# How Does Gps Rely on Geometry and Trigonometry Now That There Are Satellites? Has the Function of Geometry and Trigonometry in Triangulation and Navigation Changed Since Satellites Were Built?

Topics: Global Positioning System, Navigation, Angle Pages: 12 (3533 words) Published: August 26, 2013
Area:
Mathematics
Topic:
GPS

Research Question:
How does GPS rely on geometry and trigonometry now that there are satellites? Has the function of geometry and trigonometry in triangulation and navigation changed since satellites were built?

IB MATH
Candidtate name: Tristan Stevenson
Candidate Number: dwq773 (001366 – 016)
School: Prem tinsulalonda International School
November 14, 12
Word Count:2090

Abstract:
This essay examines the question: How does GPS rely on geometry and trigonometry now that there are satellites? Has the function of geometry and trigonometry in triangulation and navigation changed since satellites were built?

My main resources were websites and articles that I found online. I tried to find recent sources so they would be more valid. The sources gave me equations and lots of details about how GPS works and other forms of navigation that were used before.

GPS still relies on geometry and trigonometry but not a lot. GPS is an advanced method of the LORAN method that was discovered during World War II. GPS uses advanced trigonometry and geometry in the programing to help pinpoint locations. The function of geometry and trigonometry in triangulation and navigation has completely changed since satellites were built. People no longer use calculations using geometry and trigonometry. And satellites are now mainly used in navigation of ships and aircraft. Table of Contents

1. Abstract………………………………………………………………………………………2 2. Table of contents………………………………………………………………………...3 a. Introduction……………………………………………………………………………...4 b. Background Information…………………………………………………………..4 3. Practical investigations………………………………………………………………5 i. Before GPS……………………………………………………………………………….6 a. Problems and improvements…………………………………………………..7 i. Function of Geometry and trigonometry in examples …………….11 1. PREM Cluster to Gate………………………………………………………………..15 4. Conclusion………………………………………………………………………………..16 5. Works Cited………………………………………………………………………………17

Introduction

Geometry and trigonometry triangulation are critical elements in the functional application of navigation (for example global positioning system). Understanding the evolution of these elements in the context of navigation may provide insights into how to further refine their practical use. The research question for this extended essay is: How does GPS rely on geometry and trigonometry now that there are satellites? Has the function of geometry and trigonometry in triangulation and navigation changed since satellites were built? More specifically, over the years how has the change in the functional use of geometry and trigonometry in triangulation affected the accuracy of navigation?

This research will provide information on which math applications are most suitable for different circumstances. For example, is it critical and appropriate to use complex satellite-based mathematical models when accuracy is required over short distances?

Why it is important (to study the change)
We use navigation in our daily lives, much more today than we did 10 years ago. GPS systems on our iPhones and in our cars has replaced the need for a compass or a map, however, as we move towards the future, Navigation using satellites is becoming more accessible, user friendly and important. Over time the mathematical application of satellites for navigation has increased drastically. It is important to know if using satellites for every situation or circumstance is necessary. Over the years satellites have helped to increase the accuracy of navigation.

Background Information:
Geometry is a branch of mathematics that studies the relationship between points, lines, angles, surfaces and solids. Geometry can be broken down into many different topics but this paper will cover two topics within geometry: Euclidian...