by akash ganguly

hello! i have a fun piece of math for you that i think really characterizes a few of the things i love about math so much — the multitude of different viewpoints on the same topic, and the use of abstraction. i hope to highlight the value of these ideas! i try to focus on the mathematics and building intuition, so most of the definitions are purely intuitionistic and are not ‘rigorous’. if anyone is curious, please don’t hesitate to leave a comment or look it up! let’s get started

part i: the shapes

here’s our friend alice.

hi alice!

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as you can see, she really loves breaking down numbers. she could do any number if she really tried.

by the way alice, why do you have those blocks?

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a partition of a number is a way of breaking down a number such that its parts sum to our original number. for instance, as alice pointed out, 5 can be written in many ways. here are all of the partitions of 5.

5

4+1

3+2

3+1+1

2+2+1