7점 (18/20) May 2022 IB Maths AA HL IA

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본 IA는 2022년 May 2022 Session에 작성한 수학 IA입니다. 주제는 “Does Giwa (Korean traditional house roof) actually inhabit the feature of brachistochrone curve?”로, 계단함수와 계단삼각함수를 사용한 다변수 모델링, Calculus of variations, 다양한 적분 기술들을 포함하고 있습니다. 한옥 지붕에 사용된 곡선을 사이클로이드 모델로 모델링하고, 각 함수의 최소 강하 시간을 Calculus of Variations로 구하여 분석하는 IA 입니다.

IB Maths AA HL 수준보다 약간 높은 수준으로, Criterion E Use of Mathematics 에서 고득점을 노리시거나, Advanced 미적분 내용으로 수학 IA를 작성하시려는 분들께 추천드립니다.

본 IA는 총 2505 단어 19페이지로 구성되어 있습니다.

 

[본문내용]

Rationale
When I was young, I used to visit Andong, South Korea, where my dad spent his childhood, during festive seasons. In line with the city’s slogan of “Capital of the Spiritual Culture of
Korea”, Andong still maintains its Giwajib, a traditional Korean house which could be directly translated into “Tiled house”, in a good condition that there are sill people residing in. My grandfather noticed that I was fascinated by the antique and traditional patterns inscribed on Giwa, the tile which is used to cover the roof of Giwajib, and explained me that Giwajib was a house where people of aristocratic class could live and that our ancestors designed Giwa in a way that the raindrops can flow down from Giwa the fastest, as frames of Giwajib are consisted of wood and it can rot when water penetrates in… (이하 생략)…

 

Modelling Giwa
For this exploration, I will attempt to model an arbitrary roof of Giwajib, by finding out the best fit curve using polynomial regression analysis and the pre-existing function, and compare the time taken for a raindrop to flow down for those two different functions. However, as the proposed Giwa to model seems to have a discontinuity in the middle of the roof due to the traditional way of designing, which is to split layers of Giwa roof to flaunt wealth. Hence, I will find curve of best fit for each partition, and then merge them in form of piecewise function.

 

  • 총 페이지수: 20 pages
  • 과목명: Mathematics
  • 주제: Does Giwa (Korean traditional house roof) actually inhabit the feature of brachistochrone curve?
  • The file is in PDF format.
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7점 (18/20) May 2022 IB Maths AA HL IA

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