Technique
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Squared Squares; Perfect Simples, Perfect Compounds and Imperfect Simples
There are 4 main kinds of squared squares which have been of sufficient interest to be searched for, counted and recorded; That is, the three types depicted below, and the fourth type, Mrs Perkin's Quilts, which can include those three types and in addition, squared squares which are 'imperfect' and 'compound' as well. All four kinds of squared square have the squares in the dissection (the 'elements') reduced by any common factor so their GCD = 1. A chronology of the significant square dissection discoveries and the people who made them;
A square or rectangle is said to be 'squared' into n squares if it is tiled into n squares of sizes s 1 ,s 2 ,s 3 ,..s n . A rectangle can be squared if its sides are commensurable (in rational proportion, both being integral mutiples of the same quantity) The sizes of the squares s i are shown as integers and the number of squares n is called the order .
Tiling by Squares
Kokichi Sugihara's English Homepage
SUGIHARA Kokichi Specially Appointed Professor, Dr. of Engineering
Dissections - Construction de Dudeney
Dissections de polygones La construction de Herny Ernest Dudeney (1857 - 1930) [ Transformations en croix ou étoiles ] [ Transformations de quadrilatères ] [ Transformations "fun" ]
Le découpage de Dudeney
Remarque Quand on transforme le triangle, on obtient un quadrilatère convexe ( les angles plats sur les côtés sont conservés par rotation de 180° ) ; ce quadrilatère a par construction 4 angles droits.