Elliptic Curves and the Hopf Fibration
Nadir Hajouji, Steve Trettel
TL;DR
This paper introduces a method for visualizing elliptic curves over various fields in three dimensions, integrating algebraic and geometric insights to enhance understanding.
Contribution
It presents a novel approach that combines tools from multiple mathematical areas to produce faithful 3D visualizations of elliptic curves.
Findings
Successful visualization of elliptic curves over different fields
Enhanced understanding of algebraic and geometric properties
Framework for future mathematical visualizations
Abstract
By combining tools from different areas of mathematics, we obtain 3D visualizations of elliptic curves over different fields that faithfully capture the underlying algebra and geometry.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Algebraic Geometry and Number Theory · Mathematics and Applications