median
don steward
mathematics teaching 10 ~ 16

Friday, 10 March 2017

in the limit

puntmat posted an interesting idea (7th August 2014) involving various functions and exploring their limit as n gets very large indeed (tends to infinity)

these resources involve two of their functions plus another one

what fractions are shaded with a colour (out of the whole rectangle) at each stage?
what happens to this fraction as the shape (n) grows bigger and bigger?

all give rise to a common set (or subset) of fractions
with the same limit...
why?



















the puntmat post helpfully included some animated gifs for two of these sequences:




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