![]() ![]() ![]() 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. In order to navigate on a ship or on land, you need to know two basic facts: which direction you’re heading, and how far you have traveled. You may be familiar with the concepts of length and angle from using rulers or protractors. Maybe this is something that you could explore? Also, it's possible to mention GPS if you follow this idea. The two key units of measure in Euclidean geometry are length and angle. 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. However, there's one question that has been on my mind since I first studied geography. So I don't think i can give you any suggestions for something to do with GPS. I only encountered in the study of relativity, but that has nothing to do with the geometry of the Earth. Tbh, I'm quite unfamiliar with this topic of non-euclidean geometry. Because it is round if you just look at it from space! so there's really nothing to show. ![]() I don't get what you mean by "showing that the earth is round". Each Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes. I am really lost, i just need a path to follow. 1.2 Non-Euclidean Geometry: non-Euclidean geometry is any geometry that is different from Euclidean geometry. i have thought of showing that the earth is round and also doing something with GPS signals. Non-Euclidean geometry is the study of geometry on surfaces which are not flat. The non-Euclidean geometry of Lobachevsky is negatively curved, and any triangle angle sum < 180 degrees. In 2-dimensions: Euclidean geometry is at (curvature 0) and any triangle angle sum 180 degrees. There are two main types of non-Euclidean geometries, spherical (or elliptical) and hyperbolic. I would love some help and ideas of problems i could solve. He made a general study of curvature of spaces in all dimensions. I have chosen to do my math exploration on Non-Euclidean Geometry but i have a hard time finding a specific topic to explore. ![]()
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