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Hyperbolic paraboloid

Most popular on HH this week was the fact that the shape of a Pringle crisp (or chip, should you be so inclined) is a hyperbolic paraboloid:

 

 

 

 There’ll no doubt be lots of interesting facts about paraboloids, but mathematics isn’t the HH game BECAUSE MATHS. But we can at least tell you a little bit more about those two words.

 

The adjective hyperbolic relates to a hyperbola, which our trusty dictionary defines as “a plane curve having two branches formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone.” Yeah, one of those. Hyperbola, in turn, comes from the Greek for “excess”—which makes it an etymological sibling of hyperbole, the rhetorical term for exaggeration. 

 

paraboloid meanwhile is “a geometric surface whose sections parallel to two coordinate planes are parabolic, and whose sections parallel to the third plane are either elliptical or hyperbolic.” Aye, that thing, yeah. 

 

Words like parabolaparabolic and paraboloid all come from a Greek word meaning “application”, “juxtaposition”, or literally a “throwing beside”.

 

Mathematically, as the Oxford English Dictionary explains, the name was given to curves of this type by a third century BC mathematician named Apollonius of Perga, who chose it as it “referred to the fact that a rectangle bounded by the abscissa and the latus rectum has an area equal to that of a square on the ordinate, without either excess or deficiency”. Of course. 

 

Etymologically, all of that makes parabola is a none-too-distant cousin of parable—a story in which a secondary, less direct meaning or interpretation is “juxtaposed” beside another more overt one. 

 

 

 

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