A note on medial quasigroups

In this short note we prove two results about medial quasigroups. First, let φ and ψ be binary operations defined by multiplication, left and right division in a medial quasigroup. Then φ and ψ are mutually medial, i.e. φ(ψ(a,b),ψ(c,d))=ψ(φ(a,b),φ(c,d)). Second, four points a, b, c, d in an idempotent medial quasigroup form a parallelogram if and only if d=(a/b)(bc)

A note on medial quasigroups

In this short note we prove two results about medial quasigroups. First, let φ and ψ be binary operations defined by multiplication, left and right division in a medial quasigroup. Then φ and ψ are mutually medial, i.e. φ(ψ(a,b),ψ(c,d))=ψ(φ(a,b),φ(c,d)). Second, four points a, b, c, d in an idempotent medial quasigroup form a parallelogram if and only if d=(a/b)(bc)

Covering all points except one

In many point-line geometries, to cover all points except one, more lines are needed than to cover all points. Bounds can be given by looking at the dimension of the space of functions induced by polynomials of bounded degree