Lattice dissections: plainer and less fancy

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The title of this Article pays homage to Greg Frederickson's widelyknown book on geometrical dissections, Dissections: Plane & Fancy [1]. I enjoyed the book so much, I built an honours geometry course around it − a terminal mathematics course for honours students needing a mathematics credit for their general education requirements. Not only is there significant geometry involved, but there is a fair amount of number theory relevant to finding infinite families of dissections of, for example, m squares to n squares.

However, although many dissections from one regular polygon to another are quite elegant, the mathematics involved in specifying the dissections is often formidable.