Dyadic Polygons

Dyadic rationals are rationals whose denominator is a power of 2. Dyadic triangles and dyadic polygons are respectively de ned as the intersections with the dyadic plane of a triangle or polygon in the real plane whose vertices lie in the dyadic plane. The one-dimensional analogues are dyadic intervals. Algebraically, dyadic polygons carry the structure of a commutative, entropic and idempotent algebra under the binary operation of arithmetic mean. In this talk, dyadic intervals and triangles will be classi ed to within a ne or algebraic isomorphism, and dyadic polygons will be shown to be nitely generated as algebras.