수의세계 1 주차. Early Number Systems and Symbols
학습내용 1. Early number systems 2. Symbols of numbers 학습목표 고대문명의수체계와기호체계 고대문명의계산방식
교재 1. The history of mathematics, 6 th edition, David M. Burton 2. 수학의세계, 박세희 3. ( 눈으로보며이해하는 ) 아름다운수학, 클라우디알시나외
수의세계 1 주차. Early Number Systems and Symbols
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
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
1 Numbers 1 1) Mathematics and Numbers Ishango Bone, Museum of Natural Sciences, Brussels Quipu from Inca Empire, Larco Museum Collection
1 Numbers 1 1) Mathematics and Numbers (3) Egyptian Numerals
1 Numbers 1 1) Mathematics and Numbers +
1 Numbers 1 1) Mathematics and Numbers -
1 Numbers 1 1) Mathematics and Numbers (4) Egyptian Hieratic Numeration = = 37
1 Numbers 1 1) Mathematics and Numbers (5) Babylonians number recording - Positional Number system - Sexagesimal, base 60, system
1 Numbers 1 1) Mathematics and Numbers (6) Ancient chinese numerals
1 Numbers 1 1) Mathematics and Numbers (7) Roman numerals
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
1 Numbers 1 1) Mathematics and Numbers (9) Greek Numerals
1 Numbers 1 1) Mathematics and Numbers (10) 0 - Ancient mayans used 0 - But 0 was first used in India
수의세계 1 주차. Early Number Systems and Symbols
1 2 Arithmetic 1) Egyptian Arithmetic Rhind Papyrus, British Museum
1 2 Arithmetic 1) Egyptian Arithmetic Product of 19 and 71 1349 = 71 + 142 + 1136 = (1 + 2 + 16) x 71 = 19 x 71 or
1 2 Arithmetic 1) Egyptian Arithmetic Divide 91 by 7 (doing multiplication in reverse) 1+4+8=desired quotient
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?
1 Arithmetic 2 1) Egyptian Arithmetic (1) Solving an equation False position
1 2 Arithmetic 2) Egyptian Geometry (1) Approximating the area of a circle
1 2 Arithmetic 2) Egyptian Geometry (1) Approximating the area of a circle
1 2 Arithmetic 3) Babylonian Mathematics (1) Solving quadratic equation
1 2 Arithmetic 3) Babylonian Mathematics (2) Quadratic equation ax 2 +bx+c=0 Cubic equation ax 3 +bx 2 +cx+d=0
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
1 2 Arithmetic 3) Babylonian Mathematics (4) Diophantus Integers satisfying x 2 +y 2 =z 2
1 2 Arithmetic 3) Babylonian Mathematics (4) Diophantus
1 2 Arithmetic 3) Babylonian Mathematics (5) Approximation of the square root of a number
1 Arithmetic 2 1) Greek arithmetic
1 2 Arithmetic 4) Babylonian Greek Mathematics Babylonians computed its approximations to a high accuracy. Greeks proved that it is irrational.
1 Arithmetic 2 (8) Positional systems - Arithmetic is much easier using the positional system - Chinese overcame the difficulty by using abacus
수의세계 1 주차. Early Number Systems and Symbols
평가하기 문제1. Which number system was positional? 1 Egyptian 2 Greek 3 Babylonian 4 Ancient chinese 정답 : 3 해설 : 바빌로나아에서는 60 진법위치기수법을사용하였다.
평가하기 문제2. What is the value of? 1 1232 2 2321 3 1234 4 322 정답 : 1 해설 : 각기호의값을모두더한다.
평가하기 문제3. Who used alphabetic numeral system?? 1 Egyptian 2 Greek 3 Babylonian 4 Ancient chinese 정답 : 1 해설 : 그리스인들은알파벳을숫자로사용하였다.
평가하기 문제4. Who used 0? 1 Egyptian 2 Greek 3 Babylonian 4 Ancient mayan 정답 : 4 해설 : 마야인들은 0 을사용하였다.
평가하기 문제5. What is the value Egyptian used for π? 1 3 2 13/4 3 3.1 4 256/81 정답 : 4 해설 : 정 8 각형을이용해근삿값을구하였다.
수의세계 1 주차. Early Number Systems and Symbols
정리하기 1강. Early Number Systems and Symbols - 원시문명의숫자시스기템. - 기본적인산술.
정리하기 2강 Arithmetic - 원시문명에서의산술. - 위치기수법.