Date arithmetic

This morning I got up at eight minutes past six. So what, you ask? Well, that means I got out of bed at 06:08 10/12/14*, which is a very nice arithmetic progression.┬áThat is, today’s date is a series of numbers with a constant difference (in this case, the constant difference is 2).

Question: Which dates (and times, if you wish) next year will form arithmetic progressions? And which, if any, will form a geometric progression (in which each term after the first is found by multiplying its predecessor by a fixed constant)?

*Unless you live in the US — in which case, pretend today is October 12th.

hexahexaflexagons

Whatever happened to hexahexaflexagons? During my teenage years in the Seventies they seemed to be omnipresent – probably due to Martin Gardner’s column in Scientific American.

This morning – for a reason that escapes me now – I remembered a story about a mathematician who caught his tie in a hexahexaflexagon. He tried to ‘flex’ it free, but the tie only disappeared further. As he continued flexing his tie, and eventually himself, became more and more deeply entwined. Eventually he disappeared completely, never to be seen again.

I don’t recall seeing one for maybe twentyfive years now. Whatever happened to hexahexaflexagons?

Update, 18-may-05
A brief history of hexahexaflexagons, together with folding instructions, can be found here and here.