Taylor's magic splines

Abstract

Although the presentation of the spline is routine for many of us, classical textbooks have not paid sufficient tribute to Brook Taylor in explaining such a concept whose roots can be found on his historic work Methodus Incrementorum Directa et Inversa, published in London in 1715. As our modest memorial to such a genius, we discuss the development of polynomial splines on the basis of Taylor's series. The specific steps for the construction of parabolic, cubic, tetra and splines are given here.

Keywords:

• Splines
• Taylor series

Mathematical Index:

• 41A15
• 41A58

C.R. Category:

• G1.2