Pitágoras
Pitágoras (575-495 a.C.) Nació en Samos, fue un filósofo y matemático griego considerado el primer matemático puro. Contribuyó de manera significativa en el avance de la matemática helénica, la geometría, la aritmética, derivadas particularmente de las relaciones numéricas, y aplicadas a la teoría de pesos y medidas. (“Wikipedia, “s.f.).
Fue el fundador de la Escuela pitagórica, una sociedad que, aunque era de naturaleza religiosa, se interesaba también en disciplinas como la política y la cosmología. El pitagorismo formuló principios que influyeron tanto en Platón como en Aristóteles y, de manera más general, en el posterior desarrollo de la matemática y en la filosofía racional en Occidente.
Principales aportes matemáticos
Los pitagóricos no estaban interesados en “formular o resolver problemas matemáticos”, ni existían para ellos “problemas abiertos” en el sentido tradicional del término. Su interés era el de “los principios” de la matemática, “el concepto de número”, “el concepto de triángulo” y la idea abstracta de “prueba”. Entre los aportes matemáticos que se atribuyen a la escuela pitagórica se encuentran los siguientes.
El teorema de Pitágoras: En un triángulo rectángulo, la suma de los cuadrados de los catetos es igual al cuadrado de la hipotenusa. Aunque este resultado y las ternas pitagóricas eran conceptos conocidos y empleados por los matemáticos babilonios y de la india, fueron los pitagóricos los primeros en enunciar una demostración formal del teorema. También demostraron el inverso del teorema, que establece que si los lados del triángulo satisfacen la ecuación, entonces el triángulo es rectángulo.
Sólidos perfectos: Los pitagóricos demostraron que sólo existen 5 poliedros regulares. Se cree que Pitágoras sabía cómo construir los tres o cuatro primeros.
Ángulos interiores de un triángulo: Hallaron que la suma de los ángulos interiores de un triángulo es igual a dos rectos, así como la generalización de este resultado a polígonos de n-lados.
La irracionalidad de la raíz cuadrada de 2: Los pitagóricos descubrieron que la diagonal de un cuadrado de lado 1 no puede expresarse como un cociente de números enteros. Este evento marca el descubrimiento de los números irracionales.
Pythagoras (575-495 BC) was born in Samos, he was a Greek mathematician and philosopher, considered as the first pure mathematician. He contributed significantly to the progress of Hellenistic mathematic, geometry, arithmetic, derived particularly from numeric relationships, and applied to the theory of weights and measurements. He was the founder of the Pythagorean School, a society that, in spite of its religious nature, was interested in disciplines such as politics and cosmology. The Pythagoreans formulated principles that influenced Plato and Aristotle, and in a more general way, in the development of mathematic and the rational Philosophy of the West.
Main mathematical contributions: Pythagoras of Samos has become synonymous with the birth of Greek mathematics. Indeed, he is believed to have coined both the words "philosophy" (love of wisdom) and "mathematics" (that which is learned). Pythagoras was perhaps the first to realize that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers. Pythagoras’ Theorem (or the Pythagorean Theorem) is one of the best known of all mathematical theorems.
Three geometrical problems in particular, often referred to as the Three Classical Problems, and all to be solved by purely geometric means using only a straight edge and a compass, date back to the early days of Greek geometry: “the squaring (or quadrature) of the circle”, “the doubling (or duplicating) of the cube” and “the trisection of an angle”. These intransigent problems were profoundly influential on future geometry and led to many fruitful discoveries, although their actual solutions (or, as it turned out, the proofs of their impossibility) had to wait until the 19th Century.
Pythagoras
Pythagoras (575-495 BC) was born in Samos, he was a Greek mathematician and philosopher, considered as the first pure mathematician. He contributed significantly to the progress of Hellenistic mathematic, geometry, arithmetic, derived particularly from numeric relationships, and applied to the theory of weights and measurements. He was the founder of the Pythagorean School, a society that, in spite of its religious nature, was interested in disciplines such as politics and cosmology. The Pythagoreans formulated principles that influenced Plato and Aristotle, and in a more general way, in the development of mathematic and the rational Philosophy of the West.
Main mathematical contributions: Pythagoras of Samos has become synonymous with the birth of Greek mathematics. Indeed, he is believed to have coined both the words "philosophy" (love of wisdom) and "mathematics" (that which is learned). Pythagoras was perhaps the first to realize that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers. Pythagoras’ Theorem (or the Pythagorean Theorem) is one of the best known of all mathematical theorems.
Three geometrical problems in particular, often referred to as the Three Classical Problems, and all to be solved by purely geometric means using only a straight edge and a compass, date back to the early days of Greek geometry: “the squaring (or quadrature) of the circle”, “the doubling (or duplicating) of the cube” and “the trisection of an angle”. These intransigent problems were profoundly influential on future geometry and led to many fruitful discoveries, although their actual solutions (or, as it turned out, the proofs of their impossibility) had to wait until the 19th Century.
