Abstract
The analytic and difference engines were designed by Charles Babbage in the nineteenth century. The difference engine was designed to produce mathematical tables for various mathematical functions, and the machine was designed to compute polynomial functions (many mathematical functions may be approximated by polynomials). The analytic engine was designed to execute all tasks expressed in algebraic notation, and it provided the vision of a modern computer.
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Notes
- 1.
The power series expansion of the Sine function is given by Sin(x) = x−x 3/3! + x 5/5!−x 7/7! + …. The power series expansion for the Cosine function is given by Cos(x) = 1−x 2/2! + x 4/4!−x 6/6! + … Functions may be approximated by interpolation, and the approximation of a function by a polynomial of degree n requires n + 1 points on the curve for the interpolation. That is, the curve formed by the polynomial of degree n that passes through the n + 1 points of the function is an approximation of the function. The error function also needs to be considered.
- 2.
Each wheel has 10 teeth and represents a decimal digit.
References
Ada, Augusta, Countess of Lovelace (1842) Sketch of the Analytic Engine invented by Charles Babbage. L.F. Menabrea, Bibliothèque Universelle de Genève, October, 1842, No. 82 Translated by Ada, Augusta, Countess of Lovelace
Lada Ada Lovelace (1842) Sketch of the Analytic Engine. Invented by Charles Babbage. L.F. Menabrea. Bibliothèque Universelle de Genève. Translated by Lada Ada Lovelace. 1842
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O’Regan, G. (2018). Analytic and Difference Engines. In: The Innovation in Computing Companion. Springer, Cham. https://doi.org/10.1007/978-3-030-02619-6_6
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DOI: https://doi.org/10.1007/978-3-030-02619-6_6
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