introduccion_algoritmos.pdf

8/11/2019 Introduccion_algoritmos.pdf

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UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIAUNAD

ESCUELA DE CIENCIAS BASICAS TECNOLOGIA E INGENIERACONTENIDO DIDCTICO DEL CUSO: 301303ALGORITMO

Origen de los Algoritmos

Sobre el origen de la palabra algoritmo (Zahoo, 2005)1

MUHAMMAD BIN MUSA AL-KHWARIZMI (Algorizm)

(770 - 840 C. E.)

A Portrait of Al-Khwarizmi

byDr. A. Zahoor

Abu Abdullah Muhammad Ibn Musa al-Khwarizmi was born at Khwarizm (Kheva),a town south of river Oxus in present Uzbekistan. (Uzbekistan, a Muslim countryfor over a thousand years, was taken over by the Russians in 1873.) His parents

migrated to a place south of Baghdad when he was a child. The exact date of hisbirth is not known. It has been established from his contributions that he flourishedunder Khalifah (Calif) Al-Mamun at Baghdad during 813 to 833 C.E. and diedaround 840 C.E. He is best known for introducing the mathematical concept

Algorithm, which is so named after his last name.

Al-Khwarizmi was one of the greatest mathematicians ever lived. He was thefounder of several branches and basic concepts of mathematics. He is also famousas an astronomer and geographer. Al-Khwarizmi influenced mathematical thoughtto a greater extent than any other medieval writer. He is recognized as the founderof Algebra, as he not only initiated the subject in a systematic form but also

developed it to the extent of giving analytical solutions of linear and quadraticequations. The name Algebra is derived from his famous book Al-Jabr wa-al-Muqabilah. He developed in detail trigonometric tables containing the sinefunctions, which were later extrapolated to tangent functions. Al-Khwarizmi also

1http://www.contactpakistan.com/newsletter/ksa/May031st/Muslimscontribution.htm


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developed the calculus of two errors, which led him to the concept ofdifferentiation. He also refined the geometric representation of conic sections

The influence of Al-Khwarizmi on the growth of mathematics, astronomy andgeography is well established in history. His approach was systematic and logical,

and not only did he bring together the then prevailing knowledge on variousbranches of science but also enriched it through his original contributions. Hesynthesized Greek and Hindu knowledge and also contained his own contributionof fundamental importance to mathematics and science. He adopted the use ofzero, a numeral of fundamental importance, leading up to the so-called arithmeticof positions and the decimal system. His pioneering work on the system ofnumerals is well known as "Algorithm," or "Algorizm." In addition to introducing the

Arabic numerals, he developed several arithmetical procedures, includingoperations on fractions.

In addition to an important treatise on Astronomy, Al-Khwarizmi wrote a book on

astronomical tables. Several of his books were translated into Latin in the early l2thcentury by Adelard of Bath and Gerard of Cremona. The treatises on Arithmetic,Kitab al-Jam'a wal-Tafreeq bil Hisab al-Hindi, and the one on Algebra, Al-Maqala fiHisab-al Jabr wa-al-Muqabilah, are known only from Latin translations. It was thislater translation which introduced the new science to the West "unknown till then."This book was used until the sixteenth century as the principal mathematical textbook of European universities. His astronomical tables were also translated intoEuropean languages and, later, into Chinese.

The contribution of Al-Khwarizmi to geography is also outstanding. He not onlyrevised Ptolemy's views on geography, but also corrected them in detail. Seventy

geographers worked under Khwarizmi's leadership and they produced the first mapof the globe (known world) in 830 C.E. He is also reported to have collaborated inthe degree measurements ordered by khalifah (Caliph) Mamun al-Rashid wereaimed at measuring of volume and circumference of the earth. His geography bookentitled "Kitab Surat-al-Ard," including maps, was also translated. His othercontributions include original work related to clocks, sundials and astrolabes. Healso wrote Kitab al-Tarikh and Kitab al-Rukhmat (on sundials).

Definicin de Algoritmos

Existen muchas definiciones referentes a algoritmos, entre las cuales tenemos:

1. un algoritmo es un conjunto de instrucciones las cuales le dicen a lacomputadora cmo ejecutar una tarea especfica

2. Un algoritmo es un conjunto ordenado y finito de instrucciones queconducen a la solucin de un problema

3. Una lista de instrucciones donde se especifica una sucesin deoperaciones necesarias para resolver cualquier problema de un tipo dado.


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Un algoritmo est compuesto por tres elementos esenciales

a- Cabecera ->donde se da el nombre del algoritmo y se declaran las variables

b- Cuerpo -> donde se realizan todas las acciones del programac- Final ->donde se da finalizacin, porque debe ser finito

Ejemplo:

Retomado el primer ejercicio de los diagramas, Leer dos nmeros, sumarlos y

obtener su resultado

Como el anlisis del ejercicio ya se realizo, pasamos a su solucin mediante un

algoritmo

Explicacin:

Seccin encabezado (lneas 1,2,3)

Lnea 1 ->definicin del nombre, todo algoritmo debe ser identificado con un

nombre

Lnea 2 -> Palabra para identificar las variables a utilizar

Lnea 3 -> variables utilizadas y el tipo de las mismas, para este caso de tipoentero (recordemos que los datos numricos se dividen en enteros y reales)

Lnea 4 -> Damos inicio al cuero del algoritmo

Lnea 5 ->La palabra escriba es una directiva de salida, es decir todo lo que se

ingresa dentro de esta instruccin son comentarios o valores, que sern

1. Algoritmo Suma;2. Var3. a,b,suma: entero;4. inicio5. escriba(por favor ingrese un nmero);6. lea (a);7. escriba(por favor ingrese otro nmero);8. lea (b);9. suma = a+b;10.escriba (el resultado es: ,suma)

11.fin

Prueba de escritorio

a b suma

4 4 8(4+4)

a b suma

20 5878 5898(20+5878)

Prueba de escritorio

a b suma

4 4 8(4+4)

a b suma

20 5878 5898(20+5878)


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