The field-equivalence problem for transcendental-curve intersections
Consider the fields obtained by allowing general intersections with the transcendental curves mentioned in the source, namely trigonometric functions, the Quadratrix of Hippias, and the Archimedean spiral. Transcendental-curve field conjecture. These fields are identical, and possibly form a larger field denoted . The source gives no resolution and presents this as an unresolved question about general intersections with transcendental curves.
References
Primary source
Nicole Venner, “Algebraic Properties of Euclidean Geometry with Transcendental Curves”, arXiv:2303.12514 (2023).
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