수의세계. 1 주차. Early Number Systems and Symbols

Transcription

1 수의세계 1 주차. Early Number Systems and Symbols

2 학습내용 1. Early number systems 2. Symbols of numbers 학습목표 고대문명의수체계와기호체계 고대문명의계산방식

3 교재 1. The history of mathematics, 6 th edition, David M. Burton 2. 수학의세계, 박세희 3. ( 눈으로보며이해하는 ) 아름다운수학, 클라우디알시나외

4 수의세계 1 주차. Early Number Systems and Symbols

5 1 Numbers 1 1) Mathematics and Numbers (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

6 1 Numbers 1 1) Mathematics and Numbers (2) Primitive counting - One, two, many - tally --- to scratch, to notch - fingers --- five - The peruvian Quipus: Knots as Numbers

7 1 Numbers 1 1) Mathematics and Numbers Ishango Bone, Museum of Natural Sciences, Brussels Quipu from Inca Empire, Larco Museum Collection

8 1 Numbers 1 1) Mathematics and Numbers (3) Egyptian Numerals

9 1 Numbers 1 1) Mathematics and Numbers +

10 1 Numbers 1 1) Mathematics and Numbers -

11 1 Numbers 1 1) Mathematics and Numbers (4) Egyptian Hieratic Numeration = = 37

12 1 Numbers 1 1) Mathematics and Numbers (5) Babylonians number recording - Positional Number system - Sexagesimal, base 60, system

13 1 Numbers 1 1) Mathematics and Numbers (6) Ancient chinese numerals

14 1 Numbers 1 1) Mathematics and Numbers (7) Roman numerals

15 1 Numbers 1 1) Mathematics and Numbers (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

16 1 Numbers 1 1) Mathematics and Numbers (9) Greek Numerals

17 1 Numbers 1 1) Mathematics and Numbers (10) 0 - Ancient mayans used 0 - But 0 was first used in India

18 수의세계 1 주차. Early Number Systems and Symbols

19 1 2 Arithmetic 1) Egyptian Arithmetic Rhind Papyrus, British Museum

20 1 2 Arithmetic 1) Egyptian Arithmetic Product of 19 and = = ( ) x 71 = 19 x 71 or

21 1 2 Arithmetic 1) Egyptian Arithmetic Divide 91 by 7 (doing multiplication in reverse) 1+4+8=desired quotient

22 1 Arithmetic 2 1) Egyptian Arithmetic (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?

23 1 Arithmetic 2 1) Egyptian Arithmetic (1) Solving an equation False position

24 1 2 Arithmetic 2) Egyptian Geometry (1) Approximating the area of a circle

25 1 2 Arithmetic 2) Egyptian Geometry (1) Approximating the area of a circle

26 1 2 Arithmetic 3) Babylonian Mathematics (1) Solving quadratic equation

27 1 2 Arithmetic 3) Babylonian Mathematics (2) Quadratic equation ax 2 +bx+c=0 Cubic equation ax 3 +bx 2 +cx+d=0

28 1 2 Arithmetic 3) Babylonian Mathematics (3) Number triple Integers satisfying x 2 +y 2 =z 2 Plimpton 322 Babylonians knew the Pythagorean Theo rem

29 1 2 Arithmetic 3) Babylonian Mathematics (4) Diophantus Integers satisfying x 2 +y 2 =z 2

30 1 2 Arithmetic 3) Babylonian Mathematics (4) Diophantus

31 1 2 Arithmetic 3) Babylonian Mathematics (5) Approximation of the square root of a number

32 1 Arithmetic 2 1) Greek arithmetic

33 1 2 Arithmetic 4) Babylonian Greek Mathematics Babylonians computed its approximations to a high accuracy. Greeks proved that it is irrational.

34 1 Arithmetic 2 (8) Positional systems - Arithmetic is much easier using the positional system - Chinese overcame the difficulty by using abacus

35 수의세계 1 주차. Early Number Systems and Symbols

36 평가하기 문제1. Which number system was positional? 1 Egyptian 2 Greek 3 Babylonian 4 Ancient chinese 정답 : 3 해설 : 바빌로나아에서는 60 진법위치기수법을사용하였다.

37 평가하기 문제2. What is the value of? 정답 : 1 해설 : 각기호의값을모두더한다.

38 평가하기 문제3. Who used alphabetic numeral system?? 1 Egyptian 2 Greek 3 Babylonian 4 Ancient chinese 정답 : 1 해설 : 그리스인들은알파벳을숫자로사용하였다.

39 평가하기 문제4. Who used 0? 1 Egyptian 2 Greek 3 Babylonian 4 Ancient mayan 정답 : 4 해설 : 마야인들은 0 을사용하였다.

40 평가하기 문제5. What is the value Egyptian used for π? / /81 정답 : 4 해설 : 정 8 각형을이용해근삿값을구하였다.

41 수의세계 1 주차. Early Number Systems and Symbols

42 정리하기 1강. Early Number Systems and Symbols - 원시문명의숫자시스기템. - 기본적인산술.

43 정리하기 2강 Arithmetic - 원시문명에서의산술. - 위치기수법.

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