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I'm attempting to read a book from 1978 called A Practical Guide to Splines by Carl de Boor. In it he says: A polynomial of order n or of degree < n is a function of the form $p(x) = a_1 + a_2x + \ldots + a_nx^{n-1}$

I'm getting a bit confused as Wolfram and Wikipedia both say order and degree are the same. Has the meaning of the word order changed in recent decades?

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    @DJC I think order in de Boor's eyes is always degree + 1. Thanks for your kind words.2011-06-09

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At least in the study of splines, order still has the same meaning as the one used by de Boor. Makes sense, order counts the number of control points. And if the best chunk determined by $5$ control points happens to have degree $2$, it is still determined by $5$ control points.

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The meaning has not changed, here $\deg p = n - 1$ which is as he says less than $n$. Order and Degree are interchangeable.