Re: [HM] Finite difference arrays
Anne Michel-Pajus (Annie.Michel-pajus@wanadoo.fr)
Thu, 28 Jan 1999 07:38:34 -0000
Some indications (not exhaustive):
Finite differences are related to the problem of interpolation, and
construction of tables.
They are used by Indian and Arab mathematicians: among others,
Brahmagupta, in 665 (Khanda Khadyaka), and Al-Biruni (X-XI, Qanun
al-Mas'udi) for the calculation of sinus tables for astronomy.
Then by Briggs for the tables of logarithms (Aritmetica logarithmica,
1624), with methods maybe found by Harriot (around 1610).
A general formula is given by Gregory (letter to Collins 1670), but
the main work is done by Newton (from 1675, letter to John Smith, then in
Methodus differentialis, Letter to Oldenburg 1676, Principia...)
Leibniz (in Historia and Origo... 1715) tells that finite differences
are the source of his invention of Calculus.
Bibliography: History of algorithms, Chabert et alii, Springer-Verlag,
translation of Histoire d'Algorithmes, Belin.
Best wishes from Versailles,
Anne Michel-Pajus
-----Message d'origine-----
De : M. Robert Showalter <showalte@vms2.macc.wisc.edu>
A : historia-matematica@chasque.apc.org
Date : mercredi 27 janvier 1999 16:25
Objet : [HM] Finite difference arrays
> ...
> I'm sure these finite difference arrays must have a history that
> goes back farther. It seems likely that finite differencing arrays
> for calculating polynomials must have been familiar objects for many
> mathematicians in times past. How might I trace the matter back
> farther? What resources might I use? Could someone please tell
> me more about the history of these finite difference arrays?