Subdivisions of Numbers

Joshua Zucker took the lead on this activity for the 2012 Circle on the Road festival.

AUDIENCE:

PLANNING ABSTRACT:
3 = 2+1 = 1+2 = 1+1+1 are all the ways of making 3 as the total of a
list of positive integers. How can we organize results like these in
different ways to identify patterns? For instance, how many ways are
there of writing 10 where the first number is 4? How many ways of
writing 10 where there are 4 numbers in the list? How many ways of
writing 10 where the largest number is 4? How many ways are there of
writing 10 when all the numbers in the list are odd?

PUBLIC ABSTRACT:
3 = 2+1 = 1+2 = 1+1+1 are all the ways of making 3 as the total of a
list of positive integers. How can we organize results like these in
different ways to identify patterns? For instance, how many ways are
there of writing 10 where the first number is 4? How many ways of
writing 10 where there are 4 numbers in the list? How many ways of
writing 10 where the largest number is 4? How many ways are there of
writing 10 when all the numbers in the list are odd?

APPRENTICES: Gloria Brown Brooks, Beth Rogers, Virginia Watson, Vinton Geistfeld, Oleg Gleizer

DISCUSSION: