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Applying 2-descent on elliptic curves to prove the non-existence of a certain triangle-rhombus pair

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)
Supervisor:
Supervisor nameSupervisor E mail
Top, J.J.Top@rug.nl
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 05 Aug 2019
Last Modified: 20 Aug 2019 10:47
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/20542

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