IB Math SL IA 7점 - 모범 예시, 미적분과 회귀분석 등의 수학적 방식을 이용한 사이클로이드 곡선의 현실 적용성 레포트

소개

이 IA의 타이틀은 "Is flying down in the form of a cycloid really effective?"이며, 직선 위로 원을 굴렸을 때 원 위의 정점이 그리는 곡선인 사이클로이드 (Cycloid) 곡선을 주제로 한 Math SL IA입니다. 사이클로이드 곡선의 형태로 이동하는 것은 A와 B점을 가장 단기간에 이동할 수 있는 방법이라고 알려져 있는데 과연 이것이 정말로 실생활에 적용이 되는지에 대한 의문점을 갖게되어서 미적분과 회귀분석 등의 수학적 방식을 통하여 직접 실행한 실험의 결과를 분석을 한 IA입니다. Math SL IA는 수학적 원리를 이해하고 활용하는 것 뿐만 아니라 Rationale, IA의 목적, 한계점 등등을 서술하는 것도 매우 중요한데 그 부분을 매우 열심히 작성하여 수학 선생님께서도 학생들에게 모범 예시로 보여줬을 정도로 굉장히 잘 작성된 IA입니다. 이 자료를 활용하여 Math IA에서 고득점을 받아 목표를 이루시길 소망합니다.

목차

1. Introduction & Rationale
2. Aim
3. Cycloid in real-life
4. Distance-time scatter plot & Regression analysis
5. Differentiation to find out velocity
6. Velocity of beads on each line and curve
7. The time that eagles take to reach the location of prey from trees
8. Conclusion
9. Evaluation (Limitations and Improvements)
10.Bibliography
11.Appendix

본문내용

A cycloid is a curve traced by a point on a circle when a circle is rolled over a straight line. This curve is also known as the curve of fastest descent time as an object on the cycloid can go faster than any other curves or lines, when the object moves between two points. A cycloid is also famous for its application in real-life. The design of roller coasters was based on the cycloid to maximise the speed and give a great thrill, and electric fans and helicopters’ rotors are also associated with the shape of a cycloid to maximise the power and speed of the wind. Thus, the investigation regarding a cycloid was considered to be very crucial to the world externally.

While watching the documentary introducing the traditional houses of the world, I realised that the cycloid was applied to the roof of traditional Korean houses. I was surprised that the design of the roof, which was based on a cycloid, significantly reduced the amount of water percolating the roof by minimizing the time that the rainwater stays on the roof to prevent erosion (See the picture below).

참고자료

· Paul Bourke (2018). Cycloid curve . [online] Available at: http://paulbourke.net/geometry/cycloid/ [Accessed 11 Oct. 2018].
· Naver Blog (2016). Cycloid- Google Search . [online] Available at: https://www.google.co.kr/search?q=%EA%B8%B0%EC%99%80%EC%A7%91+%EC%82%AC%EC%9D%B4%ED%81%B4%EB%A1%9C%EC%9D%B4%EB%93%9C&safe=active&rlz=1C5CHFA_enSG770SG770&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiBmvjG_v3dAhXLS7wKHcK2DXQQ_AUIDigB&biw=1440&bih=789#imgrc=8A71MRf9Ny0k7M: [Accessed 11 Oct. 2018].
· University of Winnipeg. (2008). The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem. [online] Available at: https://pdfs.semanticscholar.org/9b3a/d2b4062e9541f07ca06b816c49efb165ad6e.pdf [Accessed 5 Dec. 2018].
· www.dictionary.com. (2018). the definition of regression analysis . [online] Available at: https://www.dictionary.com/browse/regression-analysis [Accessed 11 Oct. 2018].
· Minitab (2013). Regression Analysis: How Do I Interpret R-squared and Assess the Goodness-of-Fit? . [online] Blog.minitab.com. Available at: https://blog.minitab.com/blog/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit [Accessed 11 Oct. 2018].
· Detroit Zoo. (2018). Bald eagle - Detroit Zoo . [online] Available at: https://detroitzoo.org/animals/zoo-animals/bald-eagle/ [Accessed 12 Oct. 2018].
· Journeynorth.org. (2018). Bald Eagles: Nest Building . [online] Available at: https://journeynorth.org/tm/eagle/annual/facts_nest.html [Accessed 12 Oct. 2018].
· Shawn McClain. (2018). The Average Height of Pine Trees | Hunker . [online] Hunker.com. Available at: https://www.hunker.com/12424331/the-average-height-of-pine-trees [Accessed 12 Oct. 2018].