# M22 Math AA HL IA (7)

INTERNAL ASSESSMENT TITLE
Application of Spherical Trigonometry in Identifying the Distance between Two International Airports

RESEARCH QUESTION
How can I mathematically calculate the shortest distance between MNL, Philippines and JFK, U.S.A. by only using the latitude and longitude coordinates as a given?

2022년에 Math AA HL IA로 제출해 7 (22/24) 받았습니다. 솔직히 말해서 다른 Math IA 토픽들과 방식들과 달리 좀 주제가 만만?합니다. 하지만 그럼에도 불구하고 높은 점수를 받을 수 있었던 것에는 확고한 실험 방식과 데이터 분석이라고 생각합니다. 수학에 크게 자신은 없지만 높은 점수를 받고 싶은 분들께 추천합니다.

3달 뒤 삭제 예정이니 빨리 구매하세요 ㅎㅎ

[본문내용]

## Introduction

What we know as common knowledge is oftentimes taken for granted and overlooked from becoming a source of curiosity. This premise would fit me very well, as I also did not have any notion to question the 2D maps we use in our daily life until my first history classes that I took when I was in 4th grade. As I exposed myself to more and more maps of the 7 continents to become more familiar with the different city names and regions mentioned in my exams, I realized a major shortcoming to those maps printed out in 2D — because Earth is composed of 3 dimensions, it is inevitable for errors to occur as the cartographers project a sphere on a flat surface like paper. This meant that the straight lines I would draw on the 2D map would have to become an arc to properly represent the distance between two points. Hence, the map scales printed at one of the corners of the map were not enough to guarantee the measurement of distance I would make between points on the map — the origin of my inspiration for this investigation…(이하 생략)

## Background Knowledge

Since it is not physically possible for me to get a flexible tape measure or a long piece of rope to count the meters between Manila and New York, the overall field of spherical geometry must first be understood.

Spherical Geometry

It is first important to note that spherical geometry does not fall under the category of Euclidean geometry — the most common type taught in schools and classrooms across the world. Instead, spherical geometry is referred to as non-Euclidean geometry. The Russian mathematician Nikolay Lobachevsky first established the concept of non-Euclidean geometry in 1929, which proved the existence of a geometry that “except for the parallel postulate, satisfied all of Euclid’s postulates and common notions” (Taimina & Henderson, 2020). As the name suggests, spherical geometry studies the planes on the surface of a sphere. Unlike how the fundamentals of Euclidean geometry are points and lines, spherical geometry is

4 composed of points and great circles. It is very important to note that because of this unique

feature, it is impossible to have parallel lines in spherical geometry…

• 총 페이지수: 14 pages
• 과목명: Mathematics
• 주제: Application of Spherical Trigonometry in Identifying the Distance between Two International Airports
• The file is in PDF format.