20/20 (7) Math HL IA May 2022 – Grade 7

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본 문서는 가장 최근 2022년 May에 제출된 Math HL IA이며, 학교에서 모범 예시로 사용할 만큼 20/20점인 만점을 받았습니다.
Non-exam route로 IA 비중이 급격히 커졌음에 불구하고 공식 IBO에서도 최종 7을 받은 IA입니다.

선택한 주제는 Brachistochrone: The shortest path of descent in 2D and 3D space Introduction입니다.
해당 주제를 2D space, 3D space, 그리고 거기서 더 나아가 직접 모형을 만들고 프로그램을 돌려 증명해 보였습니다.
주제 선정 이유 -> 수학적 이론 -> 주제에 적용 -> 심화 -> 실험 및 증명 -> 결과로 이어져서 모든 영역에서 만점을 받을 수 있었습니다.
꽤 어려운 주제인 만큼 초반에는 깊이 있는 수학적 이론과 설명이 힘들 순 있으나 그만큼 쉽게 고득점을 노릴 수 있는 주제이니 참고하시면 안정적으로 7을 받는 데 어려움이 없을 것입니다.

 

[본문내용]

Brachistochrone: The shortest path of descent in 2D and 3D space

 

Introduction

Near my house, there is an amusement park called Everland that I used to go to often and the world’s No. 1 roller coaster at that time called the T-Express. This ride is in the shape of a curve which is the fastest way to descend with a maximum speed of 104 kilometers. This curve is called cycloid and has a unique name, “Brachistochrone”. Whenever I went to the park, I wondered why this is a curve and not a straight line as from co-ordinate geometry, we know that the shortest distance between 2 points is a straight line.

This absurdity made me want to research this, which made me pick this as my exploration. The aim of this exploration is to find the shortest time taken to descend between two points. I know how to calculate the shortest distance between 2 points but must research how to find the shortest time between 2 points. I can also compare different curves and understand them in the time-space to understand the time taken on these curves. The distance between 2 points on a 2-dimensional system can be extended to a 3-dimensional time-space to find the shortest distance between the capital, Seoul, and my city, Daejeon.

I picked this as my Math Internal Assessment topic as this will have a real-life advantage of formulating the best possible air trajectory between the capital to my city.

 

Plan of execution

2D Space – Time taken on a straight line, quadratic curve, exponential curve, radical curve, and cycloid curve
3D Space – Time taken on a hypocycloid and the shortest time taken between Seoul capital city and Daejeon city
Physical modeling – Time taken on a straight line, quadratic curve, exponential curve, and cycloid curve
  • 총 페이지수: 24 pages
  • 과목명: Mathematics
  • 주제: Brachistochrone: The shortest path of descent in 2D and 3D space Introduction
  • The file is in Word format.
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20/20 (7) Math HL IA May 2022 – Grade 7

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