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I have always loved etymology (the study of word origins) and its potential for adding a rich narrative to my lessons – especially in geometry. As a mathematics teacher, I immensely enjoyed comparing sept- and hept-, trotting out the Roman emperors at any opportunity, and watching my class happily construct the names for thirty-five-sided polygons once they grasped the nominative structures underneath. Like characters in a play, the history of the words we use in mathematics reveal a deeper meaning about how the concepts have been constructed and viewed in the past, and this stuff can be extraordinarily interesting. In the spirit of Mark Forsyth’s The Etymologicon – going from interesting connection to connection – here are a few of my favourite back stories behind some gorgeous mathematical words that you may not have heard of.
I remember the first time I learned that ‘hippopotamus’ was Greek for ‘river horse’, with ‘hippo’ being the horsey part (and that a group of them was called a ‘bloat’) – often said to be named because they are large mammals who can walk or ‘run’ on the river floor. Beautiful. You have a hippo inside you, too – your hippocampus, located in your brain; except this one is a ‘sea monster horse’, or less alarmingly, a ‘seahorse’, so named because it is shaped like the animal. We’re awfully good at naming things after other unrelated things that look the same. Have you ever heard of a ‘hippopede’? We know that the ‘hippo’ is horse-related (hippophagous is a lovely and very specific word meaning ‘eating horse meat’) and ‘pede’ (Latin) is to do with feet, as in ‘bipede’ (two-footed) and ‘pedal’ (from ‘pedalis’, the length of a foot). So, a hippopede is a horse’s foot – and here it is (in red):
It is a curve defined by the intersection of a torus and a plane, and one example you might be familiar with is more of a sideways ‘eight’ shape – it’s that pesky old infinity sign. This is called a ‘lemniscate’, from the Greek for ‘garland of ribbons’, which derives from a place called Lemnos where they used to wear particularly memorable ribbon garlands on their heads. So why the association with the inifinite? It’s something of a beautiful mystery. It appeared in the 17th century, usually credited to John Wallis, and rumoured to be a representative of Greek for ‘many’ or a subverted omega. One theory is that it is associated with the self-eating serpent ouroborus, representing not just an endlessly large quantity but a process or cycle of recreation.
It might reasonably also be described as ‘ophidian’ (snake-like), which is a lovely word, but not as interesting as ‘botuliform’, which translates literally and alluringly as ‘sausage-shaped’ and gives us ‘Botox’ (injectable toxin of the type first identified in sausage-meat). Unbelievably, there are not one but two Greek words for this concept: ‘allantoid’ is an equally beautiful alternative – and we’re back to the human body, as is so often the case, with the ‘allantois’ being a sausage-shaped sac that developing baby animals use to exchange gas and waste with the parent. This isn’t just present in mammals, but is in birds and reptiles too (even dinosaurs had them).
Speaking of the human body, do you know where your bicuspids are? You might recognise this term as often used to denote teeth, specifically those with two points (as ‘cusp’ is from the Latin for ‘sharp point’). You may also have a biscuspid valve in your heart, too – it’s a congenital heart defect that affects around 1-2% of the population, meaning the valve has only two parts instead of the usual three. Here is a biscuspid curve, with two clear points and looking much like a tooth:
‘Cusp’, aside from meaning a sharp point and a significant moment (and it is such an important concept it’s also used in geography and psychology), has a particular mathematical meaning, which is a singular point, a point on a curve where the curve is continuous, but which has no derivative whereas points nearby do. Another word for this is ‘spinode’, which derives from ‘spine’ (in the sense of ‘thorn or prickle’) and ‘node’ (a knot, or point where threads meet).
A word that sounds like ‘spine’ that you might not have heard of is ‘spline’ – mathematically, a piecewise polynomial function, so named after the engineering tools used to draw flexible curves.
Although you might see the connection with ‘spine’, this word is more likely to be related to its origins in woodworking and shipbuilding and therefore ‘splinter’, which is a Middle English and Dutch word meaning ‘to split off into pointy bits’. However, who’s to say they’re not related – the delightfully named ‘kiki/bouba effect’ suggests a non-arbitrary mapping between speech sounds (across languages) and shapes. You might have seen this on an episode of QI, where they asked contestants to match ‘kiki’ and ‘bouba’ with these two shapes:
Surprisingly easy, isn’t it! (See here for more info.) The implications – that geometric names are not arbitrary and may share characteristics across language barriers – are fascinating. Which etymological back stories are your favourites? Tweet us yours @CambridgeMaths.
All images in the above text are sourced from Wikipedia