Notes from ICME13

Gila Hanna mentioned the carpet proof of the irrationality of $\sqrt{2}$. A little digging reveals that it was due to Tennenbaum (1950s) and popularized by Conway (1990s). The original proof appeared in a book but the simple idea is described in this paper “Picturing Irrationality” by Steven Miller and David Montague in the Mathematics Magazine (2012). What is more interesting is the expanded version of their paper on arXiv called “Irrationality from the Book”. One can only infer the amount of editing and changes that took place from submission to publication.

This is a quote from Guershon Harel that I am trying to piece together from memory.

Some of us are constructing open neighbourhoods* but these neighbourhoods are in no way compact.

By neighbourhoods, he was referring to the impact of mathematics education on the curriculum.

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