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Kuan-Yi's Math IA topic—Hyperbolic Navigation - Coggle Diagram
Kuan-Yi's Math IA topic—Hyperbolic Navigation
Math concepts
Linear functions
Quadratic function/modelling
Graphing with a coordinate plane
Graph and formula of a circle
Formula and graph of a hyperbola
Definitions
Hyperbola
Parabola
Hyperbolic navigation (LORAN)
Focus of parabola and hyperbola
Relationship between the focus point and parabola/hyperbola
Sonar, radar, and radio waves
Kinematic equations
Real life applications
Satellites tracking the location of an electronic device
A tower finding the location of a ship
GPS tracking using satellites
Resources
Video about hyperbolic navigation:
https://www.youtube.com/watch?v=8nPMlW5NZSo
Video about the application of hyperbolic navigation:
https://www.youtube.com/watch?v=rDNMgEBdvro
Article introducing hyperbolic navigation (or LORAN):
https://www.britannica.com/technology/loran
Oxford IB Diploma Programme Mathematics: Applications and Interpretation HL textbook
Oxford IB Study Guides: Physics for the IB Diploma 2014 edition
Research question
How could hyperbolic navigation and basic kinematics model how tracking devices use waves to locate objects on a 2-dimensional plane?
Sub-topic 2
How can a hyperbolic equation be found using various coordinate points?
Sub-topic 3
How could the rule of the relationship between a hyperbola and its focus point be used to find the location of an object?
Sub-topic 1
How can the distance be found from a wave’s traveling speed and traveling time?
Materials for investigation
Tables
Diagrams
Coordinate planes