Hectoquads: A new class of square dissections, with a smallest identified

Abstract

Medical and demographic data arrive as whole percentage points, so carry that constraint into geometry: squared squares and rectangles whose element sides all lie between 1 and 100 and hold both extremes. The perfect members are finite — order at most 100, side at most 581 — so the class can be counted. Of 244,099 dissections inside the scale, exactly eight are perfect squared squares; the smallest, 26:274A, is the only one whose median reaches fifty. (The full census deposited as data alongside the paper.)