Pierre de fermat
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Pierre de Fermat was a French mathematician born in 1601 in Beaumont de Lomagne, France. He worked as a lawyer but considered mathematics a hobby, making contributions anonymously through theorems he shared with others. His most famous conjecture, now known as Fermat's Last Theorem, stated that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than 2. It took over 300 years for Andrew Wiles to provide the first full proof of this theorem in 1993. Fermat made other contributions as one of the founders of analytic geometry and probability theory.
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Pierre de Fermat
This document provides an overview of the life and mathematical contributions of Pierre de Fermat. It discusses that Fermat was a 17th century French mathematician, lawyer, and government official who made significant contributions to geometry, calculus, number theory, and probability. Some of his most important works included Fermat's Little Theorem, Fermat numbers, and his infamous Last Theorem, which was unproven for over 300 years until it was finally solved in 1994.
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René Descartes was a French philosopher, mathematician, and scientist born in 1596. He is known as the "father of modern western philosophy" and developed analytical geometry, bridging algebra and geometry. Descartes doubted all knowledge that was uncertain and developed his famous saying "I think, therefore I am" to establish certainty. He created a systematic method of doubt and reasoning to develop knowledge, establishing rationalism as a means to derive truth through reasoning alone rather than experience. His works had significant influence on the development of modern mathematics, philosophy, and science.
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Leonardo de Pisa, Leonardo Pisano o Leonardo Bigollo (c. 1170 - 1250), también llamado Fibonacci, fue un matemático italiano, famoso por haber difundido en Europa el sistema de numeración arábiga actualmente utilizado, el que emplea notación posicional (de base 10, o decimal) y un dígito de valor nulo: el cero; y por idear la sucesión de Fibonacci.
El apodo de Guglielmo (Guillermo), padre de Leonardo, era Bonacci (simple o bien intencionado). Leonardo recibió póstumamente el apodo de Fibonacci (por filius Bonacci, hijo de Bonacci). Guglielmo dirigía un puesto de comercio en Bugía (según algunas versiones era el cónsul de Pisa), en el norte de África (hoy Bejaia, Argelia), y de niño Leonardo viajó allí para ayudarlo. Allí aprendió el sistema de numeración árabe.
Consciente de la superioridad de los numerales árabes, Fibonacci viajó a través de los países del Mediterráneo para estudiar con los matemáticos árabes[1] más destacados de ese tiempo, regresando cerca de 1200. En 1202, a los 32 años de edad, publicó lo que había aprendido en el Liber Abaci (libro del ábaco o libro de los cálculos). Este libro mostró la importancia del nuevo sistema de numeración aplicándolo a la contabilidad comercial, conversión de pesos y medidas, cálculo, intereses, cambio de moneda, y otras numerosas aplicaciones. En estas páginas describe el cero, la notación posicional, la descomposición en factores primos, los criterios de divisibilidad. El libro fue recibido con entusiasmo en la Europa ilustrada, y tuvo un impacto profundo en el pensamiento matemático europeo.
Leonardo fue huésped del Emperador Federico II, que se interesaba en las matemáticas y la ciencia en general. En 1240, la República de Pisa lo honra concediéndole un salario permanente (bajo su nombre alternativo de Leonardo Bigollo).
Conocido por Fibonacci, hijo de Bonaccio, no era un erudito, pero por razón de sus continuos viajes por Europa y el cercano oriente, fue el que dio a conocer en occidente los métodos matemáticos de los hindúes.
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Su quinta obra
En el año 1225 publica su cuarto y principal libro: Liber Quadratorum 'El Libro de los Números cuadrados', a raíz de un desafío de un matemático de la corte de Federico II (Teodoro) que le propuso encontrar un cuadrado tal que si se le sumaba o restaba el número cinco diera como resultado en ambos casos números cuadrados. Curiosamente, el año de publicación del libro es un número cuadrado.
Fibonacci comienza con los rudimentos de lo que se conocía de los números cuadrados desde la antigua Grecia y avanza gradualmente resolviendo proposiciones hasta dar solución al problema de análisis indeterminado que le habían lanzado como desafío.
En la parte original de la obra introduce unos números que denomina congruentes (Proposición IX) y que define, en terminología actual, como c = m.n (m² - n²), donde m y n son enteros positivos impares, m > n. De esta forma, el menor de ellos es 24. Enuncia y muestra que el producto de un número congruente por un cuadrado es otro número congruente.
Utiliza estos números como herramientas para sus posteriores proposiciones y los hace intervenir en una identidad que es conocida como Identidad de Fibonacci (Proposición XI). La identidad es: [1/2(m²+n²)]² ± mn (m² - n²) = [1/2(m² - n²) ± mn]². Esta permite pasar con facilidad de un triángulo rectángulo a otro.
Leonardo de Pisa utiliza frecuentemente las proposiciones precedentes como lemas para las siguientes, por lo que el libro lleva un encadenamiento lógico. Sus demostraciones son del tipo retórico y usa segmentos de recta como representación de cantidades. Algunas proposiciones no están rigurosamente demostradas, sino que hace una especie de inducción incompleta, dando ejemplos prácticos y específicos, pero su dominio algorítmico es excelente y todo lo que afirma puede ser demostrado con las herramientas actuales. No se encuentran errores important
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- 1. Pierre de Fermat By: Jeein Yoon
- 2. Pierre de Fermat Facts: DOB: August 17, 1601 Birthplace: Beaumont de Lomagne, France Death: January 12, 1665 Death place: Castres, France Occupation: Mathematician Best Known Work: Fermat’s Last Theorem
- 3. Fermat’s Rise Pierre de Fermat first started out as a lawyer and considered math a hobby. He never wanted to publish any of his theorems, but the ones he did, he did so anonymously. His link with Marin Mersenne gave Fermat his international reputation. He also rarely provided proofs with his theorems. Fermat’s favorite area of math was the development of modern number theories which led to Fermat’s Last Theorem.
- 4. Fermat’s Last Theorem Fermat’s last theorem states: xn + yn = zn has no non-zero integer solutions for x, y, and z when n> 2. Afterwards Fermat wrote: “I have discovered a truly remarkable proof which this margin is too small to contain.” In 1993 Andrew J. Wiles provided the first proof.
- 5. Fermat’s Additional Contributions Fermat is considered to be one of the “Fathers of Analytic Geometry” along with Rene Descaretes. One of the founders of the probability theory along with Blaise Pascal. Provided a law on light travel and wrote a few papers about calculus.
- 6. Works Cited http://math.about.com/library/blfermatbio.htm http://www.nndb.com/people/768/000087507/