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MARTIN GARDNER, ALICIA Y LA LEY DE LA GRAVEDAD
Diego Pareja Heredia, Universidad del Quindío<= /b> = ;
Jairo Urrea Henao, Universidad del Quindío
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MART= IN GARDNER
Martin Gardner nació en Tulsa, Oklahoma en = = 1914
Su formación básica la recibió= ; en la Universidad de Chi= cago donde recibió el título de pregrado en Filosofía.
Participó del Seminario sobre Ciencia que <= /span>= dirigió el gran filósofo austriaco e integrante del llamado Círculo de Viena: el profesor Rudolf Carnap (1891-1970).
•<= /span>Las notas del seminario (hoy convertidas en el libro I= ntroducción a la filosofía de la ciencia), son famosas, porque fue Martin = Gardner quien las rescató de las grabacione= s = magnetofónicas hechas por la esposa de = Carnap y las publicó con la anuencia de Carnap en 1966.
3D"Martin
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SU OBRA=
•<= /span>Libros (60)
•<= /span>Columnas: Juegos Matemáticos en la revista Scientific American, que = mantuvo por 25 años.
•<= /span>
•<= /span>Fads and Fallacies in the Name of Science (M= odas y Falacias en N= ombre de la Ciencia) en 1952. &#= 13;
•<= /span>Science: Good, Bad and Bogus (C= iencia: Buena, Mala y Espúrea)
•<= /span>The New Age. Notes of a Fringe Watcher(La nueva era. N= otas de un o= bservador Marginal). =
•<= /span>
•<= /span>Juegos Matemáticos, Carnaval Matemático, Máquinas y Diagramas Lógicos, La Nueva Era, La Ciencia: lo Bueno, lo Malo y lo Falso. Ed. Alianza.
= 3;
•<= /span>The Annotaded Alice (más de un millón de copias vend= idas) , cuya última, y definitiva edición, apareció publicada en el año 2000= .
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 Charles = Lutwidge Dogson Lewis Carroll (1832 – 1898) =
Enseñanza de la lógica y de las matemáticas.
Pionero de la Fotografía
OBRAS.
El juego de la lógica. Una paradoja lógica. =
La lógica simbólica, parte I.
Euclides y sus modernos rivales,
Fórmulas de geometría plana,
Tratado elemental de los determinantes,
El libro V de Euclides,
Lo que le dijo la tortuga a Aquiles, y muchos <= /span>juegos y acertijos lógicos.
Silvia y Bruno,
Alicia en el país de las maravillas y Alicia a = través del espejo.
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La Ley de la Gravedad
Philosophiae Naturalis Princ= ipia Mathematica(1687).
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>
<= span class=3DBB style=3D'position:absolute;left:-4.43%'>•Isaac = Newton(1643-1727)
La ley de= la gravitación universal
F=3DGmM/x² =3DMa
Junto a Arquímedes y Gauss está catalogado como los más gran= des matemáticos de la historia.
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LAS INQUIETUDES DE ALICIA
<= span style=3D'font-size:75%;visibility:hidden'>
<= span style=3D'font-size:75%'>La caída libre
<= span style=3D'font-size:75%'>Las especulaciones de Carroll
<= span style=3D'font-size:75%'>Una pregunta de Alicia.
<= span style=3D'font-size:75%'>“¿Cuanto tiempo toma llegar a la Antípoda?”
La respuesta de Martin Gardner. T=3D 42 Min. Aprx.= Para alcanzar el centro de la tierra. Para hallar una solución debemos situarnos = en un modelo de la estructura del interior de la tierra, partiendo de nociones básicas de mecánica clásica y usando las herramientas del cálculo diferencial e integral.
<= span style=3D'font-size:75%;visibility:hidden'>
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IDEAS BÁSICAS DE MECÁNICA CLÁSICA
P=3D(0,0,s), punto particular d= e la tierra,        = ;   Q=3D(x,y,z), punto arbitrario con masa m
Ψ =3D ángulo entre los vectores k y PQ        = ;          G=3DCo= nstante de gravitación universal
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Content-Location: file:///C:/65395235/AlliciaUIS,121305_archivos/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" mauro
Deducción de la Fórmula para la aceleración
&#= 8226;a(s) =3D <= /b>aceleración gravitacional sobre el punto P(0,0,s) en la dirección PQ =3D Gm/(x²+y²+(z-s)²).
<= span style=3D'font-family:"Times New Roman";font-size:75%'>a(s) =3D cos ΨGm/(x² + y&s= up2; + (z-s)²)
<= span style=3D'visibility:hidden'>
(1)=
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Modelos para la estructura de la tierra
&#= 8226;Planetas ideales<= /b> formados por cascar= ones esféricos concéntricos de densidad constante y de radio R. Sea= = S una burbuja ideal d= e masa M con densidad constante, radio r y centro en (0,0,0). Para este caso la <= /span>= aceleración gravitacional sobre el punto P originada por la burbuja S es
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file:///C:/65395235/AlliciaUIS,121305_archivos/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" mauro
Deducción de la Fórmula
<= span style=3D'font-size:75%'>Parametrizando S en términos de
 r =3D (rcosθ senφ,  rsenθ senφ,  rcosφ ), con las variaciones= apropiadas de los ángulos θ y φ y= los correspondientes ajust= es para la masa puntual m, la aceleración será
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<= span style=3D'font-size:75%'>Tomando u =3D cos φ,  tenemos
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<= span style=3D'font-size:156%'>Al integr= ar por partes y simplificando da
Esta formula es equivalente a (2), si 0 < <= b>s < r, entonces a(s)=3D0,
si r <  s ob= tenemos a(s)=3D GM/s².
para  r =3D s, debemos cancelar términos= antes de hacer la integración y encontramos la 2ª parte de la fórmula (2)
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