Como calcular el numero Pi sin la ayuda de los griegos

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Por los comentarios del post anterior que solo era a simple informacion voy a tratar de desarrollar un metodo para calcular areas limitadas por funciones (integrales definidas) de una manera facil y sin conocer ni siquiera la palabra integral (la uso solo para verificar el metodo).
¡¡¡¡¡¡¡ OBVIO QUE EL METODO ES COMPLEJO PERO VOY A SER LO MAS DIDACTICO POSIBLE. Y NO SE OLVIDEN QUE NO TODAS LAS INTEGRALES TIENEN SOLUCION ANALITICA NI NUMERICA !!!!!!!!!!


Nuestra meta es calcular el famoso numero PI=3.14159....
Para ello vamos a graficar una funcion de la forma siguiente


Como calcular el numero Pi sin la ayuda de los griegos

Se observa que es un cuarto de circulo de radio 1 ahora si queremos calcula el area por debajo de la curva tendriamos que hacer lo siguiente

curioso

Ahora para saber el valor de numero Pi solo tendriamos que multiplicar por 4 al valor obtenido.

Bueno aca empieza la magia del metodo. Vamos a encuadrar la funcion anterior para luego ¡¡¡¡IMAGINARNOS!!!! que tenemos muchos dardos en las manos y lanzarlos sobre el grafico de manera tal que nuestra punteria sea tal que caigan todos adentro del recuadro. Esto graficamente seria de la siguiente forma (marcando con puntos a las puntas de los dardos en el dibujo)

matematica
Ahora existe una relacion entre los cantidad de dardos lanzados y la cantidad de ellos que cayeron por debajo de la curva con respecto al area limitada por debajo de la curva y el area del recuadro, esto es:
ingenioso
Ahora si aumentamos la cantidad de dardos lanzados el valor obtenido se aproxima al numero PI. Fijense en la siguiente tabla donde la primera columna representa la cantidad de dardos
Como calcular el numero Pi sin la ayuda de los griegos

!!!!!USTEDES DIRIAN QUE ME ESTOY COMPLICANDO MUCHO PARA CALCULAR UNA MISERABLE INTEGRAL ¡¡¡¡¡
Bueno, es verdad pero hay funciones que no poseen integrales y solo pueden ser calculadas por metodos numericos, tambien hay otras que ni por los metodos numericos se las puede resolver. POr ejemplo la siguiente que si tiene resolucion aproximada por metodos numericos pero ....ANDA SACALA POR METODOS ANALITICOS!!!!!!!!!!

curioso
La aproximacion realizada es la siguiente, segun la "cantidad de dardos"
matematica
BUENO ESPERO QUE LES SIRVA DE ALGO Y SINO EL SABER NUNCA ESTA DEMAS......
SALUDOS A TODOS

13 comentarios - Como calcular el numero Pi sin la ayuda de los griegos

@50_Cent
prefiero usar la calculadora
@staticpo
El último dígito es 1.

ingenioso
@polylb




Curse hasta analisis 3 en la facultad para.....
@cheky25
pero como haces para calcular eso?

porque tenes que provarlo en forma real si no que valores pones en: dardos arriva y dardos abajo?

le rajas cualkier numero?

na para mi no sirve. pero alla vos.
@Snakeeyes92
jajjaja, buen aporte,jeje pero aguanten los griegos,

Sus metodos son mas faciles,o por lo menos ya los se.

Un abrazo.
@gatochuzzo
gente ojo con la HORTOGRAFIA, buen post gracias!!
@maxi_modelo82
Hola hijo
de mil puta
como andas
al reverenda concha de tu madre
esa cajeta de tiburon que tiene
come trapo
hijo de re mil puta
vos
y toda tu familia cosecha porongas
que tiene cara de concha
en la granja de los hermanos PIJUDOS
se puede ir un rato
a la recontra archi putamil madre concha mil pario
hijo de una tremenda puta
aa y otra cosa
CUANDO QUIRAS TOMAR MATE SIN GASTAR TANTA LLERVA
ABRI EL OGETE ASI TE METO ESTA VERGA

CHAU HIJO DE MIL PUTA
@El_chino
maxi_modelo82 dijo:Hola hijo
de mil puta
como andas
al reverenda concha de tu madre
esa cajeta de tiburon que tiene
come trapo
hijo de re mil puta
vos
y toda tu familia cosecha porongas
que tiene cara de concha
en la granja de los hermanos PIJUDOS
se puede ir un rato
a la recontra archi putamil madre concha mil pario
hijo de una tremenda puta
aa y otra cosa
CUANDO QUIRAS TOMAR MATE SIN GASTAR TANTA LLERVA
ABRI EL OGETE ASI TE METO ESTA VERGA

CHAU HIJO DE MIL PUTA

@cototion +1
El_chino dijo:
maxi_modelo82 dijo:Hola hijo
de mil puta
como andas
al reverenda concha de tu madre
esa cajeta de tiburon que tiene
come trapo
hijo de re mil puta
vos
y toda tu familia cosecha porongas
que tiene cara de concha
en la granja de los hermanos PIJUDOS
se puede ir un rato
a la recontra archi putamil madre concha mil pario
hijo de una tremenda puta
aa y otra cosa
CUANDO QUIRAS TOMAR MATE SIN GASTAR TANTA LLERVA
ABRI EL OGETE ASI TE METO ESTA VERGA

CHAU HIJO DE MIL PUTA



Como calcular el numero Pi sin la ayuda de los griegos
@chipero
El_chino dijo:
maxi_modelo82 dijo:Hola hijo de mil puta como andas al reverenda concha de tu madre esa cajeta de tiburon que tiene come trapo hijo de re mil puta vos y toda tu familia cosecha porongas que tiene cara de concha en la granja de los hermanos PIJUDOS se puede ir un rato a la recontra archi putamil madre concha mil pario hijo de una tremenda puta aa y otra cosa CUANDO QUIRAS TOMAR MATE SIN GASTAR TANTA LLERVA ABRI EL OGETE ASI TE METO ESTA VERGA CHAU HIJO DE MIL PUTA




Que lindo, como se quiere la gente...un rosario de puteadas le mandó el pibe....
@Alvaro_98
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@Alvaro_rg
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