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Results tagged with algebraic-number-theory
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user 104330
Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
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Accepted
Is the maximal packing density of identical circles in a circle always an algebraic number?
Yes indeed, they are all algebraic. The idea is that we can describe the critical $r$ as a first-order formula in the language of fields, something like
$$\forall r_1\quad ((0 < r_1 \wedge r_1 \le r)\ …
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