From the Diophantine equation ab − (a + b + c) = k2 − 1 to LMFDB Curve 1576.a1 and a Degree-Two del Pezzo Surface
Year: 2026
Type: preprint
Abstract: This preprint/report explores the Diophantine condition where twice the area minus the perimeter of a right-angled triangle is one less than a perfect square (2K - U = k² - 1). What begins as an elementary numerical observation on Pythagorean triples naturally unfolds into a rigorous study of algebraic surfaces!
Author: Grülling, Pascal T.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204277314
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