# Math HL IA Non Euclidian Geometry

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PLEASE HELP. For my Mathematics HL IA I was planning on calculating the Earth's perimeter, radius and then calculate the Earth's curvature using no technology.

To calculate the perimeter I need to measure the shadow length of an object in two different locations at the same time. In or Der to not deal with having to do measurements on a second location, I decided to pick the date as 21 of December and the location somewhere on the tropic of Capricorn so I know that the shadow length is zero and I only have to take into account the shadow length of my stick. (I live in the North hemisphere) By using the function arctangent I would find the angle between the two locations and I would only need the distance between them. This is where my problem is. In the past, people traveled to measure the distance between the two places. They found results like 6.6 camel days (It took a camel 6.6 days to travel the distance) and made rough estimates. Then I thought maybe I could do the same thing but using how many hours it takes to travel with a plane. But I had initially planned to calculate the distance using spherical geometry, but in order to do that I think I need coordinates (which would mean I have to use navigation). Then I could find out the radius and then prove how curvature is calculated using calculus and calculate the curvature of the Earth and then compare it to the actual results to see how far maths can take me.

Do you think this would be a good topic for IA and is the level of math going to be enough? And also what method should I use to calculate the distance between the two locations?

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The length of shadow method, by my understanding, is just a simple ratio. The reason is that you can just find your latitude and that of the Tropic of Capricorn. Then it's a simple angle and solution follows as the above link. I couldn't really follow your explanation very well and with all due respect I think you should find something else to use calculus to find distance on a sphere.

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