying x²+y²=z²

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2 1

Arithmetic

(4) Diophantus

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2 1

Arithmetic

(5) Approximation of the square root of a number

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1 Arithmetic 2

1) Greek arithmetic

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2 1

4) Babylonian Greek Mathematics

Arithmetic

Babylonians computed its

approximations to a high accuracy.

Greeks proved that it is irrational.

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1 Arithmetic 2

(8) Positional systems

- Arithmetic is much easier using the positional system

- Chinese overcame the difficulty by using abacus

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수의 세계

Systems and Symbols

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문제1. Which number system was positional?

① Egyptian

② Greek

③ Babylonian

④ Ancient chinese

정답 : ③

해설 : 바빌로나아에서는 60진법 위치기수법을 사용하였다.

평가하기

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문제2. What is the value of ?

① 1232

② 2321

③ 1234

④ 322

정답 : 1

해설 : 각 기호의 값을 모두 더한다.

평가하기

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문제3. Who used alphabetic numeral system??

① Egyptian

② Greek

③ Babylonian

④ Ancient chinese

정답 : 1

해설 : 그리스인들은 알파벳을 숫자로 사용하였다.

평가하기

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문제4. Who used 0?

① Egyptian

② Greek

③ Babylonian

④ Ancient mayan

정답 : 4

해설 : 마야인들은 0을 사용하였다.

평가하기

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문제5. What is the value Egyptian used for π?

① 3

② 13/4

③ 3.1

④ 256/81

정답 : 4

해설 : 정8각형을 이용해 근삿값을 구하였다.

평가하기

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수의 세계

Systems and Symbols

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정리하기

- 원시문명의 숫자 시스기템.

- 기본적인 산술.

1강 . Early Number Systems and Symbols

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정리하기

- 원시문명에서의 산술.

- 위치기수법.

2강 Arithmetic

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