SI DIBUJAMOS un circulo donde esté inscrito un octágono y circunscrito un hexágono, entonces el área de hexágono es dos veces la raíz de tres, mientras que la del octágono es de dos veces la raíz de dos.
De tal modo que el promedio es aprox. el número pi.
El rumor dice que el filosofo Platón propuso esta aproximación de pi.
Sin embargo, falta evidencia directa de que Platón conociera esta aproximación;
de hecho, parece ser una especulación del filósofo científico Karl Popper.
En el libro la “Sociedad abierta y sus enemigos” Cap. 6 (Vol 1, pp. 252–253) se encuentra una descripción que inspira la imagen que realice y encabeza este post:
“A kind of explanation of this curious fact is that it follows from the fact that the arithmetical mean of the areas of the circumscribed hexagon and the inscribed octagon is a good approximation of the area of the circle. Now it appears, on the one hand, that Bryson operated with the means of circumscribed and inscribed polygons,… and we know, on the other hand (from the Greater Hippias), that Plato was interested in the adding of irrationals, so that he must have added . There are thus two ways by which Plato may have found out the approximate equation, and the second of these ways seems almost inescapable. It seems a plausible hypothesis that Plato knew of this equation, but was unable to prove whether or not it was a strict equality or only an approximation.”
Paginas adelante, Popper termina con una disculpa de que no exista evidencia directa de que Plantón
fuera el autor de tal aproximación:
“I must again emphasize that no direct evidence is known to me to show that this was in Plato’s mind; but if we consider the indirect evidence here marshalled, then the hypothesis does perhaps not seem too far-fetched.”
