Friday 26 January 2018

Friday Factoid: Once in a blue moon is one tenth of donkey's years!

Our Friday Factoid: Once in a blue moon is one tenth of donkey's years!

This month sees a blue supermoon occurring at the same time as a lunar eclipse. But how rare are these things compared to others? The Maths at ( team investigate)

We all know the phrase “Once in a blue moon”, but how long is this period? We compare this periods with other well known periods to enable better mathematical precision on these matters. 

A blue moon
Traditionally, a blue moon occurs when there are 13 moons in a year or, in a more recent definition when there are 2 moons in a calendar month…. Whichever moon we designate as the blue moon, this occurs once ever 2.7145 years, or once every 991.47 days.

Donkey’s years
Once in Donkey’s years is a common expresison, from the fact that donkey’s ears are  very long thing. The Guineess world record for the oldest donkey ever is 54 years, but 25-30 years is more common. Thus "Once in Donkey’s years" is around once in 27.5 years, or once every 10044 days.

A super moon
This means that a full moon is closer in its orbit than at other times. Not that rare at all- and occurs about 25% of all moons. This term is not well defined, so this happens around once every 109 days.

A lifetime
A "once in a lifetime" experience clearly depends on how long someone lives, but from official UK statistics a newborn boy will expect to live 79.2 years and a girl 82.9 years. Thus a man will have the advantage of experiencing a once in a lifetime event slightly more often at once every 28927.8 days, and a woman once every 30279.23 days. You may be lucky and experience it more often!

Total Lunar Eclipses
Eclipses occur very frequently, but total eclipses only rarely. Of course, they’re not visible everywhere on Earth, but somewhere. Encyclopedia Brittanica lists these as 66 per century, or once every 1.512 years or every 553 days.

A fortnight
A fortnight is something Brits use to confuse Americans, like rubbers and irony, and is defined in British law as the frequency of rural buses, and is once every 14 days.

Super Blue Total Lunar Eclipses
OK, for all these to occur together, these are quite rare. Forbes estimates this as once every 265 years, or around once every 10 Donkey’s Years, or once every 96791.25 days. The last one was on December 30, 1982. However, just by chance, there’s another one coming along next year. Like buses- none come for a fortnight, then two come at once.

Super Blue Total Donkey Lunar Eclipses
Now you’re just being silly. This won't happen in a month of Sundays. This is mathematics- are you paying attention, as it will be on the test?

A month of Sundays.
This is a way of saying never, colloquially. Every  days.

This means once every six months, or once ever 182.75 days.

Who invents these things? This means once every two years, not to be confused with the above, or once every 731 days.

Time immemorial
Defined in English Law to be since before the reign of King Richard 1st, 1189, or longer ago than anyone can remember. There’s over 828 years or around 302,600 days.

Conclusion: "Once in a blue moon" is a well defined phrase. A blue moon happens 10 times in donkey years, or about once every 71 fortnights, or about 30 times in a lifetime. It never happens in a month of Sundays, but has happened around 305 times since time immemorial.

For these and other interesting mathematical facts, listen to Dr Thomas Woolley and Dr Ben Parker, as well as the mysterious Liz, on the popular Maths podcast “Maths at:”, available at, iTunes, and wherever you get your podcasts.

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