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HL math IA Non-Euclidean Geometry help


rayadam

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Hello,

I have chosen to do my math exploration on Non-Euclidean Geometry but i have a hard time finding a specific topic to explore. I would love some help and ideas of problems i could solve. i have thought of showing that the earth is round and also doing something with GPS signals. I am really lost, i just need a path to follow. 

Thank you 

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Hello,

I have chosen to do my math exploration on Non-Euclidean Geometry but i have a hard time finding a specific topic to explore. I would love some help and ideas of problems i could solve. i have thought of showing that the earth is round and also doing something with GPS signals. I am really lost, i just need a path to follow. 

 

I don't get what you mean by "showing that the earth is round". Because it is round if you just look at it from space! so there's really nothing to show. Tbh, I'm quite unfamiliar with this topic of non-euclidean geometry. I only encountered in the study of relativity, but that has nothing to do with the geometry of the Earth. So I don't think i can give you any suggestions for something to do with GPS.

 

However, there's one question that has been on my mind since I first studied geography. How do people make maps? How do we transform the 3D-map of the Earth into a 2D-version? What mathematical technique do we use? What kind of information do we lose? and how can we compromise with these losses? And all of these questions are all related to the relationship between non-euclidean geometry of the earth's surface and the euclidean geometry that exists on our 2D-maps. Maybe this is something that you could explore? Also, it's possible to mention GPS if you follow this idea. You could try to measure the distance between 2 places on Earth using satellites' data, and then compare this distance with the calculations that you do with 2D-flat & 3D-curved geometry.

 

A link that might get you started: http://www.science4all.org/scottmckinney/non-euclidean-geometry-and-map-making/

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Thank you a lot I find this very useful and a very nice idea :) when I said showing the earth is round I meant back when they had not satellites they did it by measuring shadows made from poles on two different places at the same time. The shadows length varied which shows that the earth is not flat. The Making of maps is a very good idea!! More suggestions are welcome, the problem is that i went with a topic I thought I had many ideas for but in the end I ended up getting lost and it is too late for me to change topic.

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