I was studying interpolation by Splines in numerical analysis and started to wonder the word's origin. I've found that it was a system used in technical drawings using weights but couldn't find why they where called like that in that context. Any idea?


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    $\begingroup$ See spline : "Originally, spline was a term for elastic rulers that were bent to pass through a number of predefined points ("knots"). These were used to make technical drawings for shipbuilding and construction by hand". $\endgroup$ – Mauro ALLEGRANZA Jul 24 '16 at 19:29
  • $\begingroup$ That's what I meant with "system used in technical drawings" but the word doesn't refer to anything in particular, even a company. I was wondering if it is an acronym of something like "Smooth Polynomic Lines". Thanks. $\endgroup$ – bk.us Jul 25 '16 at 20:38
  • $\begingroup$ See the (presumed) etymology of spline : it is of "mechanical" origin (1700-1800) and not ot mathematical origin. $\endgroup$ – Mauro ALLEGRANZA Jul 26 '16 at 5:48
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    $\begingroup$ Wikipedia:"The word "spline" originally meant a thin wood or metal slat in East Anglian dialect. By 1895 it had come to mean a flexible ruler used to draw curves. These splines were used in the aircraft and shipbuilding industries. For years ship designers had employed models to design hulls in small scale. The successful design was then plotted on graph paper and the key points of the plot were re-plotted on larger graph paper to full size. The thin wooden strips provided an interpolation of the key points into smooth curves" en.wikipedia.org/wiki/Spline_(mathematics)#History $\endgroup$ – Conifold Jul 27 '16 at 21:26

My dictionary has this as origin of the word:

East Anglian dialect, perhaps related to splinter.

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  • $\begingroup$ Splinter 1. a very small sharp piece of wood, glass, metal, etc, characteristically long and thin, broken off from a whole. Seems possible. Thanks! $\endgroup$ – bk.us Jul 25 '16 at 20:40
  • $\begingroup$ Or perhaps splint, from other dictionaries. $\endgroup$ – David Hammen Jul 26 '16 at 14:22
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    $\begingroup$ In my dictionary: splint is definitely related to splinter, but spline is only perhaps related to splinter $\endgroup$ – Gerald Edgar Jul 26 '16 at 14:30
  • $\begingroup$ Burden's numerical analysis book states that "spline" has the same origin as splint: initially flexible wood strips (like the used in baskets), then applied to metal strips like the used in technical drawings for shipbuilding like Sophia said. Thanks everyone! $\endgroup$ – bk.us Jul 26 '16 at 21:48

The term comes from shipbuilding in the old days: A long thin flat spline which was fixed at discrete points by newts, flexes just like a cubic spline with natural boundary condition. In this case, the strain energy becomes a minimum. The technique is still in use in experimental ship building.

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In his 1946 paper, "Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions". Quart. Appl. Math., mathematician Isaac Jacob Schoenberg explains that:

A spline is a simple mechanical device for drawing smooth curves. It is a slender flexible bar made of wood or some other elastic material. The spline is place on the sheet of graph paper and held in place at various points by means of certain heavy objects (called "dogs" or "rats") such as to take the shape of the curve we wish to draw.

It is also called a flat spline or a flexible curve:

a long strip fixed in position at a number of points that relaxes to form and hold a smooth curve passing through those points for the purpose of transferring that curve to another material

depicted below:

Flat spline or flexible curve

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