Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces
| Autor: | Ronald van Luijk, Robin Hartshorne |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Function field of an algebraic variety
Mathematics - Number Theory General Mathematics Birational geometry Combinatorics Mathematics - Algebraic Geometry math.NT math.AG History and Philosophy of Science Diophantine geometry Pythagorean triple Rational point Algebraic surface FOS: Mathematics Real algebraic geometry 11D (primary) 11G 14G 14J (secondary) Number Theory (math.NT) 14J Differential algebraic geometry Algebraic Geometry (math.AG) 11D (primary) 11G Mathematics 14G |
| Zdroj: | Hartshorne, R; & Luijk, RV. (2016). Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces. UC Berkeley: Retrieved from: http://www.escholarship.org/uc/item/2xx6c4wz |
| Popis: | We discover suprising connections between three seemingly different problems: finding right triangles with rational sides in a non-Euclidean geometry, finding three integers such that the difference of the squares of any two is a square, and the problem of finding rational points on an algebraic surface in algebraic geometry. We will also reinterpret Euler's work on the second problem with a modern point of view. 11 pages, 1 figure |
| Databáze: | OpenAIRE |
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