수학이 가득한 코딩 DESMOS 그래프
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| Publication Date | 2022/03/01 |
| Pages/Weight/Size | 190*260*20mm |
| ISBN | 9791191346268 |
| Categories | IT 모바일 > 프로그래밍 언어 |
Description
「수학이 가득한 코딩-Desmos 그래프」라고 제목을 정한 이유는 그래프로 원하는 주제를 구현할 때 교실에서 배우는 수학개념을 조건과 반복, 함수설정, 변수 업데이트 등의 코딩 방법으로 녹여내는 경우가 상당히 많았기 때문이다. Desmos 그래핑 계산기는 학교에서 배운 수학이 어떻게 실용적으로 활용될 수 있는지 연습할 수 있는 도구다. 다시 열어보길 반복하였고 주제마다 꾸준히 들여다본 결과 대부분 중고등학교 수학교육과정안에서 충분히 이해할 수 있는 내용들임을 알게 되었다. 이 책의 3장에서는 시어핀스키 삼각형, 탁구게임, 이항분포기 구현 등 13가지 그래프 주제를 자세하게 분석하였고 차근차근 이해할 수 있도록 앞장에 3장과 관련있는 비교적 쉬운 실습문제를 제시하였다.
물체의 움직임을 시뮬레이션하기 위해, 3차원 공간을 평면에 투영시켜 컴퓨터 화면에서 관찰할 수 있도록 하기 위해 삼각함수가 얼마나 유용한지 데스모스 그래프 작업을 통해 새삼 깨달았다. 행렬식의 부호는 3차원 입체관찰을 자연스럽게 해주며 주기함수는 이미지의 멋진 움직임을 만들어 낼 수 있게 한다. 탁구게임에서 공이 튕기는 모습을 표현하기 위해 이차함수를 사용하고 원근법이 적용되는 화면을 만들기 위해 분수함수를 사용한다. 특히 이항분포기를 구현할 때 사용되는 수학개념은 수열, 역함수, 수열의 합, 이차함수, 주기함수, 선분의 내분점, 도형의 이동 등으로 다양하여 매우 흥미롭다. 그래핑 계산기의 활용방법이 무궁무진하여 아직도 모르는 것이 많지만 제가 지금까지 공부한 주제만으로도 너무나 귀한 수학적 아이디어를 많이 접하였다. 이 아이디어들은 수학을 공부하는 학생들이 수학을 더욱 흥미롭게 여기도록 하는데 도움을 줄 것이라 확신한다. 또한 코딩의 방법적 측면 뿐만아니라 심화된 수학적 내용을 갈망하는 독자라면 분명 얻을 점이 많은 책이라고 자신한다.
물체의 움직임을 시뮬레이션하기 위해, 3차원 공간을 평면에 투영시켜 컴퓨터 화면에서 관찰할 수 있도록 하기 위해 삼각함수가 얼마나 유용한지 데스모스 그래프 작업을 통해 새삼 깨달았다. 행렬식의 부호는 3차원 입체관찰을 자연스럽게 해주며 주기함수는 이미지의 멋진 움직임을 만들어 낼 수 있게 한다. 탁구게임에서 공이 튕기는 모습을 표현하기 위해 이차함수를 사용하고 원근법이 적용되는 화면을 만들기 위해 분수함수를 사용한다. 특히 이항분포기를 구현할 때 사용되는 수학개념은 수열, 역함수, 수열의 합, 이차함수, 주기함수, 선분의 내분점, 도형의 이동 등으로 다양하여 매우 흥미롭다. 그래핑 계산기의 활용방법이 무궁무진하여 아직도 모르는 것이 많지만 제가 지금까지 공부한 주제만으로도 너무나 귀한 수학적 아이디어를 많이 접하였다. 이 아이디어들은 수학을 공부하는 학생들이 수학을 더욱 흥미롭게 여기도록 하는데 도움을 줄 것이라 확신한다. 또한 코딩의 방법적 측면 뿐만아니라 심화된 수학적 내용을 갈망하는 독자라면 분명 얻을 점이 많은 책이라고 자신한다.
Contents
제목 차례
1. 데스모스 ·········································································································································· 5
가. 데스모스 역사와 뜻 ································································································································· 5
나. 데스모스 둘러보기 ··································································································································· 6
1) 데스모스 회원가입 ································································································································ 6
2) 데스모스 교사 홈페이지 구성 ············································································································ 7
3) 액티비티 수업에 사용하기 ················································································································ 10
4) 액티비티 번역하기 ····························································································································· 12
5) 액티비티 새로 만들기 ························································································································ 13
2. 그래핑 계산기 ······························································································································ 17
가. 그래핑 계산기 사용법 기본 ················································································································· 17
1) 그래프 저장하여 붙여넣기 ················································································································ 17
2) 점 표현하기 ········································································································································· 19
3) 색깔추가하기 ······································································································································· 22
4) 다각형 표현하기 ································································································································· 23
5) 선분 표현하기 ····································································································································· 25
6) 원 표현하기 ········································································································································· 26
7) 삼각함수 활용하기 ····························································································································· 27
8) 조건이 걸린 함수 ······························································································································· 30
9) 여러 가지 함수 사용하기 ·················································································································· 32
나. 실습문제 풀며 그래프 사용 익숙해지기 ··························································································· 36
1) 그래프에서 이미지 활용하기 ············································································································ 36
2) 매개변수로 도형표현하기 ·················································································································· 45
3) 수열의 합을 활용한 코딩 ·················································································································· 49
3. 그래프로 코딩하기 ······················································································································ 57
가. 별 반짝이기 ············································································································································ 57
나. 낙엽 휘날리기 ········································································································································ 61
다. 따라오는 물체표현 ································································································································ 65
라. 통과시 크기가 변하는 사각형 ············································································································· 72
마. 펄럭이는 깃발 표현 ······························································································································ 78
바. 시어핀스키 삼각형 표현 ······················································································································· 83
사. 톱니바퀴 회전 표현 ······························································································································ 90
아. 자리 비켜주는 도형 표현 ····················································································································· 96
자. 수식으로 원근법 표현하기 ················································································································ 100
차. 수식으로 3차원 표현하기 ·················································································································· 104
카. 구 → 원기둥 → 평면 펼치기 표현 ································································································· 113
타. 탁구 게임 만들기 ································································································································ 121
파. 이항분포 실험기 표현 ························································································································ 129
〈부록1: 그래핑 계산기 자료 안내〉-------------------------------------------------145
〈부록2: 액티비티 제작에 관한 자료 안내〉--------------------------------------146
1. 데스모스 ·········································································································································· 5
가. 데스모스 역사와 뜻 ································································································································· 5
나. 데스모스 둘러보기 ··································································································································· 6
1) 데스모스 회원가입 ································································································································ 6
2) 데스모스 교사 홈페이지 구성 ············································································································ 7
3) 액티비티 수업에 사용하기 ················································································································ 10
4) 액티비티 번역하기 ····························································································································· 12
5) 액티비티 새로 만들기 ························································································································ 13
2. 그래핑 계산기 ······························································································································ 17
가. 그래핑 계산기 사용법 기본 ················································································································· 17
1) 그래프 저장하여 붙여넣기 ················································································································ 17
2) 점 표현하기 ········································································································································· 19
3) 색깔추가하기 ······································································································································· 22
4) 다각형 표현하기 ································································································································· 23
5) 선분 표현하기 ····································································································································· 25
6) 원 표현하기 ········································································································································· 26
7) 삼각함수 활용하기 ····························································································································· 27
8) 조건이 걸린 함수 ······························································································································· 30
9) 여러 가지 함수 사용하기 ·················································································································· 32
나. 실습문제 풀며 그래프 사용 익숙해지기 ··························································································· 36
1) 그래프에서 이미지 활용하기 ············································································································ 36
2) 매개변수로 도형표현하기 ·················································································································· 45
3) 수열의 합을 활용한 코딩 ·················································································································· 49
3. 그래프로 코딩하기 ······················································································································ 57
가. 별 반짝이기 ············································································································································ 57
나. 낙엽 휘날리기 ········································································································································ 61
다. 따라오는 물체표현 ································································································································ 65
라. 통과시 크기가 변하는 사각형 ············································································································· 72
마. 펄럭이는 깃발 표현 ······························································································································ 78
바. 시어핀스키 삼각형 표현 ······················································································································· 83
사. 톱니바퀴 회전 표현 ······························································································································ 90
아. 자리 비켜주는 도형 표현 ····················································································································· 96
자. 수식으로 원근법 표현하기 ················································································································ 100
차. 수식으로 3차원 표현하기 ·················································································································· 104
카. 구 → 원기둥 → 평면 펼치기 표현 ································································································· 113
타. 탁구 게임 만들기 ································································································································ 121
파. 이항분포 실험기 표현 ························································································································ 129
〈부록1: 그래핑 계산기 자료 안내〉-------------------------------------------------145
〈부록2: 액티비티 제작에 관한 자료 안내〉--------------------------------------146