don steward
mathematics teaching 10 ~ 16

Tuesday, 4 March 2014

overlapping squares 1

 art by Richard Anuszkiewicz

an interesting growing sequence, formed by overlapping two squares, based on one produced by Michael Fenton

different ways of viewing the patterns produces various generalisations

reasons for their equivalence (algebraically) can then be explored

in this case, the 'increases' for each stage can be identified

generalisations can involve quadratic expansions

these are two examples of families of a growing sequence of overlapping squares
what other families are possible?
what might the simplest case look like?

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