Cats, Sven (2019) Applying 2-descent on elliptic curves to prove the non-existence of a certain triangle-rhombus pair. Bachelor's Thesis, Mathematics.
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Abstract
We call a triangle rational if its side lengths are rational and we call a rhombus θ-rational if both its side length is rational and the sine and cosine of its smallest angle are rational. In this thesis we prove that there do not exist a rational isosceles triangle and a θ-rational rhombus with the same area and the same perimeter. This is already shown in an article by Zhang and Peng, but this thesis contains a fully explicit proof using the underlying theory. To that end, (hyper)elliptic curves, algebraic number theory and p-adic numbers were studied.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 05 Aug 2019 |
| Last Modified: | 20 Aug 2019 10:47 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/20542 |
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