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Showing posts from June, 2016

WTF is a Number Bond?

Not chemistry, as it happens. I was searching for similar images to one of my line drawings (always fun) and came across these 'number bond things' :

The one on the left - hilariously - is just "1 + 1 = 2". Ok, so that's a deliberately jokey example; real ones have larger numbers and one of the three numbers is for the student to fill in. On the right is a more complex example, drawn as a DAG (directed acyclic graph) although at least one of the example I saw had a node at the bottom with three parents!

In any case, what these things really are representing is partitions of numbers - which are usually drawn as Ferrer's diagrams (or Young tableaux) which I'll refer to as "Ferrer's-Young diagrams". These have a superior feature as shown here:

So one FY-diagram can represent two different number bonds. Note that I've made the crazy leap of making number bonds with more than two parts (or 'addends'). Clearly 1+1+3+4 = 9 = 1+2+2+4 as …